Journal's Papers : Scipedia

Reduction methods and explicit time integration technique in structural dynamics
S. Idelsohn, A. Cardona

Advances in Engineering Software (1984). Vol. 6 (1), pp. 36-44

Abstract
A computer procedure for economically time-integrating large structural dynamics problems is presented. The main process is described as a two-step discretisation, the first one being performed by the finite element method. An error measure is proposed in order to check the validity of the results. The reduced system of equations is integrated by using the central differences explicit scheme. Linear and physical nonlinear examples of applications are shown. The entire procedure seems to be particularly well-suited to be programmed in small computers, where the core and velocity characteristics impose severe restrictions on the problems to be directly solved.
Abstract
A computer procedure for economically time-integrating large structural dynamics problems is presented. The main process is described as a two-step discretisation, the first [...]
- 14
- read
A simple hidden line algorithm for a structural model of planar elements
E. Laitano, S. Idelsohn

Advances in Engineering Software (1986). Vol. 8 (1), pp. 2-7

Abstract
A simple and efficient hidden line algorithm for finite element models is described here. The algorithm runs quickly, it has low computer storage and core size requirements. The method does not require any calculation of trigonometric functions and is able to treat planar quadrilateral polygons without subdividing them into triangles. Detailed flowcharts are presented for a better understanding.
Abstract
A simple and efficient hidden line algorithm for finite element models is described here. The algorithm runs quickly, it has low computer storage and core size requirements. [...]
- 7
- read
Numerical implementation of a discontinuous finite element algorithm for phase-change problems
M. Storti, L. Crivelli, S. Idelsohn

Advances in Engineering Software (1987). Vol. 9 (2), pp. 66-73

Abstract
This paper is devoted to the numerical solution of phase-change problems in two dimensions. The technique of finite elements is employed. The discretization is carried out using linear isoparametric elements and special attention is given to the accurate integration of functions presenting discontinuities at arbitrarily curved interfaces. This type of function arises in a natural way when dealing with phase-change problems because the enthalpy attains a discontinuity at the phase change temperature. To integrate the discontinuous functions in the phase-changing elements a second mapping is performed from the master element onto a new one for which the interface iis a straight line. The integrals are calculated using the Gaussian technique applied to each part of the divided element, which may be triangular or quadrilateral. The discontinuous integration technique improves the behaviour of the numerical method avoiding any possible loss of latent heat due to an inaccurate evaluation of the residual vector. Some important aspects of the solution of the nonlinear system of equations are discussed and several numerical examples are presented together with the details of the computational implementation of the algorithm.
Abstract
This paper is devoted to the numerical solution of phase-change problems in two dimensions. The technique of finite elements is employed. The discretization is carried out [...]
- 7
- read
Upwind parameters for the numerical solution of the compressible flow Euler equations
S. Idelsohn

Advances in Engineering Software and Workstations (1991). Vol. 13 (2), pp. 58-67

Abstract
The present work generalises the earlier work in which a variational principle technique was presented in order to evaluate the magnitude of upwind required to solve the compressible flow equations. The technique proposed allows the choice of nodes where upwind is required in each of the relevant equations. It is a simple and mathematically consistent way of evaluating the amount of upwind or artificial viscosity to be introduced at every node and every equation involved.
Abstract
The present work generalises the earlier work in which a variational principle technique was presented in order to evaluate the magnitude of upwind required to solve the compressible [...]
- 12
- read
On load interaction in the non linear buckling analysis of cylindrical shells
L. Godoy, S. Idelsohn, E. Barbero

Advances in Engineering Software and Workstations (1991). Vol. 13 (1), pp. 46-50

Abstract
The elastic stability of shells or shell-like structures under two independent load parameters is considered. One of the loads is associated to a limit point form of buckling, whereas the second is a bifurcation. A simple one degree of freedom mechanical system is first investigated, for which an analytical solution is possible. Next, a cylindrical shell under the combined action of axial load and localised lateral pressure is studied via a non linear, two-dimensional, finite element discretization. It is shown that both problems display the same general behaviour, with a stability boundary in the load space which is convex towards the region of stability. The results show the need of performing a full non-linear analysis to evaluate the stability boundary for the class of interaction problems considered.
Abstract
The elastic stability of shells or shell-like structures under two independent load parameters is considered. One of the loads is associated to a limit point form of buckling, [...]
- 7
- read
Fluid flows around turbomachinery using an explicit pseudo‐temporal Euler FEM
N. Nigro, M. Storti, S. Idelsohn

Commun. Numer. Meth. Engng (1995). Vol. 11 (3), pp. 199-211

Abstract
This work is devoted to the simulation by finite elements of nearly incompressible inviscid flows in real 3D geometries, by means of an Euler code based on the SUPG (streamline upwind Petrov–Galerkin) method, explicit forward Euler pseudo‐temporal time integration and periodic and absorbing boundary conditions, among other features. The main goal is the application to flow around turbomachinery, with special emphasis on the performance analysis of a given machine, that involves several numerical computations at different operation points. Finally, these results are summarized in the form of characteristic curves.
Abstract
This work is devoted to the simulation by finite elements of nearly incompressible inviscid flows in real 3D geometries, by means of an Euler code based on the SUPG (streamline [...]
- 15
- read
A Panel-Fourier Method for Free-Surface Flows
J. D'ELIA, M. Storti, S. Idelsohn

Journal of Fluids Engineering (1999). Vol. 122 (2), 309-317

Abstract
A panel Fourier method for ship-wave flow problems is considered here. It is based on a three-dimensional potential flow model with a linearized free surface condition, and it is implemented by means of a low order panel method coupled to a Fourier series. The wave resistance is computed by pressure integration over the static wet hull and the wave pattern is obtained by a post-processing procedure. The strategy avoids the use of numerical viscosity, in contrast with the Dawson-like methods, widely used in naval panel codes, therefore a second centered scheme can be used for the discrete operator on the free surface. Numerical results including the wave pattern for a ferry along fifteen ship lengths are presented.
Abstract
A panel Fourier method for ship-wave flow problems is considered here. It is based on a three-dimensional potential flow model with a linearized free surface condition, and [...]
- 0
- read
A discrete non‐local (DNL) outgoing boundary condition for diffraction of surface waves
R. Bonet Chaple, N. Nigro, M. Storti, S. Idelsohn

Commun. Numer. Meth. Engng (1998). Vol. 14 (9), pp. 849-861

Abstract
A discrete non‐local (DNL) boundary condition is used to solve the water waves propagation problem over variable depth. This condition is obtained by means of full solution of the discrete Helmholtz operator in a structured network. We consider a simulation of wave propagation around a circular island located on either a paraboloidal shoal or constant depth bathymetry. Such examples confirm the important improvement in accuracy for the DNL method over standard conditions in the near field.
Abstract
A discrete non‐local (DNL) boundary condition is used to solve the water waves propagation problem over variable depth. This condition is obtained by means of full solution [...]
- 8
- read
Numerical methods in phase-change problems
S. Idelsohn, M. Storti, L. Crivelli

Archives of Comp. Meths. Engng. (1994). Vol. 1 (1), pp. 49-74

Abstract
This paper summarizes the state of the art of the numerical solution of phase-change problems. After describing the governing equations, a review of the existing methods is presented. The emphasis is put mainly on fixed domain techniques, but a brief description of the main front-tracking methods is included. A special section is devoted to the Newton-Raphson resolution with quadratic convergence of the non-linear system of equations.
Abstract
This paper summarizes the state of the art of the numerical solution of phase-change problems. After describing the governing equations, a review of the existing methods is [...]
- 13
- read
A general algorithm for compressible and incompressible flow. Stability analysis and explicit time integration
N. Nigro, M. Storti, S. Idelsohn

Int. J. of Num. Meths. for Heat and Fluid Flow (1997). Vol. 7 (2/3), pp. 141-168

Abstract
Addresses two difficulties which arise when using a compressible code with equal order interpolation (non‐staggered grids in the finite‐difference nomenclature) to capture a steady‐state solution in the incompressible limit, i.e. at low Mach numbers. Explains that, first, numerical instabilities in the form of spurious oscillations in pressure pollute the solution and, second, the convergence to the steady state becomes extremely slow owing to bad conditioning of the different speeds of propagation. By using a stabilized method, allows the use of equal‐order interpolations in a consistent (weighted‐residual) formulation which stabilizes both the convection and the continuity terms at the same time. On the other hand, by using specially devised preconditioning, assures a rate of convergence independent of Mach number.
Abstract
Addresses two difficulties which arise when using a compressible code with equal order interpolation (non‐staggered grids in the finite‐difference nomenclature) to capture [...]
- 5
- read
CVBEM Formulation for Multiple Profiles and Cascades
M. Storti, J. D'ELIA, S. Idelsohn

Appl. Mech. Rev. (1995). Vol. 48 (11), pp. 203-210

Abstract
A numerical algorithm based on the CVBEM (from Complex Variable Boundary Element Method) for plane incompressible potential flow around aerofoils and cascades is described. The method is based on the representation of the complex disturbance velocity by means of a Cauchy-type integral around the foil. The Cauchy density function is approximated piecewise linearly and a linear system on the nodal values is obtained by collocation at the nodes. The Kutta condition is imposed via a Lagrange multiplier, in contrast with the least-squares formulation used in a previous work. For cascades, the problem is conformally mapped by a simple hyperbolic function (exponential or hyperbolic tangent) to a related problem with only one profile and one or two poles. Thus, the cascade problem is accurately solved with minor modifications to the single profile code and at the same cost of a single profile computation. Finally, several numerical examples are shown: single Joukowski and NACA profiles, interference coefficients for the flat plate cascade and a plane cascade at the external cylindrical section of an industrial fan.
Abstract
A numerical algorithm based on the CVBEM (from Complex Variable Boundary Element Method) for plane incompressible potential flow around aerofoils and cascades is described. [...]
- 2
- read
Buckling of circular, annular plates of non-uniform thickness
P. Laura, R. Gutiérrez, V. Sonzogni, S. Idelsohn

Ocean Engng. (1997). Vol. 24 (1), pp. 51-62

Abstract
This paper deals with the solution of the title problem in the case where the outer boundary is subjected to uniform, hydrostatic pressure while the inner edge of the plate is free. It is assumed that the plate thickness varies (a) in a discontinuous fashion and (b) linearly. An approximate approach is proposed using polynomial coordinate functions which identically satisfy the boundary conditions at the outer edge, only. The eigenvalues are determined using the optimized Rayleigh-Ritz method and good engineering agreement is shown to exist with buckling parameters obtained by means of a finite element code.
Abstract
This paper deals with the solution of the title problem in the case where the outer boundary is subjected to uniform, hydrostatic pressure while the inner edge of the plate [...]
- 4
- read
Applied hydrodynamic wave-resistance computation by Fourier transform
J. D'ELIA, M. Storti, S. Idelsohn

Ocean Engng. (2002). Vol. 29 (3), p. 261-278

Abstract
An applied Fourier transform computation for the hydrodynamic wave-resistance coefficient is shown, oriented to potential flows with a free surface and infinity depth. The presence of a ship-like body is simulated by its equivalent pressure disturbance imposed on the un-perturbed free surface, where a linearized free surface condition is used. The wave-resistance coefficient is obtained from the wave-height downstream. Two examples with closed solutions are considered: a submerged dipole, as a test-case, and a parabolic pressure distribution of compact support. In the three dimensional case, a dispersion relation is included which is a key resource for an inexpensive computation of the wave pattern far downstream like fifteen ship-lengths.
Abstract
An applied Fourier transform computation for the hydrodynamic wave-resistance coefficient is shown, oriented to potential flows with a free surface and infinity depth. The [...]
- 0
- read
Fluid flows around turbomachinery using an explicit pseudo‐temporal Euler FEM
N. Nigro, M. Storti, S. Idelsohn

Commun. Numer. Meth. Engng (1995). Vol. 11 (3), pp. 199-211

Abstract
This work is devoted to the simulation by finite elements of nearly incompressible inviscid flows in real 3D geometries, by means of an Euler code based on the SUPG (streamline upwind Petrov–Galerkin) method, explicit forward Euler pseudo‐temporal time integration and periodic and absorbing boundary conditions, among other features. The main goal is the application to flow around turbomachinery, with special emphasis on the performance analysis of a given machine, that involves several numerical computations at different operation points. Finally, these results are summarized in the form of characteristic curves.
Abstract
This work is devoted to the simulation by finite elements of nearly incompressible inviscid flows in real 3D geometries, by means of an Euler code based on the SUPG (streamline [...]
- 12
- read
Computing ship wave resistance from wave amplitude with a non‐local absorbing boundary condition
M. Storti, J. D'ELIA, S. Idelsohn

Commun. Numer. Meth. Engng (1998). Vol. 14 (11), pp. 997-1012

Abstract
A method for computing ship wave resistance from a momentum flux balance is presented. It is based on computing the momentum flux carried by the gravity waves that exit the computational domain through the outlet plane. It can be shown that this method ensures a non‐negative wave‐resistance, in contrast with straightforward integration of the normal pressure forces. However, this calculation should be performed on a transverse plane located far behind the ship. Traditional Dawson‐like methods add a numerical viscosity that dampens the wave pattern so that some amount of momentum flux is lost, and resulting in an error in the momentum balance. The flow field is computed, then, with a centred scheme with absorbing boundary conditions.
Abstract
A method for computing ship wave resistance from a momentum flux balance is presented. It is based on computing the momentum flux carried by the gravity waves that exit the [...]
- 7
- read
Iterative solution of panel method discretizations for potential flow problems. The modal multipolar preconditioning
J. D'ELIA, M. Storti, S. Idelsohn

Int. J. Numer. Meth. Fluids (2000). Vol. 32 (1), pp. 1-22

Abstract
The iterative solution of linear systems arising from panel method discretization of three‐dimensional (3D) exterior potential problems coming mainly from aero‐hydrodynamic engineering problems, is discussed. An original preconditioning based on an approximate eigenspace decomposition is proposed, which corrects bad conditioning arising from a pair of surfaces that are very close to each other, which is a very common situation in slender wings and other aerodynamic profiles. This preconditioning has been tested with the standard Bi‐conjugate gradient (Bi‐CG) and conjugate gradient squared (CGS) iterative methods.
Abstract
The iterative solution of linear systems arising from panel method discretization of three‐dimensional (3D) exterior potential problems coming mainly from aero‐hydrodynamic [...]
- 0
- read
Stability analysis of mixed finite element formulations with special mention of equal‐order interpolations
S. Idelsohn, M. Storti, N. Nigro

Int. J. Numer. Meth. Fluids (1995). Vol. 20 (8-9), pp. 1003-1022

Abstract
We present a method to assess the stability of pairs of interpolation spaces for mixed formulations. The method is based on a straightforward calculation of the eigenvalues of the discrete matrices through Fourier decomposition in plane waves and is intended to give, via straightforward numerical computations, a sharper determination of stability than the well‐known ‘patch test’ of Zienkiewicz et al. Special attention is devoted to the study of stability and accuracy of equal‐order interpolations
Abstract
We present a method to assess the stability of pairs of interpolation spaces for mixed formulations. The method is based on a straightforward calculation of the eigenvalues [...]
- 8
- read
GMRES physics‐based preconditioner for all Reynolds and Mach numbers: numerical examples
N. Nigro, M. Storti, S. Idelsohn

Int. J. Numer. Meth. Fluids (1997). Vol. 25 (12), pp. 1347-1371

Abstract
This paper presents several numerical results using a vectorized version of a 3D finite element compressible and nearly incompressible Euler and Navier–Stokes code. The assumptions were set on laminar flows and Newtonian fluids. The goal of this research is to show the capabilities of the present code to treat a wide range of problems appearing in laminar fluid dynamics towards the unification from incompressible to compressible and from inviscid to viscous flow codes. Several authors with different approaches have tried to attain this target in CFD with relative success. At the beginning the methods based on operator splitting and perturbation were preferred, but lately, with the wide usage of time‐marching algorithms, the preconditioning mass matrix (PMM) has become very popular. With this kind of relaxation scheme it is possible to accelerate the rate of convergence to steady state solutions with the modification of the mass matrix under certain restrictions. The selection of the mass matrix is not an easy task, but we have certain freedom to define it in order to improve the condition number of the system. In this paper we have used a physics‐based preconditioner for the GMRES implicit solver developed previously by us and an SUPG formulation for the semidiscretization of the spatial operator. In sections 2 and 3 we present some theoretical aspects related to the physical problem and the mathematical model, showing the inviscid and viscous flow equations to be solved and the variational formulation involved in the finite element analysis. Section 4 deals with the numerical solution of non‐linear systems of equations, with some emphasis on the preconditioned matrix‐free GMRES solver. Section 5 shows how boundary conditions were treated for both Euler and Navier–Stokes problems. Section 6 contains some aspects about vectorization on the Cray C90. The performance reached by this implementation is close to 1 Gflop using multitasking. Section 7 presents several numerical examples for both models covering a wide range of interesting problems, such as inviscid low subsonic, transonic and supersonic regimes and viscous problems with interaction between boundary layers and shock waves in either attached or separated flows.
Abstract
This paper presents several numerical results using a vectorized version of a 3D finite element compressible and nearly incompressible Euler and Navier–Stokes code. [...]
- 4
- read
Discrete non‐local absorbing boundary condition for exterior problems governed by Helmholtz equation
R. Bonet Chaple, N. Nigro, M. Storti, S. Idelsohn

Int. J. Numer. Meth. Fluids (1999). Vol. 29 (5), pp. 605-621

Abstract
The finite element method is employed to approximate the solutions of the Helmholtz equation for water wave radiation and scattering in an unbounded domain. A discrete, non‐local and non‐reflecting boundary condition is specified at an artificial external boundary by the DNL method, yielding an equivalent problem that is solved in a bounded domain. This procedure formulates a boundary value problem in a bounded region by imposing a relation in the discrete medium between the nodal values at the two last layers. For plane geometry, this relation can be found by straightforward eigenvalue decomposition. For circular geometry, the plane condition is applied at the external layer and this condition is condensed through a structured annular region, resulting in a condition at an inner radius. Exterior problems with a bounded internal physical obstacle are considered. It is well‐known that these kind of problems are well‐posed, and have a unique solution. Numerical studies based on standard Galerkin methodology examine the dependence of the DNL condition with respect to the circular annular region width. The DNL condition is compared with local boundary conditions of several orders. Numerical examples confirm the important improvement in accuracy obtained by the DNL method over standard conditions.
Abstract
The finite element method is employed to approximate the solutions of the Helmholtz equation for water wave radiation and scattering in an unbounded domain. A discrete, non‐local [...]
- 6
- read
Adaptive refinement criterion for elliptic problems discretized by FEM
M. Storti, N. Nigro, S. Idelsohn

Commun. Numer. Meth. Engng (1993). Vol. 9 (9), pp. 729-743

Abstract
In a recent paper we presented a data structure to be used with multigrid techniques on non‐homogeneously refined FEM meshes. This paper focuses on the adaptive refinement techniques used there. The error estimate is obtained from standard Taylor series. For each element we compute its efficiency in terms of the size, the norm of the second derivatives of the unknown and the parameter p, where Lp is the chosen norm. The way the norm influences the optimal mesh is studied. The number of elements to be refined at each step is such to produce a fast convergence to the optimal mesh, followed by successive homogeneous refinements. We hope that the analysis of these two subjects could be of value for people working with other (perhaps very dissimilar) adaptive refinement techniques (error estimate and data structure, for instance).
Abstract
In a recent paper we presented a data structure to be used with multigrid techniques on non‐homogeneously refined FEM meshes. This paper focuses on the adaptive refinement [...]
- 11
- read
Two‐phase flow modelling in gas‐stirred liquid vessels with SUPG‐stabilized equal‐order interpolations
N. Nigro, M. Storti, S. Idelsohn

Int. J. Numer. Meth. Fluids (1994). Vol. 19 (1), pp. 1-22

Abstract
The modelling of liquid flow in gas‐stirred vessels is described. A simple two‐phase model accounts for the buoyancy effect of bubbles. Friction between liquid and gas is modelled with the hypothesis of independent bubbles. The resulting PDE system is discretized with an original version of the SUPG‐FEM technique which stabilizes both the convection term and equal‐order interpolations for velocity and pressure, which are known to be unstable for incompressible flows. The resulting steady state discrete system is solved via pseudotemporal explicit iteration with a local time step and a preconditioning to homogenize the temporal scales for liquid and gas.
Abstract
The modelling of liquid flow in gas‐stirred vessels is described. A simple two‐phase model accounts for the buoyancy effect of bubbles. Friction between liquid and gas [...]
- 8
- read
Free vibrations of rectangular plates of exponentially varying thickness and with a free edge
V. Sonzogni, S. Idelsohn, P. Laura, V. Cortínez

Journal of Sound and Vibration (1990). Vol. 140 (3), pp. 513-522

Abstract
Transverse vibrations of the structural system described in the title are analyzed by using classical plate theory and employing two different methodologies: the recently developed “optimized Kantorovich approach”; and a finite element algorithmic procedure. It is shown that the fundamental frequency coefficients obtained by using both techniques for a rather wide variation of the governing geometric parameters are in very good agreement. Lower frequency coefficients of the plate system determined by means of the finite element method are also presented.
Abstract
Transverse vibrations of the structural system described in the title are analyzed by using classical plate theory and employing two different methodologies: the recently [...]
- 5
- read
Transverse vibrations of an isotropic, simply supported rectangular plate with an orthotropic inclusion
L. Ercoli, V. Sonzogni, S. Idelsohn, P. Laura

Journal of Sound and Vibration (1992). Vol. 135 (2), pp. 217-221

Abstract
An approximate analytical solution is obtained for the title problem by using a Navier-type solution. It is shown that the fundamental frequency coefficient obtained by means of this procedure is in reasonably good agreement with the result obtained by using a finite element algorithmic methodology. Obviously the type of material disturbance considered introduces considerable change in the dynamic behavior of the structural element and this fact is clearly shown in the variation of the fundamental frequency value.
Abstract
An approximate analytical solution is obtained for the title problem by using a Navier-type solution. It is shown that the fundamental frequency coefficient obtained by means [...]
- 5
- read
Evaluation of Finite Element Calculations in a Cracked Cylinder Under Internal Pressure by Speckle Photography
G. Kaufmann, A. Lopergolo, S. Idelsohn

J. Appl. Mech (1983). Vol. 50 (4a), pp. 896-897

Abstract
The usefulness of using the speckle photography technique in fracture mechanics to check numerical calculations is demonstrated for an internally pressurized cylinder with a surface flaw. A pointwise technique was utilized to measure the opening displacements along the crack line and the Mode I stress-intensity factor was determined by extrapolating these results to the crack tip. Finite element calculations were performed to be compared with experimental data and good agreement was obtained.
Abstract
The usefulness of using the speckle photography technique in fracture mechanics to check numerical calculations is demonstrated for an internally pressurized cylinder with [...]
- 10
- read
A comparative computational study of blood flow through prosthetic heart valves using the finite element method
S. Idelsohn, L. Costa, R. Ponso

Journal of Biomechanics (1985). Vol. 18 (2), pp. 97-115

Abstract
The steady flow of blood through three common types of prosthetic heart valves was simulated numerically using the finite element method. The velocity, pressure and stress fields were obtained for the disk-type, tilting-disk and ball-type prosthetic heart valves in aortic position, for increasing Reynolds numbers up to 900, 1500 and 2000 respectively. Computer graphics of calculated velocities are presented, showing in detail the accelerated flow, recirculation and stagnation areas developed in the prosthesis. Maximum wall shear stresses were found at 0.5, 1.4, and 1.2 diameters from the sewing ring downstream for the disk, tilting-disk and ball valves being the values of 55, 18 and 33 dyn cm−2 respectively. In the vicinity of the occluder, maximum shear stresses of 38, 30 and 47 dyn cm−2 respectively were computed. The flow characteristics and performance for each valve are compared, the results are presented in terms of energy loss and maximum shear stress. The velocity and stress fields are compared with in vitro evaluations found in the literature
Abstract
The steady flow of blood through three common types of prosthetic heart valves was simulated numerically using the finite element method. The velocity, pressure and stress [...]
- 8
- read
Inelastic seismic analysis of a building structure designed by argentine codes
V. Sonzogni, A. Cardona, S. Idelsohn

Earthquake Engineering Structural Dynamics (1984). Vol. 12 (6), pp. 721-736

Abstract
A reinforced concrete frame‐wall structure of a building designed in accordance to standard practice in Argentina was analysed by the procedures prescribed by current Argentine Codes. In addition, the inelastic step‐by‐step response of the structure to design spectrum‐compatible accelerograms was studied by means of a special element for inelastic dynamic analysis of reinforced concrete frames. Results obtained by the different methods of analysis are presented
Abstract
A reinforced concrete frame‐wall structure of a building designed in accordance to standard practice in Argentina was analysed by the procedures prescribed by current Argentine [...]
- 12
- read
Evaluation of finite-element calculations in a part-circular crack by coherent optics techniques
G. Kaufmann, A. Lopergolo, S. Idelsohn, E. Barbero

Experimental Mechanics (1987). Vol. 27 (2), pp. 154-157

Abstract
Two techniques, speckle photography and holographic interferometry, were used to test three-dimensional finite-element calculations in an internally pressurized cylinder with an external part-circular crack. Opening displacements along the crack line were measured by speckle photography. Radial displacements were obtained from holographic fringe patterns. Good agreement between experimental and numerical data is obtained. Stress-intensity factor variations along the crack front are calculated from numerical results.
Abstract
Two techniques, speckle photography and holographic interferometry, were used to test three-dimensional finite-element calculations in an internally pressurized cylinder with [...]
- 6
- read
Fracture analysis of a surface-coated ceramic by speckle photography and finite elements
E. Barbero, G. Kaufmann, S. Idelsohn

Optics & Laser Technology (1990). Vol. 22 (1), pp. 17-22

Abstract
The fracture behaviour of a four-point bend surface-coated ceramic specimen with a through-the-thickness crack was experimentally investigated. Speckle photography was used to measure opening displacements over the specimen surface and across the crack line. For a glazed and unglazed specimen, stress-intensity factors were experimentally determined by means of a method that uses data not restricted to the singularity-dominated zone. Stress-intensity factors were numerically calculated using a three-dimensional finite element analysis and their variations along the crack front were also evaluated. Experimental results agree reasonably well with the numerical results. Results show the influence of the glaze on the fracture behaviour of the composite material.
Abstract
The fracture behaviour of a four-point bend surface-coated ceramic specimen with a through-the-thickness crack was experimentally investigated. Speckle photography was used [...]
- 5
- read
Using pseudo-concentrations in the analysis of transient forming processes
H. Antúnez, S. Idelsohn

Engineering Computations (1992). Vol. 9 (5), pp. 547-559

Abstract
The pseudo‐concentration method is applied to the analysis of transient processes. A simple, easy‐to‐handle model is obtained by keeping an Eulerian description: it does not require remeshing after a certain amount of plastic deformation. The range of applicability of the method is extended to non‐confined (even with several free surfaces) processes. It is shown the need of distinct handling of free surfaces according to their orientation to the direction of the flow. A seamless tube rolling process, a cylinder upsetting and a backward extrusion are modelled. Experimental data and results obtained by other methods are used to compare and discuss the performance of the model.
Abstract
The pseudo‐concentration method is applied to the analysis of transient processes. A simple, easy‐to‐handle model is obtained by keeping an Eulerian description: it [...]
- 5
- read
Nonlinear structural dynamics via Newton and quasi-Newton methods
M. Geradin, S. Idelsohn, M. Hogge

Nuclear Engineering and Design (1980). Vol. 58 (3), pp. 339-348;

Abstract
This paper is an attempt to compare Newton and quasi-Newton methods in nonlinear structural dynamics. After a review of the classical iterative methods, several quasi-Newton updates are presented and tested. Special attention is devoted to the solution of large sparse systems for which two original procedures are described: a substructure correction and a vectorial correction. The numerical examples presented include the dynamic analyses of geometrical, material and combined nonlinearities. All the results are assorted with a complete discussion of the different methods used, of the convergence rates and of the associated computer costs. From the present results, Newton's methods appear to exhibit the best convergence rates when an efficient computational strategy is adopted. Nevertheless computational costs for the solution of large systems can be reduced drastically by using convenient quasi-Newton updates.
Abstract
This paper is an attempt to compare Newton and quasi-Newton methods in nonlinear structural dynamics. After a review of the classical iterative methods, several quasi-Newton [...]
- 20
- read
Failure internal pressure of spherical steel containments
G. Sarmiento, S. Idelsohn, A. Cardona, V. Sonzogni

Nuclear Engineering and Desing (1985). Vol. 90 (2), pp. 209-222

Abstract
An application of the British CEGB's R6 Failure Assessment Approach to the determination of failure internal pressure of nuclear power plant spherical steel containments is presented. The presence of hypothetical cracks both in the base metal and in the welding material of the containment, with geometrical idealizations according to the ASME Boiler and Pressure Vessel Code (Section XI), was taken into account in order to analyze the sensitivity of the failure assessment with the values of the material fracture properties. Calculations of the elastoplastic collapse load have been performed by means of the Finite Element System SAMCEF. The clean axisymmetric shell (neglecting the influence of nozzles and minor irregularities) and two major penetrations (personnel and emergency locks) have been taken separately into account. Large-strain elastoplastic behaviour of the material was considered in the Code, using lower bounds of true stress—true strain relations obtained by testing a collection of tensile specimens. Assuming the presence of cracks in non-perturbed regions, the reserve factor for test pressure and the failure internal pressure have been determined as a function of the flaw depth.
Abstract
An application of the British CEGB's R6 Failure Assessment Approach to the determination of failure internal pressure of nuclear power plant spherical steel containments [...]
- 7
- read
Computational strategies for the solution of large nonlinear problems via quasi-newton methods
M. Geradin, S. Idelsohn, M. Hogge

Computers and Structures (1981). Vol. 13 (1-3), pp. 73-81

Abstract
The usefulness of quasi-Newton methods for the solution of nonlinear systems of equations is demonstrated. After a review of the Newton iterative method, several quasi-Newton updates are presented and tested. Special attention is devoted to the solution of large sparse systems of equations such as those issued from spatial discretization of continua by finite elements. The numerical examples presented comprise static and dynamic analyses of geometrical, material and combined nonlinear structural problems and a model fluid flow problem with different levels of nonlinearity. All the results are assorted with a complete discussion of the different methods used, of the convergence rates and of the associated computer costs. From the present studies, it can be concluded that computational costs for the solution of large nonlinear systems of equations can be reduced drastically by using convenient quasi-Newton updates or by adequate combined Newton/quasi-Newton strategies.
Abstract
The usefulness of quasi-Newton methods for the solution of nonlinear systems of equations is demonstrated. After a review of the Newton iterative method, several quasi-Newton [...]
- 10
- read
A load-dependent basis for reduced nonlinear structural dynamics
S. Idelsohn, A. Cardona

Computers and Structures (1985). Vol. 20 (1-3), pp. 203-210

Abstract
A computational algorithm for predicting the dynamical response of a nonlinear structure by means of a reduction scheme is described. In it, the nonlinear system of ordinary differential equations obtained from the finite element discretization is reduced, by employing a Rayleigh-Ritz technique. A new criterion for the computation of the basis vectors is proposed. It is based on a sequence of basis vectors proposed by Wilson et al. for linear dynamics problems, which was augmented by adding derivatives of these vectors with respect to the generalized displacement amplitudes. The later vectors allow the treatment of nonlinear problems.
Abstract
A computational algorithm for predicting the dynamical response of a nonlinear structure by means of a reduction scheme is described. In it, the nonlinear system of ordinary [...]
- 15
- read
An effective automatic incremental/iterative method for static nonlinear structural analysis
J. Jeusette, G. Laschet, S. Idelsohn

Computers and Structures (1989). Vol. 32 (1), pp. 125-135

Abstract
In the prebuckling range of the complete nonlinear response of a structure submitted to destabilizing loads, a linearized stability analysis is generally an interesting tool. Used in conjunction with an arc-length algorithm, incremental bifurcation analyses are able to give optimal definition for the increment predictor size. When the associated eigenvalue problem is solved by minimizing the finite element discretized form of the Rayleigh quotient via a preconditioned conjugate gradient technique, it can be very easily inserted in an automatic nonlinear equations solver. Such a procedure is presented in this paper after a review of existing arc-length schemes and step-size control methods. Moreover, for tracing the postbuckling range of the nonlinear response automatically, a new recurrence formula is proposed to control the step-size. The well behaviour of this algorithm is illustrated in two classical structural applications.
Abstract
In the prebuckling range of the complete nonlinear response of a structure submitted to destabilizing loads, a linearized stability analysis is generally an interesting tool. [...]
- 8
- read
Metal forming analysis by fourier series expansion and further uses of pseudo-concentrations
H. Antúnez, S. Idelsohn, E. Dvorkin

Computers and Structures (1992). Vol. 44 (1-2), pp. 435-451

Abstract
An analysis of metal forming processes with axial geometry is performed by an expansion in Fourier series on the circumferential direction. For that purpose, an incremental form is presented on the basis of the flow formulation. For every increment of the non-null imposed boundary conditions an algebraic system is formed in which the non-linearity due to the visco-plastic properties of the material is placed as part of the load term. In this way, the global stiffness matrix is block diagonal, the coupling due to material non-linearity being included on the right-hand side. Free surfaces are treated as an interface inside the elements, as an extension of the pseudo-concentration method.
Abstract
An analysis of metal forming processes with axial geometry is performed by an expansion in Fourier series on the circumferential direction. For that purpose, an incremental [...]
- 7
- read
On the self-stressing modes in free vibration analysis
S. Idelsohn, M. Geradin

Journal of Sound and Vibration (1982). Vol. 83 (2), pp. 143-155

Abstract
The type of convergence to the eigenspectrum of a structure calculated from a finite element analysis is examined in light of the variational properties of the Rayleigh quotient and of Courant's maximum-minimum principle. The influence of the self-stressing modes on the solution is firt demonstrated theoretically and then shown practically on the results obtained via a family of equilibrium elements in which the number of self-stressing modes relative to the number of vibration modes may be varied as a parameter.
Abstract
The type of convergence to the eigenspectrum of a structure calculated from a finite element analysis is examined in light of the variational properties of the Rayleigh quotient [...]
- 9
- read
Making curved interfaces straight in phase‐change problems
M. Storti, L. Crivelli, S. Idelsohn

Int. J. Numer. Meth. Engng. (1987). Vol. 24 (2), pp. 375-392

Abstract
This paper presents a method for straightening curved interfaces arising in phase‐change problems. The method works on isoparametric finite elements, performing a second transformation which maps the master element onto a new one in which the interface looks like a straight line. This allows using the current Gaussian integration technique for squares to evaluate the integrals over each phase. The method provides a better estimation of the contribution of latent heat effects to the residual vector, compared to those obtained by using the assumption that the interface is straight. Appropriate guidelines for solving the non‐linear system of equations arising in this kind of problem are also given. Several numerical examples are presented to show the performance of the method.
Abstract
This paper presents a method for straightening curved interfaces arising in phase‐change problems. The method works on isoparametric finite elements, performing a second [...]
- 7
- read
Upwind techniques via variational principles
S. Idelsohn

Int. J. Numer. Meth. Engng. (1989). Vol. 28 (4), pp. 769-784

Abstract
The amount of upwind or magnitude of off‐centering needed in the numerical solution of second order differential equations with significant first derivatives is justified more rigorously in this paper by requiring the satisfaction of a variational principle. It will be shown that, for a discrete solution, a set of variational principles can be found which allow the problem to be solved as a self‐adjoint system. The technique presented here will give a clear indication of those regions where (i) upwind techniques are not required, (ii) upwind techniques are necessary and sufficient and (iii) upwind techniques are insufficient and artificial viscosity is required.
Abstract
The amount of upwind or magnitude of off‐centering needed in the numerical solution of second order differential equations with significant first derivatives is justified [...]
- 6
- read
Improving the convergence rate of the Petrov‐Galerkin techniques for the solution of transonic and supersonic flows
C. Baumann, M. Storti, S. Idelsohn

Int. J. Numer. Meth. Engng. (1992). Vol. 34 (2), pp. 453-568

Abstract
This paper report progress on a technique to accelerate the convergence to steady solutions when the streamline‐upwind/Petrov‐Galerkin (SUPG) technique is used. Both the description of a SUPG formulation and the documentation of the development of a code for the finite element solution of transonic and supersonic flows are reported. The aim of this work is to present a formulation to be able to treat domains of any configuration and to use the appropriate physical boundary conditions, which are the major stumbling blocks of the finite difference schemes, together with an appropriate convergence rate to the steady solution. The implemented code has the following features: the Hughes' SUPG‐type formulation with an oscillation‐free shock‐capturing operator, adaptive refinement, explicit integration with local time‐step and hourglassing control. An automatic scheme for dealing with slip boundary conditions and a boundary‐augmented lumped mass matrix for speeding up convergence. It is shown that the velocities at which the error is absorbed in and ejected from the domain (that is damping and group velocities respectively) are strongly affected by the time step used, and that damping gives an O(N2) algorithm contrasting with the O(N) one given by absorption at the boundaries. Nonetheless, the absorbing effect is very low when very different eigenvalues are present, such as in the transonic case, because the stability condition imposes a too slow group velocity for the smaller eigenvalues. To overcome this drawback we present a new mass matrix that provides us with a scheme having the highest group velocity attainable in all the components. In Section 1 we will describe briefly the theoretical background of the SUPG formulation. In Section 2 it is described how the foregoing formulation was used in the finite element code and which are the appropriate boundary conditions to be used. Finally in Section 3 we will show some results obtained with this code
Abstract
This paper report progress on a technique to accelerate the convergence to steady solutions when the streamline‐upwind/Petrov‐Galerkin (SUPG) technique is used. Both the [...]
- 7
- read
A preconditioning mass matrix to accelerate the convergence to the steady Euler solutions using explicit schemes
M. Storti, C. Baumann, S. Idelsohn

Int. J. Numer. Meth. Engng. (1992). Vol. 34 (2), pp. 519-541

Abstract
When explicit time marching algorithms are used to reach the steady state of problems governed by the Euler equations, the rate of convergence is strongly impaired both in the zones with low Mach number and in the zones with transonic flow, e.g. Mach ⩽ α and | Mach − 1| ⩽ α, with α ⩽ 0·2. The rate of convergence becomes slower as α diminishes. We show in this paper, with analytical and numerical results, how the use of a preconditioning mass matrix accelerates the convergence in the aforementioned ranges of Mach numbers. The preconditioning mass matrix (PMM) we advocate in this paper can be applied to any FEM/FVM that uses an explicit time marching scheme to find the steady state. The method's rate of convergence to the steady state is studied, and results for the one‐ and two‐dimiensional cases are presented. In Sections 1‐3, using the one‐dimensional Euler equations, we first explain why there exists a slow rate of convergence when the plain lumping of mass is used. Then the convergence rate to steady solutions is analysed from its two constituents, that is, convergence by absorption at the boundaries and by damping in the domain. Next we give the natural solution to this problem, and with several examples we show the effectiveness of the proposed mass matrix when compared with the plain scheme. In Sections 4‐8 we give the multidimensional version of the preconditioning mass matrix. We make a stability analysis and compare the group velocities and damping with and without the new mass matrix. To finish, we show the velocity of convergence for a common test problem
Abstract
When explicit time marching algorithms are used to reach the steady state of problems governed by the Euler equations, the rate of convergence is strongly impaired both in [...]
- 6
- read
Transient analysis of tube rolling processes by a semi‐analytical formulation
H. Antúnez, S. Idelsohn

Int. J. Numer. Meth. Engng. (1994). Vol. 37 (21), pp. 3621-3632

Abstract
A semi‐analytical formulation is presented for transient metal‐forming processes which, being axisymmetric in geometry, are subjected to non‐axisymmetric loads and boundary conditions. The problems are described in terms of the flow formulation, and the pseudo‐concentration method (two material based) is used to account for time integration and non‐axisymmetric free surfaces. Proper Fourier series expansion of both the scalar fields defined to identify the free surfaces and of all the variables of the mechanical problem allows the performance of an advective transport–corresponding to time integration–for a non‐axisymmetric velocity field. A block diagonal matrix is obtained for each harmonic component, as it has been achieved for the constant time solution. The new configuration found as a result of this analysis is taken to calculate the velocity field for the incremented time, which in turn is used to perform the following time step
Abstract
A semi‐analytical formulation is presented for transient metal‐forming processes which, being axisymmetric in geometry, are subjected to non‐axisymmetric loads and boundary [...]
- 7
- read
Non‐reflective planar boundary condition based on Gauss filter
R. Bonet Chaple, N. Nigro, M. Storti, S. Idelsohn

Int. J. Numer. Meth. Engng. (2000). Vol. 47 (5), pp. 969-983

Abstract
A non‐reflecting boundary condition based on the Gauss filter is employed for the determination of scattered potential governed by the equation. A filtering layer is used for closing infinite domain calculations. An expression for the reflection coefficient is derived and an optimal filtering layer is designed. Numerical results validate the performance of this method for unbounded wave guide problems.
Abstract
A non‐reflecting boundary condition based on the Gauss filter is employed for the determination of scattered potential governed by the equation. A filtering layer is used [...]
- 8
- read
All‐hexahedral mesh smoothing with a node‐based measure of quality
N. Calvo, S. Idelsohn

Int. J. Numer. Meth. Engng. (2001). Vol. 50 (8), pp. 1957-1967

Abstract
This research work deals with the analysis and test of a normalized‐Jacobian metric used as a measure of the quality of all‐hexahedral meshes. Instead of element qualities, a measure of node quality was chosen. The chosen metric is a bound for deviation from orthogonality of faces and dihedral angles. We outline the main steps and algorithms of a program that is successful in improving the quality of initially invalid meshes to acceptable levels. For node movements, the program relies on a combination of gradient‐driven and simulated annealing techniques. Some examples of the results and speed are also shown.
Abstract
This research work deals with the analysis and test of a normalized‐Jacobian metric used as a measure of the quality of all‐hexahedral meshes. Instead of element qualities, [...]
- 7
- read
All‐hexahedral element meshing: automatic elimination of self‐intersecting dual lines
N. Calvo, S. Idelsohn

Int. J. Numer. Meth. Engng. (2002). Vol. 55 (12), pp. 1439-1449

Abstract
There has been some degree of success in all‐hexahedral meshing. Standard methods start with the object geometry defined by means of an all‐quadrilateral mesh, followed by the use of the combinatorial dual to the mesh in order to define the internal connectivities among elements. For all of the known methods using the dual concept, it is necessary to first prevent or eliminate self‐intersecting (SI) dual lines of the given quadrilateral mesh. The relevant features of SI lines are studied, giving a method to remove them, which avoids deforming the original geometry. Some examples of resulting meshes are shown where the current meshing method has been successfully applied.
Abstract
There has been some degree of success in all‐hexahedral meshing. Standard methods start with the object geometry defined by means of an all‐quadrilateral mesh, followed [...]
- 3
- read
Elemental enriched spaces for the treatment of weak and strong discontinuous fields
S. Idelsohn, J. Gimenez, J. Marti, N. Nigro

Comput. Methods Appl. Mech. Engrg., (2017). Vol. 313, pp. 535-559

Abstract
This paper presents a finite element that incorporates weak, strong and both weak plus strong discontinuities with linear interpolations of the unknown jumps for the modeling of internal interfaces. The new enriched space is built by subdividing each triangular or tetrahedral element in several standard linear sub-elements. The new degrees of freedom coming from the assembly of the sub-elements can be eliminated by static condensation at the element level, resulting in two main advantages: first, an elemental enrichment instead of a nodal one, which presents an important reduction of the compunting time when the internal interface is moving all around the domain and second, an efficient implementation involving minor modifications allowing to reuse existing finite element codes. The equations for the internal interface are constructed by imposing the local equilibrium between the stresses in the bulk of the element and the tractions driving the cohesive law, with the proper equilibrium operators to account for the linear kinematics of the discontinuity. To improve the continuity of the unknowns on both sides of the elements on which a static condensation is done, a contour integral has been added. These contour integrals named inter-elemental forces can be interpreted as a “do nothing” boundary condition (Coppola-Owen and Codina, 2011) published in another context, or as the usage of weighting functions that ensure convergence of the approach as proposed by J.C. Simo (Simo and Rifai, 1990). A series of numerical tests for scalar unknowns as a simple representation of more general numerical simulations are presented to illustrate the performance of the enriched elemental space.
Abstract
This paper presents a finite element that incorporates weak, strong and both weak plus strong discontinuities with linear interpolations of the unknown [...]
- 8
- read
A family of conforming finite elements for deep shell analysis
G. Sander, S. Idelsohn

Int. J. Numer. Meth. Engng. (1982). Vol. 18 (3), pp. 363-380

Abstract
The problem related to the derivation of conforming deep shell finite elements is examined in the light of the thin shell theory and using the classical Loves strain energy formulation. A family of quadrangular finite elements allowing for variable curvature is developed. It is shown how an exact conformity of the displacements can be ensured in a large number of cases. Various static and dynamic applications are used to illustrate the advantages of these elements.
Abstract
The problem related to the derivation of conforming deep shell finite elements is examined in the light of the thin shell theory and using the classical Loves strain energy [...]
- 12
- read
A temperature‐based finite element solution for phase‐change problems
L. Crivelli, S. Idelsohn

Int. J. Numer. Meth. Engng. (1986). Vol. 23 (1), pp. 99-119

Abstract
A finite element procedure for solving multidimensional phase change problems is described. The algorithm combines a temperature formulation with a finite element treatment of the differential equation and discontinuous integration within the two‐phase elements to avoid the necessity of regularization. A new criterion for the computation of the iteration matrix is proposed. It is based on a quasi‐Newton correction of the Jacobian matrix for conduction problems without change of phase. A set of test problems with exact solution is analysed and demonstrates that the procedure can accurately evaluate the front position and temperature history with a reasonable computational effort.
Abstract
A finite element procedure for solving multidimensional phase change problems is described. The algorithm combines a temperature formulation with a finite element treatment [...]
- 8
- read
Solution of non‐linear thermal transient problems by a reduction method
A. Cardona, S. Idelsohn

Int. J. Numer. Meth. Engng. (1986). Vol. 23 (6), pp. 1023-1042

Abstract
A new algorithm for solving transient thermal problems in a reduced subspace of the original space of discretization is described. The basis of the subspace is formed by using the system response at the first time step (or an approximation to it) and a set of orthogonal vectors obtained by the algorithm of Lanczos. Derivatives of these vectors are included when treating non‐linear cases. The method allows one to handle the sharp gradients that appear in thermally loaded structures, and the response is accurately predicted by using only a small number of degrees of freedom in the reduced system. The algorithm is specially well suited for treating large‐scale problems. Examples dealing with one‐, two‐ and three‐dimensional cases of linear and non‐linear conduction problems are presented.
Abstract
A new algorithm for solving transient thermal problems in a reduced subspace of the original space of discretization is described. The basis of the subspace is formed by using [...]
- 6
- read
Pre- and post-degradation analysis of composite materials with different moduli in tension and compression
S. Idelsohn, G. Laschet, C. Nyssen

Comput. Methods Appl. Mech. Engrg., (1982). Vol. 30 (2), pp. 133-149

Abstract
An isoparametric finite element tor the analysis of multi-layer composite materials is presented. Several linear and nonlinear stress-strain relations are discussed. Special attention is given to the composite materials with different moduli in tension and compression, for which a new mathematical model is presented and tested. Different failure criteria for the matrix degradation are incorporated in the element and several post-degradation behaviors are also considered. Finally we discuss the role of the Newton-Raphson method in composite materials, especially in the presence of geometrical nonlinearities.
Abstract
An isoparametric finite element tor the analysis of multi-layer composite materials is presented. Several linear and nonlinear stress-strain relations are discussed. Special [...]
- 12
- read
A reduction method for nonlinear structural dynamic analysis
S. Idelsohn, A. Cardona

Comput. Methods Appl. Mech. Engrg., (1985). Vol. 49(3), pp. 253-279

Abstract
A computational algorithm for predicting the nonlinear dynamic response of a structure is presented. The nonlinear system of ordinary differential equations resulting from the finite element discretization is highly reduced by means of a Rayleigh-Ritz analysis. The basis vectors are chosen to be the current tangent eigenmodes together with some modal derivatives that indicate the way in which the spectrum is changing. Only a few basis updatings are required during the whole time integration. The truncation error introduced at every change of basis is pointed out as the cause for a divergence-type behaviour, and some means for eliminating it are discussed. Results for examples involving large displacements are shown and compared to the results obtained by integrating the complete system of equations.
Abstract
A computational algorithm for predicting the nonlinear dynamic response of a structure is presented. The nonlinear system of ordinary differential equations resulting from [...]
- 30
- read
An efficient tangent scheme for solving phase-change problems
M. Storti, L. Crivelli, S. Idelsohn

Comput. Methods Appl. Mech. Engrg., (1988). Vol. 66(1), pp. 65-86

Abstract
Using weak formulations and finite elements to solve heat-conduction problems with phase change finally leads to the solution, at each time step, of a nonlinear system of equations in the nodal temperatures. The Newton-Raphson scheme is an effective procedure to cope with this type of problems; however, the choice of a good approximation to the tangent matrix is critical when the latent heat is comparatively large. In this work we derive an exact expression for the tangent matrix and analyze the behavior of its terms for different values of the physical parameters of the system. We demonstrate that this method has good convergence properties. In fact, the rate of convergence is quadratic when the trial approximation is sufficiently close to the solution. Finally, several numerical examples are given.
Abstract
Using weak formulations and finite elements to solve heat-conduction problems with phase change finally leads to the solution, at each time step, of a nonlinear system of [...]
- 5
- read
Multigrid methods and adaptive refinement techniques in elliptic problems by finite element methods
M. Storti, N. Nigro, S. Idelsohn

Comput. Methods Appl. Mech. Engrg., (1991). Vol. 93(1), pp. 13-30

Abstract
Multigrid and adaptive refinement techniques are powerful tools in the resolution of problems arising from computational mechanics. In structured grids the number of numerical operations needed in the resolution via the multigrid method is of order N, the number of degrees of freedom, regardless the dimensionality of the problem. In this work a multigrid technique, which works on unstructured meshes, is described. These meshes are obtained from a user defined tesselation through bisection refinement upon any element. Original techniques for nodes numbering, irregular nodes detection and nodes classification are developed in view of multigrid method implementation. The error indicator used in the refinement process is based on truncation error estimates. The refinement strategy is oriented toward error reduction at constant computational effort. Finally several numerical examples are presented.
Abstract
Multigrid and adaptive refinement techniques are powerful tools in the resolution of problems arising from computational mechanics. In structured grids the number of numerical [...]
- 7
- read
A Petrov-Galerkin technique for the solution of transonic and supersonic flows
C. Baumann, M. Storti, S. Idelsohn

Comput. Methods Appl. Mech. Engrg., (1992). Vol. 95 (1), pp. 49-70

Abstract
This paper is both the description of a streamline-upwind/Petrov-Galerkin (SUPG) formulation and the documentation of the development of a code for the finite element solution of transonic and supersonic flows. The aim of this work is to present a formulation to be able to treat domains of any configuration and to use the appropriate physical boundary conditions, which are the major stumbling blocks of the finite difference schemes. The implemented code has the following features: the Hughes' SUPG-type formulation with an oscillation-free shock-capturing operator, adaptive refinement, explicit integration with local time-step and hourglassing control. An automatic scheme for dealing with slip boundary conditions and a boundary-augmented lumped mass matrix for speeding up convergence. The theoretical background of the SUPG formulation is described briefly. How the foregoing formulation was used in the finite element code and which are the appropriate boundary conditions to be used are also described. Finally some results obtained with this code are discussed.
Abstract
This paper is both the description of a streamline-upwind/Petrov-Galerkin (SUPG) formulation and the documentation of the development of a code for the finite element solution [...]
- 8
- read
Steady state incompressible flows using explicit schemes with an optimal local preconditioning
M. Storti, N. Nigro, S. Idelsohn

Comput. Methods Appl. Mech. Engrg., (1995). Vol. 124 (3), pp. 231-252

Abstract
Solving large systems of equations from CFD problems by the explicit pseudo-temporal scheme requires a very low amount of memory and is highly parallelizable, but the CPU time largely depends on the conditioning of the system. For advective systems it is shown that the rate of convergence depends on a condition number defined as the ratio of the maximum and the minimum group velocities of the continuum system. If the objective is to reach the steady state, the temporal term can be modified in order to reduce this condition number. Another possibility consists in the addition of a local preconditioning mass matrix. In this paper an optimal preconditioning for incompressible flow is presented, also applicable to compressible ones with locally incompressible zones, like stagnation points, in contrast with the artificial compressibility method. The preconditioned system has a rate of convergence independent from Mach number. Moreover, the discrete solution is highly improved, eliminating spurious oscillations frequently encountered in incompressible flows.
Abstract
Solving large systems of equations from CFD problems by the explicit pseudo-temporal scheme requires a very low amount of memory and is highly parallelizable, but the CPU [...]
- 8
- read
A Petrov-Galerkin formulation for advection-reaction-diffusion problems
S. Idelsohn, N. Nigro, M. Storti, G. Buscaglia

Comput. Methods Appl. Mech. Engrg., (1996). Vol. 136 (1–2), pp. 27-46

Abstract
In this work we present a new method called (SU + C)PG to solve advection-reaction-diffusion scalar equations by the Finite Element Method (FEM). The SUPG (for Streamline Upwind Petrov-Galerkin) method is currently one of the most popular methods for advection-diffusion problems due to its inherent consistency and efficiency in avoiding the spurious oscillations obtained from the plain Galerkin method when there are discontinuities in the solution. Following this ideas, Tezduyar and Park treated the more general advection-reaction-diffusion problem and they developed a stabilizing term for advection-reaction problems without significant diffusive boundary layers. In this work an SUPG extension for all situations is performed, covering the whole plane represented by the Peclet number and the dimensionless reaction number. The scheme is based on the extension of the super-convergence feature through the inclusion of an additional perturbation function and a corresponding proportionality constant. Both proportionality constants (that one corresponding to the standard perturbation function from SUPG, and the new one introduced here) are selected in order to verify the ‘super-convergence’ feature, i.e. exact nodal values are obtained for a restricted class of problems (uniform mesh, no source term, constant physical properties). It is also shown that the (SU + C)PG scheme verifies the Discrete Maximum Principle (DMP), that guarantees uniform convergence of the finite element solution. Moreover, it is shown that super-convergence is closely related to the DMP, motivating the interest in developing numerical schemes that extend the super-convergence feature to a broader class of problems.
Abstract
In this work we present a new method called (SU + C)PG to solve advection-reaction-diffusion scalar equations by the Finite Element Method (FEM). The SUPG (for Streamline [...]
- 11
- read
Equal-order interpolations: a unified approach to stabilize the incompressible and advective effects
M. Storti, N. Nigro, S. Idelsohn

Comput. Methods Appl. Mech. Engrg., (1997). Vol. 143 (3–4), pp. 317-331

Abstract
In this paper we present a new SUPG formulation for compressible and near incompressible Navier-Stokes equations [5]. It introduces an extension of the exact solution for one-dimensional systems to the multidimensional case, in a similar way to that arising in the scalar problem. It is important to note that this formulation satisfies both the one-dimensional advective-diffusive system limit case and the advection-dominated multidimensional system case presented by Mallet et al. Another interesting feature of this formulation is that it introduces naturally a stabilizing term for the incompressibility condition, in a similar way to that found by other authors [1–4]. However, in our formulation the stabilization is introduced to the whole system of equations, while other authors introduce a term to stabilize the incompressibility condition and another one for the advective term. In Section 1 we present Navier-Stokes equations for compressible flow and, then, we pass to detail several topics related to the numerical discretization of such advective-diffusive multidimensional systems of PDEs, in the Petrov-Galerkin context. The method is applicable and described for the general Re > 0 laminar flow, but the nature of the stabilizing effect of the artificial diffusion matrix introduced is discussed in depth for the simpler Stokes (Re = 0) flow. Several numerical results are shown in Section 5, taking the well-known test problem of the square-cavity and a variant of this, namely a multiply connected square-cavity, as a validation for this code
Abstract
In this paper we present a new SUPG formulation for compressible and near incompressible Navier-Stokes equations [5]. It introduces an extension of the exact solution for [...]
- 8
- read
Physics based GMRES preconditioner for compressible and incompressible Navier-Stokes equations
N. Nigro, M. Storti, S. Idelsohn, T. Tezduyar

Comput. Methods Appl. Mech. Engrg., (1998). Vol. 154 (3–4), pp. 203-228

Abstract
This paper presents the implementation of a local physics preconditioning mass matrix [8] for an unified approach of 3D compressible and incompressible Navier-Stokes equations using an SUPG finite element formulation and GMRES implicit solver. During the last years a lot of effort has been dedicated to finding a unified approach for compressible and incompressible flow in order to treat fluid dynamic problems with a very wide range of Mach and Reynolds numbers [10,26,37]. On the other hand, SUPG finite element formulation and GMRES implicit solver is one of the most robust combinations to solve state of the art CFD problems [1,6,9,22,29,30,31]. The selection of a good preconditioner and its performance on parallel architecture is another open problem in CFD community. The local feature of the preconditioner presented here means that no communication among processors is needed when working on parallel architectures. Due to these facts we consider that this research can make some contributions towards the development of a unified fluid dynamic model with high rates of convergence for any combination of Mach and Reynolds numbers, being very suitable for massively parallel computations. Finally, it is important to remark that while this kind of preconditioning produces stabilized results in nearly incompressible regimes the standard version exhibits some numerical drawbacks that lead to solutions without physical meaning.
Abstract
This paper presents the implementation of a local physics preconditioning mass matrix [8] for an unified approach of 3D compressible and incompressible Navier-Stokes equations [...]
- 12
- read
The DNL absorbing boundary condition: applications to wave problems
M. Storti, J. D'ELIA, R. Bonet Chaple, N. Nigro, S. Idelsohn

Comput. Methods Appl. Mech. Engrg., (2000). Vol. 182 (3–4), pp. 483-498

Abstract
A general methodology for developing absorbing boundary conditions is presented. For planar surfaces, it is based on a straightforward solution of the system of block difference equations that arise from partial discretization in the directions transversal to the artificial boundary followed by discretization on a constant step 1D grid in the direction normal to the boundary. This leads to an eigenvalue problem of the size of the number of degrees of freedom in the lateral discretization. The eigenvalues are classified as right- or left-going and the absorbing boundary condition consists in imposing a null value for the ingoing modes, leaving free the outgoing ones. Whereas the classification is straightforward for operators with definite sign, like the Laplace operator, a virtual dissipative mechanism has to be added in the mixed case, usually associated with wave propagation phenomena, like the Helmholtz equation. The main advantage of the method is that it can be implemented as a black-box routine, taking as input the coefficients of the linear system, obtained from standard discretization (FEM or FDM) packages and giving on output the absorption matrix. We present the application of the DNL methodology to typical wave problems, like Helmholtz equations and potential flow with free surface (the ship wave resistance and sea-keeping problems).
Abstract
A general methodology for developing absorbing boundary conditions is presented. For planar surfaces, it is based on a straightforward solution of the system of block difference [...]
- 6
- read
All-hexahedral element meshing: Generation of the dual mesh by recurrent subdivision
N. Calvo, S. Idelsohn

Comput. Methods Appl. Mech. Engrg., (2000). Vol. 182 (3–4), pp. 371-378

Abstract
The domain geometry is defined by means of a closed all-quadrilateral mesh. The outer mesh imposes very strong restrictions on the possible connectivities between the inner hexahedral elements. Following the guidelines of the outer topology, the inner one is almost entirely defined. Several ways may be decided for certain configurations, some of them requiring special considerations in order to achieve a valid FEM mesh. The process is entirely performed by constructing the (graph theoretical) dual of the hexahedral mesh, this means no metric information is handled until the final (positioning and smoothing) steps. The essential steps of this scheme are described by means of examples.
Abstract
The domain geometry is defined by means of a closed all-quadrilateral mesh. The outer mesh imposes very strong restrictions on the possible connectivities between the inner [...]
- 6
- read
Objectivity tests for Navier–Stokes simulations: The revealing of non-physical solutions produced by Laplace formulations
A. Limache, R. Sánchez, L. Dalcín, S. Idelsohn

Comput. Methods Appl. Mech. Engrg., (2008). Vol. 197 (49–50), pp. 4180-4192

Abstract
Laplace formulations are weak formulations of the Navier–Stokes equations commonly used in computational fluid dynamics. In these schemes, the viscous terms are given as a function of the Laplace diffusion operator only. Despite their popularity, recently, it has been proven that they violate a fundamental principle of continuum mechanics, the principle of objectivity. It is remarkable that such flaw has not being noticed before, neither detected in numerical experiments. In this work, a series of objectivity tests have been designed with the purpose of revealing such problem in real numerical experiments. Through the tests it is shown how, for slip boundaries or free-surfaces, Laplace formulations generate non-physical solutions which widely depart from the real fluid dynamics. These tests can be easily reproduced, not requiring complex simulation tools. Furthermore, they can be used as benchmarks to check consistency of developed or commercial software. The article is closed with a discussion of the mathematical aspects involved, including the issues of boundary conditions and objectivity.
Abstract
Laplace formulations are weak formulations of the Navier–Stokes equations commonly used in computational fluid dynamics. In these schemes, the viscous terms are given [...]
- 23
- read
On the use of deep, shallow or flat shell finite elements for the analysis of thin shell structures
S. Idelsohn

Comput. Methods Appl. Mech. Engrg., (1981). Vol. 26 (3), pp. 321-330

Abstract
This paper is confined to the study of thin shells. The aim is to summarize the different theories used and to examine the assumptions upon which each of them is based. The intention is to show when it is more suitable to use a particular approximation and to indicate the errors it introduces. Beginning with the general deep shell theory, some simplifications are introduced to obtain the shallow shell theories. The special implications of this theory for the finite element method are also examined. Finally the particular case of flat elements is discussed.
Abstract
This paper is confined to the study of thin shells. The aim is to summarize the different theories used and to examine the assumptions upon which each of them is based. The [...]
- 25
- read
Current situation and trends in gate design for water conservancy and hydropower engineering in China
Z. Xuecai, W. Wenwu, W. Fan, W. Zhengzhong, X. Zhang

Journal's Papers (2018). 1

Abstract
'''To address the contradiction between supply and demand of water resources in China, mitigate flood and drought disasters, develop sustainable hydropower resources, realize the transformation of the energy industry structure, and realize the Chinese dream of building a beautiful China, the construction of high dams and large reservoirs is imperative. The gates of such conservancy and hydropower structures play an important role in regulating water resources. Only through the flexible operation of gates can the high dams and large reservoirs be adjusted in real time to meet the needs of flood control, power generation, and water resource allocation. The safety of gates largely determines the security of the dams and the life and property of people residing downstream. Therefore, the safety design of gates is of utmost importance. This paper presents a comprehensive analysis of the status of development of water conservancy and hydropower engineering gates; material selection, connection methods, classification, selection, design of gates; as well as the design codes for gates in international engineering. This paper also elucidates the emerging trends related to materials, structures, connection methods, and design methods of gates.
Abstract
'''To address the contradiction between supply and demand of water resources in China, mitigate flood and drought disasters, develop sustainable hydropower resources, [...]
- 919
- read
Surface tension problems solved with the Particle Finite Element Method using large time-steps
J. Giménez, N. Nigro, S. Idelsohn, E. Oñate

Computers and Fluids (2016). (preprint) Vol. 141, pp. 90-104

Abstract
In previous works [1,2], the authors have presented a highly efficient extension of the Particle Finite Element Method, called PFEM-2, to solve two-phase flows. The methodology which uses X-IVS [3] to treat convection terms allowing large time-steps was validated for problems where the gravity forces and/or the inertial forces dominate the flow. Although that is the target range of problems to solve with PFEM-2, most of real problems that fall in these categories also includes other flow regimes in certain regions of the domain. Maybe the most common secondary regime is when the surface tension dominates, as an example when drops or bubbles are released from the main flow, and this feature must be taken into account in any complete numerical strategy. Attending to that, in this work the treatment of the surface tension to PFEM-2 is included. An implicit CSF methodology is employed together with a coupling between the marker function with a Level Set function to obtain a smooth representation of the normal of the interface which allows an accurate curvature calculation. Examples for curvature calculation and isolated bubbles and drops are presented where the accuracy and the computational efficiency are analyzed and contrasted with other numerical methodologies. Finally, a simulation of a jet atomization is analyzed. This case presents the above mentioned features: it is a inertia-dominant flow with a surface tension phenomena on drops and ligaments break up that can not be neglected.
Abstract
In previous works [1,2], the authors have presented a highly efficient extension of the Particle Finite Element Method, called PFEM-2, to solve two-phase flows. The methodology [...]
- 285
- read
Advances in the particle finite element method for the analysis of fluid-multibody interaction and bed erosion in free surface flows
E. Oñate, S. Idelsohn, M. Celigueta, R. Rossi

Comput. Methods Appl. Mech. Engrg., (2008). Vol. 197 (19-20), pp. 1777–1800

Abstract
We present some advances in the formulation of the Particle Finite Element Method (PFEM) for solving complex fluid-structure interaction problems with free surface waves. In particular, we present extensions of the PFEM for the analysis of the interaction between a collection of bodies in water allowing for frictional contact conditions at the fluid-solid and solid-solid interfaces via mesh generation. An algorithm to treat bed erosion in free surface flows is also presented. Examples of application of the PFEM to solve a number of fluid-multibody interaction problems involving splashing of waves, large motions of floating and submerged bodies and bed erosion situations are given.
Abstract
We present some advances in the formulation of the Particle Finite Element Method (PFEM) for solving complex fluid-structure interaction problems with free surface waves. [...]
- 228
- read
Lagrangian versus Eulerian integration errors
S. Idelsohn, E. Oñate, N. Nigro, P. Becker

Comput. Methods Appl. Mech. Engrg., (2015). Vol. 293, pp. 191–206; (preprint)

Abstract
The possibility to use a Lagrangian frame to solve problems with large time-steps was successfully explored previously by the authors for the solution of homogeneous incompressible fluids and also for solving multi-fluid problems [28-30]. The strategy used by the authors was named Particle Finite Element Method second generation (PFEM-2). The objective of this paper is to demonstrate in which circumstances the use of a Lagrangian frame with particles is more accurate than a classical Eulerian finite element method, and when large time-steps and/or coarse meshes may be used.
Abstract
The possibility to use a Lagrangian frame to solve problems with large time-steps was successfully explored previously by the authors for the solution of homogeneous incompressible [...]
- 171
- read
Unified Lagrangian formulation for elastic solids and incompressible fluids. application to fluid-structure interaction problems via the PFEM
S. Idelsohn, J. Marti, A. Limache, E. Oñate

Comput. Methods Appl. Mech. Engrg., (2008). Vol. 197, pp. 1762–1776

Abstract
We present a general Lagrangian formulation for treating elastic solids and quasi/fully incompressible fluids in a unified form. The formulation allows to treat solid and fluid subdomains in a unified manner in fluid-structure interaction (FSI) situations. In our work the FSI problem is solved via the Particle Finite Element Method (PFEM). The PFEM is an effective technique for modeling complex interactions between floating and submerged bodies and free surface flows, accounting for splashing of waves, large motions of the bodies and frictional contact conditions. Applications of the unified Lagrangian formulation to a number of FSI problems are given.
Abstract
We present a general Lagrangian formulation for treating elastic solids and quasi/fully incompressible fluids in a unified form. The formulation allows to treat solid and [...]
- 110
- read
A finite point method in computational mechancis. Applications to convective transport and fluid flow.
E. Oñate, S. Idelsohn, O. Zienkiewicz, R. Taylor

Int. J. Numer. Meth. Engng. (1996). Vol. 39 (22), pp. 3839-3866

Abstract
The paper presents a fully meshless procedure fo solving partial differential equations. The approach termed generically the ‘finite point method’ is based on a weighted least square interpolation of point data and point collocation for evaluating the approximation integrals. Some examples showing the accuracy of the method for solution of adjoint and non‐self adjoint equations typical of convective‐diffusive transport and also to the analysis of compressible fluid mechanics problem are presented.
Abstract
The paper presents a fully meshless procedure fo solving partial differential equations. The approach termed generically the ‘finite point method’ is based on [...]
- 96
- read
Finite volumes and finite elements: Two ‘good friends’
E. Oñate, S. Idelsohn

Int. J. Numer. Meth. Engng. (1994). Vol. 37 (19), pp. 3323-3341

Abstract
In this paper a comparison between the finite element and the finite volume methods is presented in the context of elliptic, convective–diffusion and fluid flow problems. The paper shows that both procedures share a number of features, like mesh discretization and approximation. Moreover, it is shown that in many cases both techniques are completely equivalent.
Abstract
In this paper a comparison between the finite element and the finite volume methods is presented in the context of elliptic, convective–diffusion and fluid flow problems. [...]
- 78
- read
Advances in the simulation of multi-fluid flows with the Particle Finite Element Method. Application to bubble dynamics
M. Mier-Torrecilla, S. Idelsohn, E. Oñate

Int. J. Numer. Meth. Fluids (2010). Vol. 67 (11), pp. 1516-1539

Abstract
In this work we extend the Particle Finite Element Method (PFEM) to multi-fluid flow problems with the aim of exploiting the fact that Lagrangian methods are specially well suited for tracking interfaces. We develop a numerical scheme able to deal with large jumps in the physical properties, included surface tension, and able to accurately represent all types of discontinuities in the flow variables. The scheme is based on decoupling the velocity and pressure variables through a pressure segregation method which takes into account the interface conditions. The interface is defined to be aligned with the moving mesh, so that it remains sharp along time, and pressure degrees of freedom are duplicated at the interface nodes to represent the discontinuity of this variable due to surface tension and variable viscosity. Furthermore, the mesh is refined in the vicinity of the interface to improve the accuracy and the efficiency of the computations. We apply the resulting scheme to the benchmark problem of a two-dimensional bubble rising in a liquid column presented in [[#cite-1|[1]]], and propose two breakup and coalescence problems to assess the ability of a multi-fluid code to model topology changes.
Abstract
In this work we extend the Particle Finite Element Method (PFEM) to multi-fluid flow problems with the aim of exploiting the fact that Lagrangian methods are specially well [...]
- 71
- read
Finite element formulation for convective-diffusive problems with sharp gradients using finite calculus
E. Oñate, F. Zarate, S. Idelsohn

Comput. Methods Appl. Mech. Engrg., (2006). Vol. 195 (13-16), pp. 1793–1825

Abstract
A finite element method (FEM) for steady-state convective-diffusive problems presenting sharp gradients of the solution both in the interior of the domain and in boundary layers is presented. The necessary stabilization of the numerical solution is provided by the Finite Calculus (FIC) approach. The FIC method is based in the solution by the Galerkin FEM of a modified set of governing equations which include characteristic length parameters. It is shown that the FIC balance equation for the multidimensional convection-diffusion problem written in the principal curvature axes of the solution, introduces an orthotropic diffusion which stabilizes the numerical solution both in smooth regions as well in the vicinity of sharp gradients. The dependence of the stabilization terms with the principal curvature directions of the solution makes the method non linear. Details of the iterative scheme to obtain stabilized results are presented together with examples of application which show the efficiency and accuracy of the approach.
Abstract
A finite element method (FEM) for steady-state convective-diffusive problems presenting sharp gradients of the solution both in the interior of the domain and in boundary [...]
- 71
- read
A unified monolithic approach for multi-fluid flows and Fluid-Structure Interaction using the Particle Finite Element Method with fixed mesh
P. Becker, S. Idelsohn, E. Oñate

Computational Mechanics (2015). (preprint) Vol. 55, pp. 1091–1104

Abstract
This paper describes a strategy to solve multi-fluid and Fluid-Structure Interaction (FSI) problems using Lagrangian particles combined with a fixed Finite Element (FE) mesh . Our approach is an extension of the fluid-only PFEM-2 [1,2] which uses explicit integration over the streamlines to improve accuracy. As a result, the convective term does not appear in the set of equations solved on the fixed mesh. Enrichments in the pressure field are used to improve the description of the interface between phases.
Abstract
This paper describes a strategy to solve multi-fluid and Fluid-Structure Interaction (FSI) problems using Lagrangian particles combined with a fixed Finite Element (FE) mesh [...]
- 68
- read
Fluid-structure interaction using the Particle Finite Element Method
S. Idelsohn, E. Oñate, F. Pin, N. Calvo

Comput. Methods Appl. Mech. Engrg., (2006). Vol. 195 (17-18), pp. 2100-2123

Abstract
In the present work a new approach to solve fluid-structure interaction problems is described. Both, the equations of motion for fluids and for solids have been approximated using a material (lagrangian) formulation. To approximate the partial differential equations representing the fluid motion, the shape functions introduced by the Meshless Finite Element Method (MFEM) have been used. Thus, the continuum is discretized into particles that move under body forces (gravity) and surface forces (due to the interaction with neighboring particles). All the physical properties such as density, viscosity, conductivity, etc., as well as the variables that define the temporal state such as velocity and position and also other variables like temperature are assigned to the particles and are transported with the particle motion. The so called Particle Finite Element Method (PFEM) provides a very advantageous and efficient way for solving contact and free-surface problems, highly simplifying the treatment of fluid-structure interactions. '''Key words: '''Fluid-Structure interaction, Particle methods, Lagrange formulations, Incompressible Fluid Flows, Meshless Methods, Finite Element Method.
Abstract
In the present work a new approach to solve fluid-structure interaction problems is described. Both, the equations of motion for fluids and for solids have been approximated [...]
- 50
- read
Melting and Spread of Polymers in Fire with the Particle Finite Element Method
E. Oñate, R. Rossi, K. Butler, S. Idelsohn

Int. J. Numer. Meth. Engng. (2010). Vol. 81 (8), pp. 1046-1072

Abstract
A new computational procedure for analysis of the melting and flame spread of polymers under fire conditions is presented. The method, termed Particle Finite Element Method (PFEM), combines concepts from particle-based techniques with those of the standard finite element method (FEM). The key feature of the PFEM is the use of an updated Lagrangian description to model the motion of nodes (particles) in the thermoplastic material. Nodes are viewed as material points which can freely move and even separate from the main analysis domain representing, for instance, the effect of melting and dripping of polymer particles. A mesh connects the nodes defining the discretized domain where the governing equations are solved as in the standard FEM. An incremental iterative scheme for the solution of the nonlinear transient coupled thermal-flow problem, including loss of mass by gasification, is used. Examples of the possibilities of the PFEM for the modelling and simulation of the melting and flame spread of polymers under different fire conditions are described. Numerical results are compared with experimental data provided by NIST.
Abstract
A new computational procedure for analysis of the melting and flame spread of polymers under fire conditions is presented. The method, termed Particle Finite Element Method [...]
- 49
- read
The particle finite element method: a powerful tool to solve incompressible flows with free‐surfaces and breaking waves
S. Idelsohn, E. Oñate, F. Del Pin

Int. J. Numer. Meth. Engng. (2004). Vol. 61 (7), pp. 964-989

Abstract
Particle Methods are those in which the problem is represented by a discrete number of particles. Each particle moves accordingly with its own mass and the external/internal forces applied to it. Particle Methods may be used for both, discrete and continuous problems. In this paper, a Particle Method is used to solve the continuous fluid mechanics equations. To evaluate the external applied forces on each particle, the incompressible Navier–Stokes equations using a Lagrangian formulation are solved at each time step. The interpolation functions are those used in the Meshless Finite Element Method and the time integration is introduced by an implicit fractional‐step method. In this manner classical stabilization terms used in the momentum equations are unnecessary due to lack of convective terms in the Lagrangian formulation. Once the forces are evaluated, the particles move independently of the mesh. All the information is transmitted by the particles. Fluid–structure interaction problems including free‐fluid‐surfaces, breaking waves and fluid particle separation may be easily solved with this methodology.
Abstract
Particle Methods are those in which the problem is represented by a discrete number of particles. Each particle moves accordingly with its own mass and the external/internal [...]
- 48
- read
Modelling the vertical UL 94 test: competition and collaboration between melt dripping, gasification and combustion
F. Kempel, B. Schartel, J. Marti, K. Butler, R. Rossi, S. Idelsohn, E. Oñate

Fire and Materials (2015). Vol. 39 (6), pp. 570-584

Abstract
An experimental and numerical investigation of the effect of bisphenol A bis(diphenyl phosphate) (BDP) and polytetraﬂuoroethylene (PTFE) on the ﬁre behaviour of bisphenol A polycarbonate/acrylonitrile butadiene styrene (PC/ABS) in the vertical UL 94 scenario is presented. Four PC/ABS blends were discussed, which satisfy different UL 94 classiﬁ cations d ue to the competing ef fects of gasiﬁca ti on, charring, ﬂame inhibition and melt ﬂow/dripping. For numerical investigation, the particle ﬁnite element method (PFEM) is used. Its capability to model the complex ﬁre behaviour of polymers in the UL 94 is analysed. The materials’ properties are characterised, in particular the additives impact on the dripping behaviour during thermal exposure. BDP is an efﬁcie nt p lasticiser; adding PTFE p reve nts dripping by causing a ﬂo w limit. P FEM simulation s reproduce the dripping and burning behaviour, in particular the competition between gasiﬁcation and dripping. The thermal impact of both the burner and the ﬂame is approximated taking into account ﬂame inhibition, charring and effective heat of combustion. PFEM is a promising numerical tool for the investigation of the ﬁre behaviour of polymers, particularly when large deformations are involved. Not only the principal phenomena but also the different UL 94 classi ﬁ cations and t he exti nc tion times are well predicted.
Abstract
An experimental and numerical investigation of the effect of bisphenol A bis(diphenyl phosphate) (BDP) and polytetraﬂuoroethylene (PTFE) on the ﬁre behaviour of bisphenol [...]
- 42
- read
Advances in stabilized finite element and particle methods for bulk forming processes
E. Oñate, J. Rojek, M. Chiumenti, S. Idelsohn, F. Pin, R. Aubry

Comput. Methods Appl. Mech. Engrg., (2006). Vol. 195, pp. 6750-6777

Abstract
The paper describes some recent developments in finite element and particle methods for analysis of a wide range of bulk forming processes. The developments include new stabilized linear triangles and tetrahedra using finite calculus and a new procedure combining particle methods and finite element methods. Applications of the new numerical methods to casting, forging and other bulk metal forming problems and mixing processes are shown.
Abstract
The paper describes some recent developments in finite element and particle methods for analysis of a wide range of bulk forming processes. The developments include new stabilized [...]
- 31
- read
Polyhedrization of an arbitrary 3D point set
S. Idelsohn, N. Calvo, E. Oñate

Comput. Methods Appl. Mech. Engrg., (2003). Vol. 192, pp. 2649–2667

Abstract
Given a 3D point set, the problem of defining the volume associated, dividing it into a set of regions (elements) and defining a boundary surface is tackled. Several physical problems need to define volume domains, boundary surfaces and approximating functions from a given point distribution. This is for instance the case of particle methods, in which all the information is the particle positions and there are not boundary surfaces definition. Until recently, all the FEM mesh generators were limited to the generation of simple elements as tetrahedral or hexahedral elements (or triangular and quadrangular in 2D problems). The reason of this limitation was the lack of any acceptable shape function to be used in other kind of geometrical elements. Nowadays, there are several acceptable shape functions for a very large class of polyhedra. These new shape functions, together with a generalization of the Delaunay tessellation presented in this paper, gives an optimal marriage and a powerful tool to solve a large variety of physical problems by numerical methods. The domain partition into polyhedra presented here is not a standard mesh generation. The problem here is: for a given node distribution to find a suitable boundary surface and a suitable mesh to be used in the solution of a physical problem by a numerical method. To include new nodes or change their positions is not allowed.
Abstract
Given a 3D point set, the problem of defining the volume associated, dividing it into a set of regions (elements) and defining a boundary surface is tackled. Several [...]
- 30
- read
A stabilized finite point method for analysis of fluid mechanics problems
E. Oñate, S. Idelsohn, O. Zienkiewicz, R. Taylor, C. Sacco

Comput. Methods Appl. Mech. Engrg., (1996). Vol. 195, pp. 6750-6777

Abstract
flow type problems is presented. The method is based on the use of a weighted least square interpolation procedure together with point collocation for evaluating the approximation integrals. Some examples of application to convective trasport and compressible flow problems are presented.
Abstract
flow type problems is presented. The method is based on the use of a weighted least square interpolation procedure together with point collocation for evaluating the approximation [...]
- 27
- read
P1/P0+ elements for incompressible flows with discontinuous material properties
E. Oñate, P. Nadukandi, S. Idelsohn

Comput. Methods Appl. Mech. Engrg., (2015). Vol. 293, pp. 191-206

Abstract
We present a 3-noded triangle and a 4-noded tetrahedra with a continuous linear velocity and a discontinuous linear pressure field formed by the sum of an unknown ''constant pressure field'' and ''a prescribed linear field'' that satisfies the steady state momentum equations for a constant body force. The elements are termed P1/P0+ as the “effective” pressure field is linear, although the unknown pressure field is piecewise constant within each element. The elements have an excellent behaviour for incompressible viscous flow problems with discontinuous material properties formulated in either Eulerian or Lagrangian descriptions. The necessary numerical stabilization for dealing with the inf-sup condition imposed by the incompressibility constraint and high convective effects (in Eulerian flows) is introduced via the Finite Calculus (FIC) approach. For the sake of clarity, the element derivation is presented first for the simpler Stokes equations written in the standard Eulerian frame. The extension of the formulation to the Navier-Stokes equations written in the Eulerian and Lagrangian frameworks is straightforward and is presented in the second part of the paper. The efficiency and accuracy of the new P1/P0+ triangle is verified by solving a set of incompressible multifluid flow problems using a Lagrangian approach and a classical Eulerian description. The excellent performance of the new triangular element in terms of mass conservation and general accuracy for analysis of fluids with discontinuous material properties is highlighted.
Abstract
We present a 3-noded triangle and a 4-noded tetrahedra with a continuous linear velocity and a discontinuous linear pressure field formed by the sum of an unknown ''constant [...]
- 26
- read
The challenge of mass conservation in the solution of free‐surface flows with the fractional‐step method: Problems and solutions
S. Idelsohn, E. Oñate

Int. J. Numer. Meth. Biomed. Engng (2010). Vol. 26 (10), pp. 1313-1330

Abstract
The purpose of this paper is to put in evidence that the fractional‐step method (FSM) used to solve the incompressible transient Euler and Navier–Stokes equations for free‐surface flows has a problem inherent to the method that may produce unacceptable variations of the domain volume. A simple modification of the free‐surface boundary term is introduced in order to reduce considerably the volume loss and preserve the computational advantages of the FSM.
Abstract
The purpose of this paper is to put in evidence that the fractional‐step method (FSM) used to solve the incompressible transient Euler and Navier–Stokes equations [...]
- 26
- read
A family of residual‐based stabilized finite element methods for Stokes flows
E. Oñate, P. Nadukandi, S. Idelsohn, J. García-Espinosa, C. Felippa

Int. J. Numer. Meth. Fluids (2011). Vol. 65 (1-3), pp. 106-134

Abstract
We present a collection of stabilized finite element (FE) methods derived via first‐ and second‐order finite calculus (FIC) procedures. It is shown that several well known existing stabilized FE methods such as the penalty technique, the Galerkin Least Square (GLS) method, the Pressure Gradient Projection (PGP) method and the orthogonal sub‐scales (OSS) method are recovered from the general residual‐based FIC stabilized form. A new family of stabilized Pressure Laplacian Stabilization (PLS) FE methods with consistent nonlinear forms of the stabilization parameters are derived. The distinct feature of the family of PLS methods is that they are residual‐based, i.e. the stabilization terms depend on the discrete residuals of the momentum and/or the incompressibility equations. The advantages and disadvantages of the different stabilization techniques are discussed and several examples of application are presented.
Abstract
We present a collection of stabilized finite element (FE) methods derived via first‐ and second‐order finite calculus (FIC) procedures. It is shown that several well known [...]
- 25
- read
A coupled PFEM–Eulerian approach for the solution of porous FSI problems
A. LARESE, R. Rossi, E. Oñate, S. Idelsohn

Computational Mechanics (2012). Vol. 50 (6), pp. 805-819

Abstract
This paper aims to present a coupled solution strategy for the problem of seepage through a rockfill dam taking into account the free-surface flow within the solid as well as in its vicinity. A combination of a Lagrangian model for the structural behavior and an Eulerian approach for the fluid is used. The particle finite element method is adopted for the evaluation of the structural response, whereas an Eulerian fixed-mesh approach is employed for the fluid. The free surface is tracked by the use of a level set technique. The numerical results are validated with experiments on scale models rockfill dams.
Abstract
This paper aims to present a coupled solution strategy for the problem of seepage through a rockfill dam taking into account the free-surface flow within the solid as well [...]
- 23
- read
A Finite Element Model for the Simulation of the UL-94 Burning Test
J. Marti, S. Idelsohn, E. Oñate

Fire Technology (2018). Vol. 54 (6), pp. 1783–1805

Abstract
The tendency of the polymers to melt and drip when they are exposed to external heat source play a very important role in the ignition and the spread of fire. Numerical simulation is a promising methodology for predicting this behaviour. In this paper, a computational procedure that aims at analyzing the combustion, melting and flame spread of polymer is presented. The method models the polymer using a Lagrangian framework adopting the particle finite element method framework while the surrounding air is solved on a fixed Eulerian mesh. This approach allows to treat naturally the polymer shape deformations and to solve the thermo-mechanical problem in a staggered fashion. The problems are coupled using an embedded Dirichlet–Neumann scheme. A simple combustion model and a radiation modeling strategy are included in the air domain. With this strategy the burning of a polypropylene specimen under UL-94 vertical test conditions is simulated. Input parameters for the modelling (density, specific heat, conductivity and viscosity) and results for the validation of the numerical model has been obtained from different literature sources and by IMDEA burning a specimen of dimensions of 148×13×3.2mm3. Temperature measurements in the polymer have been recorder by means of three thermocouples exceeding the 1000 K. Simultaneously a digital camera was used to record the burning process. In addition, thermal decomposition of the material (Arrhenius coefficient A=7.14×1016 min−1 and activation energy E=240.67kJ/mol) as and changes in viscosity (μ) as a function of temperature were obtained. Finally, a good agreement between the experimental and the numerical can be seen in terms of shape of the polymer as well as in the temperature evolution inside the polymer.
Abstract
The tendency of the polymers to melt and drip when they are exposed to external heat source play a very important role in the ignition and the spread of fire. Numerical simulation [...]
- 23
- read
A finite point method for adaptive three‐dimensional compressible flow calculations
E. Ortega, E. Oñate, S. Idelsohn

Int. J. Numer. Meth. Fluids (2008). Vol. 60 (9), pp. 937-971

Abstract
The finite point method (FPM) is a meshless technique, which is based on both, a weighted least‐squares numerical approximation on local clouds of points and a collocation technique which allows obtaining the discrete system of equations. The research work we present is part of a broader investigation into the capabilities of the FPM to deal with 3D applications concerning real compressible fluid flow problems. In the first part of this work, the upwind‐biased scheme employed for solving the flow equations is described. Secondly, with the aim of exploiting the meshless capabilities, an h‐adaptive methodology for 2D and 3D compressible flow calculations is developed. This adaptive technique applies a solution‐based indicator in order to identify local clouds where new points should be inserted in or existing points could be safely removed from the computational domain. The flow solver and the adaptive procedure have been evaluated and the results are encouraging. Several numerical examples are provided in order to illustrate the good performance of the numerical methods presented.
Abstract
The finite point method (FPM) is a meshless technique, which is based on both, a weighted least‐squares numerical approximation on local clouds of points and a collocation [...]
- 23
- read
To mesh or not to mesh. That is the question. . .
S. Idelsohn, E. Oñate

Comput. Methods Appl. Mech. Engrg., (2006). Vol. 195, pp. 4681–4696

Abstract
In the last decade a family of methods called meshless methods has been developed both for structural and fluid mechanics problems. After these ideas, a possible classification for numerical formulations may be to separate the methods that make use of a standard finite element mesh (such as those made of tetrahedra or hexahedra), from those that do not need a standard mesh, namely the meshless methods. For solving a partial different equation by a numerical method, a possible alternative may be either to use a mesh method or a meshless method. This paper discusses this issue to show that this choice is not, in the large majorities of the cases, the right question.
Abstract
In the last decade a family of methods called meshless methods has been developed both for structural and fluid mechanics problems. After these ideas, a possible classification [...]
- 22
- read
A Lagrangian meshless finite element method applied to fluid–structure interaction problems
S. Idelsohn, E. Oñate, F. Del Pin

Computers and Structures (2003). Vol. 81 (8-11), pp. 655-671

Abstract
A method is presented for the solution of the incompressible fluid flow equations using a Lagrangian formulation. The interpolation functions are those used in the meshless finite element method and the time integration is introduced in a semi-implicit way by a fractional step method. Classical stabilization terms used in the momentum equations are unnecessary due to the lack of convective terms in the Lagrangian formulation. Furthermore, the Lagrangian formulation simplifies the connections with fixed or moving solid structures, thus providing a very easy way to solve fluid–structure interaction problems.
Abstract
A method is presented for the solution of the incompressible fluid flow equations using a Lagrangian formulation. The interpolation functions are [...]
- 22
- read
Flow behaviour of negatively buoyant jets in immiscible ambient fluid
A. Geyer, J. Phillips, M. Mier-Torrecilla, S. Idelsohn, E. Oñate

Experiments in Fluids (2012). Vol 52 (1), pp. 261-257

Abstract
In this paper we investigate experimentally the injection of a negatively buoyant jet into a homogenous immiscible ambient fluid. Experiments are carried out by injecting a jet of dyed fresh water through a nozzle in the base of a cylindrical tank containing rapeseed oil. The fountain inlet flow rate and nozzle diameter were varied to cover a wide range of Richardson Ri(8 × 10−4 < Ri < 1.98), Reynolds Re (467 < Re < 5,928) and Weber We (2.40 < We < 308.56) numbers. Based on the Re, Ri and We values for the experiments, we have determined a regime map to define how these values may control the occurrence of the observed flow types. Whereas Ri plays a stronger role when determining the maximum penetration height, the effect of the Reynolds number is stronger predicting the flow behaviour for a specific nozzle diameter and injection velocity.
Abstract
In this paper we investigate experimentally the injection of a negatively buoyant jet into a homogenous immiscible ambient fluid. Experiments are carried out by injecting [...]
- 20
- read
GPGPU implementation of the BFECC algorithm for pure advection equations
S. Costarelli, M. Storti, R. Paz, L. Dalcin, S. Idelsohn

Cluster computing (2014). Vol. 17 (2), pp. 243-254

Abstract
In the present work an implementation of the Back and Forth Error Compensation and Correction (BFECC) algorithm specially suited for running on General-Purpose Graphics Processing Units (GPGPUs) through Nvidia’s Compute Unified Device Architecture (CUDA) is analyzed in order to solve transient pure advection equations. The objective is to compare it to a previous explicit version used in a Navier-Stokes solver fully written in CUDA. It turns out that BFECC could be implemented with unconditional stable stability using Semi-Lagrangian time integration allowing larger time steps than Eulerian ones.
Abstract
In the present work an implementation of the Back and Forth Error Compensation and Correction (BFECC) algorithm specially suited for running on General-Purpose Graphics Processing [...]
- 20
- read
Fast fluid–structure interaction simulations using a displacement-based finite element model equipped with an explicit streamline integration prediction
P. Ryzhakov, J. Miquel, S. Idelsohn, E. Oñate

Comput. Methods Appl. Mech. Engrg., (2017). Vol. 315, pp. 1080-1097

Abstract
We propose here a displacement-based updated Lagrangian fluid model developed to facilitate a monolithic coupling with a wide range of structural elements described in terms of displacements. The novelty of the model consists in the use of the explicit streamline integration for predicting the end-of-step configuration of the fluid domain. It is shown that this prediction considerably alleviates the time step size restrictions faced by the former Lagrangian models due to the possibility of an element inversion within one time step. The method is validated and compared with conventional approaches using three numerical examples. Time step size and corresponding Courant numbers leading to optimal behavior in terms of computational efficiency are identified.
Abstract
We propose here a displacement-based updated Lagrangian fluid model developed to facilitate a monolithic coupling with a wide range of structural elements [...]
- 19
- read
Migration of a generic multi-physics framework to HPC environments
P. Dadvand, R. Rossi, M. Gil, X. Martorell, J. Cotela, E. Juanpere, S. Idelsohn, E. Oñate

Computers and Fluids (2013). Vol. 80, pp. 301-309

Abstract
Creating a highly parallelizable code is a challenge specially for Distributed Memory Machines (DMMs). Moreover, algorithms and data structures suitable for these platforms can be very different from the ones used in serial code. For this reason, many programmers in the field prefer to start their own code from scratch. However, for an already existing framework supported by a long-time expertise the idea of transformation becomes attractive in order to reuse the effort done during years of development. In this presentation we explain how a relatively complex framework but with modular structure can be prepared for high performance computing with minimum modification. Kratos Multi-Physics is an open source generic multi-disciplinary platform for solution of coupled problems consist of fluid, structure, thermal and electromagnetic fields. The parallelization of this framework is performed with objective of enforcing the less possible changes to its different solver modules and encapsulate the changes as much as possible in its common kernel. This objective is achieved thanks to the Kratos design and also innovative way of dealing with data transfers for a multi-disciplinary code. This work is completed by the migration of the framework from the 86× architecture to the Marenostrum Supercomputing platform. The migration has been verified by a set of benchmarks which show high scalability, from which we present the Telescope problem in this paper.
Abstract
Creating a highly parallelizable code is a challenge specially for Distributed Memory Machines (DMMs). Moreover, algorithms and data structures suitable for these platforms [...]
- 19
- read
Large time-step explicit integration method for solving problems with dominant convection
S. Idelsohn, N. Nigro, A. Limache, E. Oñate

Comput. Methods Appl. Mech. Engrg., (2012). Vol. 217-220, pp. 168-185

Abstract
An explicit time integrator without the CFL < 1 restriction for the momentum equation is presented. This allows stable large time-steps in problems dominated by convection, independently of the spatial discretization. The idea is to use the information existing at time t=tn in the velocity streamlines as well as in the acceleration streamlines to update the particle position as well as the velocity in an updated Lagrangian frame. The method may be used with moving or fixed meshes.
Abstract
An explicit time integrator without the CFL < 1 restriction for the momentum equation is presented. This allows stable large time-steps in problems dominated [...]
- 17
- read
Particle finite element method in fluid-mechanics including thermal convection-diffusion
R. Aubry, S. Idelsohn, E. Oñate

Computers and Structures (2005). Vol. 83 (17-18), pp. 1459-1475

Abstract
A method is presented for the solution of an incompressible viscous fluid flow with heat transfer using a fully Lagrangian description of the motion. Due to the severe element distortion, a frequent remeshing is performed in an efficient manner. An implicit time integration through a classical fractional step is presented. The non-linearities of the formulation are taken into account and solved with the fixed-point iteration method. The displacement and temperature solutions are coupled through the Boussinesq approximation. The Lagrangian formulation provides an elegant way of solving free-surface problems with thermal convection as the particles are followed during their motion. To illustrate the method, the Rayleigh–Bénard instability with and without free surface in two dimensions has been computed.
Abstract
A method is presented for the solution of an incompressible viscous fluid flow with heat transfer using a fully Lagrangian description of the motion. Due [...]
- 17
- read
The violation of objectivity in Laplace formulations of the Navier–Stokes equations
A. Limache, S. Idelsohn, R. Rossi, E. Oñate

Int. J. Numer. Meth. Fluids (2007). Vol. 54 (6-8), pp. 639-664

Abstract
The Navier–Stokes equations written in Laplace form are often the starting point of many numerical methods for the simulation of viscous flows. Imposing the natural boundary conditions of the Laplace form or neglecting the viscous contributions on free surfaces are traditionally considered reasonable and harmless assumptions. With these boundary conditions any formulation derived from integral methods (like finite elements or finite volumes) recovers the pure Laplacian aspect of the strong form of the equations. This approach has also the advantage of being convenient in terms of computational effort and, as a consequence, it is used extensively. However, we have recently discovered that these resulting Laplacian formulations violate a basic axiom of continuum mechanics: the principle of objectivity. In the present article we give an accurate account about these topics. We also show that unexpected differences may sometimes arise between Laplace discretizations and divergence discretizations.
Abstract
The Navier–Stokes equations written in Laplace form are often the starting point of many numerical methods for the simulation of viscous flows. Imposing the natural [...]
- 17
- read
Variational Framework for FIC Formulations in Continuum Mechanics: High Order Tensor-Derivative Transformations and Invariants
C. Felippa, E. Oñate, S. Idelsohn

Archives of Comp. Meths. Engng. (2018). Vol. 25 (4), pp. 919–963

Abstract
This is part of an article series on a variational framework for continuum mechanics based on the Finite Increment Calculus (FIC). The formulation utilizes high order derivatives of the classical fields of continuum mechanics integrated over control regions to construct stabilizing modification terms. Fields may include displacements, body forces, strains, stresses, pressure and volumetric strains. To support observer-invariant FIC formulations, we have catalogued field transformation equations as well as sets of linear and quadratic invariants of fields and of their derivatives up to appropriate order. Attention is focused on the two-dimensional case of a body in plane strain under the drilling-rotation transformation group. Results are presented for displacement and body-force derivatives of orders up to 4, and for stress, strain, pressure and volumetric strain derivatives of order up to 3. The material assembled here is self-contained because this catalog is believed to be useful beyond FIC applications; for example gradient-based, nonlocal constitutive models of multiscale mechanics and physics that involve finite characteristic dimensions analogous to FIC steplengths.
Abstract
This is part of an article series on a variational framework for continuum mechanics based on the Finite Increment Calculus (FIC). The formulation utilizes high order derivatives [...]
- 17
- read
A finite point method for compressible flow
R. Löhner, C. Sacco, E. Oñate, S. Idelsohn

Int. J. Numer. Meth. Engng. (2002). Vol. 53 (8), pp. 1765-1779

Abstract
A weighted least squares finite point method for compressible flow is formulated. Starting from a global cloud of points, local clouds are constructed using a Delaunay technique with a series of tests for the quality of the resulting approximations. The approximation factors for the gradient and the Laplacian of the resulting local clouds are used to derive an edge‐based solver that works with approximate Riemann solvers. The results obtained show accuracy comparable to equivalent mesh‐based finite volume or finite element techniques, making the present finite point method competitive.
Abstract
A weighted least squares finite point method for compressible flow is formulated. Starting from a global cloud of points, local clouds are constructed using a Delaunay technique [...]
- 16
- read
A finite point method for incompressible flow problems
E. Oñate, C. Sacco, S. Idelsohn

Computing and Visualization in Science (2000). Vol. 3 (1), pp. 67-75

Abstract
A stabilized finite point method (FPM) for the meshless analysis of incompressible fluid flow problems is presented. The stabilization approach is based in the finite increment calculus (FIC) procedure developed by Oñate [14]. An enhanced fractional step procedure allowing the semi-implicit numerical solution of incompressible fluids using the FPM is described. Examples of application of the stabilized FPM to the solution of two incompressible flow problems are presented.
Abstract
A stabilized finite point method (FPM) for the meshless analysis of incompressible fluid flow problems is presented. The stabilization approach is based in the finite increment [...]
- 16
- read
Numerical Simulation of the 3D Laminar Viscous Flow on a Horizontal-axis Wind Turbine Blade
R. Prado, M. Storti, S. Idelsohn

Int. J. Computational Fluid Dynamics (2002). Vol. 16 (4), pp. 283-295

Abstract
The aim of this paper is to describe the methodology followed in order to determine the viscous effects of a uniform wind on the blades of small horizontal-axis wind turbines that rotate at a constant angular speed. The numerical calculation of the development of the three-dimensional boundary layer on the surface of the blades is carried out under laminar conditions and considering flow rotation, airfoil curvature and blade twist effects. The adopted geometry for the twisted blades is given by cambered thin blade sections conformed by circular are airfoils with constant chords. The blade is working under stationary conditions at a given tip speed ratio, so that an extensive laminar boundary layer without flow separation is expected. The boundary layer growth is determined on a non-orthogonal curvilinear coordinate system related to the geometry of the blade surface. Since the thickness of the boundary layer grows from the leading edge of the blade and also from the tip to the blade root, a domain transformation is proposed in order to solve the discretized equations in a regular computational 3D domain. The non-linear system of partial differential coupled equations that governs the boundary layer development is numerically solved applying a finite difference technique using the Krause zig-zag scheme. The resulting coupled equations of motion are linearized, leading to a tridiagonal system of equations that is iteratively solved for the velocity components inside the viscous layer applying the Thomas algorithm, procedure that allows the subsequent numerical determination of the shear stress distribution on the blade surface.
Abstract
The aim of this paper is to describe the methodology followed in order to determine the viscous effects of a uniform wind on the blades of small horizontal-axis wind turbines [...]
- 16
- read
A meshless finite point method for three‐dimensional analysis of compressible flow problems involving moving boundaries and adaptivity
R. Ortega, E. Oñate, S. Idelsohn, R. Flores

Int. J. Numer. Meth. Fluids (2013). Vol. 73 (4), pp. 323-343

Abstract
A finite point method for solving compressible flow problems involving moving boundaries and adaptivity is presented. The numerical methodology is based on an upwind‐biased discretization of the Euler equations, written in arbitrary Lagrangian–Eulerian form and integrated in time by means of a dual‐time steeping technique. In order to exploit the meshless potential of the method, a domain deformation approach based on the spring network analogy is implemented, and h‐adaptivity is also employed in the computations. Typical movable boundary problems in transonic flow regime are solved to assess the performance of the proposed technique. In addition, an application to a fluid–structure interaction problem involving static aeroelasticity illustrates the capability of the method to deal with practical engineering analyses. The computational cost and multi‐core performance of the proposed technique is also discussed through the examples provided.
Abstract
A finite point method for solving compressible flow problems involving moving boundaries and adaptivity is presented. The numerical methodology is based on an upwind‐biased [...]
- 16
- read
Possibilities of the particle finite element method for fluid–soil–structure interaction problems
E. Oñate, M. Celigueta, S. Idelsohn, F. Salazar, B. Suarez

Computational Mechanics (2011). Vol. 48 (3), pp. 307-318

Abstract
We present some developments in the particle finite element method (PFEM) for analysis of complex coupled problems in mechanics involving fluid–soil–structure interaction (FSSI). The PFEM uses an updated Lagrangian description to model the motion of nodes (particles) in both the fluid and the solid domains (the later including soil/rock and structures). A mesh connects the particles (nodes) defining the discretized domain where the governing equations for each of the constituent materials are solved as in the standard FEM. The stabilization for dealing with an incompressibility continuum is introduced via the finite calculus method. An incremental iterative scheme for the solution of the non linear transient coupled FSSI problem is described. The procedure to model frictional contact conditions and material erosion at fluid–solid and solid–solid interfaces is described. We present several examples of application of the PFEM to solve FSSI problems such as the motion of rocks by water streams, the erosion of a river bed adjacent to a bridge foundation, the stability of breakwaters and constructions sea waves and the study of landslides.
Abstract
We present some developments in the particle finite element method (PFEM) for analysis of complex coupled problems in mechanics involving fluid–soil–structure [...]
- 15
- read
Boundary conditions for finite element simulations of convective flows with artificial boundaries
J. Heinrich, S. Idelsohn, E. Oñate, C. Vionnet

Int. J. Numer. Meth. Engng. (1996). Vol. 39 (6), pp. 1053-1071

Abstract
We examine the use of natural boundary conditions and conditions of the Sommerfeld type for finite element simulations of convective transport in viscous incompressible flows. We show that natural boundary conditions are superior in the sense that they always provide a correct boundary condition, as opposed to the Sommerfeld‐type conditions, which can lead to a singular formulation and a great loss of accuracy. For the Navier–Stokes equations, the natural boundary conditions must be combined with a simple method to eliminate perturbations on the pressure at the open boundary, which is the source of most errors.
Abstract
We examine the use of natural boundary conditions and conditions of the Sommerfeld type for finite element simulations of convective transport in viscous incompressible flows. [...]
- 14
- read
The meshless finite element method
S. Idelsohn, E. Oñate, N. Calvo, F. Del Pin

Int. J. Numer. Meth. Engng. (2003). Vol. 58 (6), pp. 893-912

Abstract
A meshless method is presented which has the advantages of the good meshless methods concerning the ease of introduction of node connectivity in a bounded time of order n, and the condition that the shape functions depend only on the node positions. Furthermore, the method proposed also shares several of the advantages of the finite element method such as: (a) the simplicity of the shape functions in a large part of the domain; (b) C0 continuity between elements, which allows the treatment of material discontinuities, and (c) ease of introduction of the boundary conditions.
Abstract
A meshless method is presented which has the advantages of the good meshless methods concerning the ease of introduction of node connectivity in a bounded time of order n, [...]
- 14
- read
A reduced-order model based on the coupled 1D-3D finite element simulations for an efficient analysis of hemodynamics problems
E. Soudah, R. Rossi, S. Idelsohn, E. Oñate

Computational Mechanics (2014). Vol. 54 (4), pp. 1013-1022

Abstract
A reduced-order model for an efficient analysis of cardiovascular hemodynamics problems using multiscale approach is presented in this work. Starting from a patient-specific computational mesh obtained by medical imaging techniques, an analysis methodology based on a two-step automatic procedure is proposed. First a coupled 1D-3D Finite Element Simulation is performed and the results are used to adjust a reduced-order model of the 3D patient-specific area of interest. Then, this reduced-order model is coupled with the 1D model. In this way, three-dimensional effects are accounted for in the 1D model in a cost effective manner, allowing fast computation under different scenarios. The methodology proposed is validated using a patient-specific aortic coarctation model under rest and non-rest conditions.
Abstract
A reduced-order model for an efficient analysis of cardiovascular hemodynamics problems using multiscale approach is presented in this work. Starting from a patient-specific [...]
- 14
- read
A multiresolution strategy for solving landslides using the Particle Finite Element Method
P. Becker, S. Idelsohn

Acta Geotechnica (2016). Vol. 11 (3), pp. 643-657

Abstract
We present an approach for the simulation of landslides using the Particle Finite Element Method of the second generation. In this work, the multiphase nature (granular phase and water) of the phenomenon is considered in a staggered fashion using a single, indeformable Finite Element mesh. A fractional step and a monolithic strategy are used for the water flow and granular phase, respectively. In this way, the maximum accuracy with minimal computational times is reached. The method is completed by adding the interaction terms due to drag and pressure forces, together with a moving mesh strategy to reduce the size of the computational domain.
Abstract
We present an approach for the simulation of landslides using the Particle Finite Element Method of the second generation. In this work, the multiphase nature (granular phase [...]
- 14
- read
A portable OpenCL-based unstructured edge-based finite element Navier–Stokes solver on graphics hardware
R. Rossi, F. Mossaiby, S. Idelsohn

Computers & Fluids (2013). Vol. 81, pp. 134-144

Abstract
The rise of GPUs in modern high-performance systems increases the interest in porting portion of codes to such hardware. The current paper aims to explore the performance of a portable state-of-the-art FE solver on GPU accelerators. Performance evaluation is done by comparing with an existing highly-optimized OpenMP version of the solver. Code portability is ensured by writing the program using the OpenCL 1.1 specifications, while performance portability is sought through an optimization step performed at the beginning of the calculations to find out the optimal parameter set for the solver. The results show that the new implementation can be several times faster than the OpenMP version.
Abstract
The rise of GPUs in modern high-performance systems increases the interest in porting portion of codes to such hardware. The current paper aims to explore the performance [...]
- 14
- read
An assessment of the potential of PFEM-2 for solving long real-time industrial applications
J. Gimenez, D. Ramajo, S. Damián, N. Nigro, S. Idelsohn

Comp. Part. Mech. (2016). Vol. 4 (3), pp. 251-267

Abstract
The latest generation of the particle finite element method (PFEM-2) is a numerical method based on the Lagrangian formulation of the equations, which presents advantages in terms of robustness and efficiency over classical Eulerian methodologies when certain kind of flows are simulated, especially those where convection plays an important role. These situations are often encountered in real engineering problems, where very complex geometries and operating conditions require very large and long computations. The advantages that the parallelism introduced in the computational fluid dynamics making affordable computations with very fine spatial discretizations are well known. However, it is not possible to have the time parallelized, despite the effort that is being dedicated to use space–time formulations. In this sense, PFEM-2 adds a valuable feature in that its strong stability with little loss of accuracy provides an interesting way of satisfying the real-life computation needs. After having already demonstrated in previous publications its ability to achieve academic-based solutions with a good compromise between accuracy and efficiency, in this work, the method is revisited and employed to solve several nonacademic problems of technological interest, which fall into that category. Simulations concerning oil–water separation, waste-water treatment, metallurgical foundries, and safety assessment are presented. These cases are selected due to their particular requirements of long simulation times and or intensive interface treatment. Thus, large time-steps may be employed with PFEM-2 without compromising the accuracy and robustness of the simulation, as occurs with Eulerian alternatives, showing the potentiality of the methodology for solving not only academic tests but also real engineering problems.
Abstract
The latest generation of the particle finite element method (PFEM-2) is a numerical method based on the Lagrangian formulation of the equations, which presents advantages [...]
- 13
- read
A compressible Lagrangian framework for modeling the fluid-structure interaction in the underwater implosion of an aluminum cylinder
K. Kamran, R. Rossi, E. Oñate, S. Idelsohn

Mathematical Models and Methods in Applied Sciences (2013). Vol. 23 (2), pp. 339–367

Abstract
We propose a fully Lagrangian monolithic system for the simulation of the underwater implosion of cylindrical aluminum containers. A variationally stabilized form of the Lagrangian shock hydrodynamics is exploited to deal with the ultrahigh compression shock waves that travel in both air and water domains. The aluminum cylinder, which separates the internal atmospheric-pressure air from the external high-pressure water, is modeled by a three-node rotation-free shell element. The cylinder undergoes fast transient deformations, large enough to produce self-contact along it. A novel elastic frictionless contact model is used to detect contact and compute the non-penetrating forces in the discretized domain between the mid-planes of the shell. Mesh quality in the vicinity of the cylinder is guaranteed by regenerating the mesh in the air and water domains when large displacements occur. A monolithic fluid–structure interaction (FSI) system is then solved. Two schemes are tested, implicit using the predictor/multi-corrector Bossak scheme, and explicit, using the forward Euler scheme. The results of the two simulations are compared with experimental data.
Abstract
We propose a fully Lagrangian monolithic system for the simulation of the underwater implosion of cylindrical aluminum containers. A variationally stabilized form of the Lagrangian [...]
- 13
- read
A mesh-free finite point method for advective-diffusive transport and fluid flow problems
E. Oñate, S. Idelsohn

Computational Mechanics (1998). Vol. 21 (4-5), pp. 283-292

Abstract
The finite point method (FPM) is a gridless numerical procedure based on the combination of weighted least square interpolations on a cloud of points with point collocation for evaluating the approximation integrals. In the paper, details of a procedure for stabilizing the numerical solution for advective-diffusive transport and fluid flow problems using the FPM are given. The method is based on a consistent introduction of the stabilizing terms in the governing differential equations. One example showing the applicability of the FPM is given.
Abstract
The finite point method (FPM) is a gridless numerical procedure based on the combination of weighted least square interpolations on a cloud of points with point collocation [...]
- 12
- read
Reduced-order subscales for POD models
J. Baiges, R. Codina, S. Idelsohn

Comput. Methods Appl. Mech. Engrg., (2015). Vol. 291; pp. 173-196

Abstract
In this work the Reduced-Order Subscales for Proper Orthogonal Decomposition models are presented. The basic idea consists in splitting the full-order solution into the part which can be captured by the reduced-order model and the part which cannot, the subscales, for which a model is required. The proposed model for the subscales is defined as a linear function of the solution of the reduced-order model. The coefficients of this linear function are obtained by comparing the solution of the full-order model with the solution of the reduced-order model for the same initial conditions, which, for convenience, are evaluated in the snapshots used to train the original reduced-order-model. The difference between both solutions are the subscales, for which a model can be built using a least-squares procedure. The subscales are then introduced as a correction in the reduced-order model, resulting in an important improvement in accuracy. The enhanced reduced-order model is tested in several numerical examples. These practical cases show that the use of the subscales leads to more accurate solutions, successfully corrects errors introduced by hyper-reduction, and allows to solve complex flow problems using a reduced number of degrees of freedom.
Abstract
In this work the Reduced-Order Subscales for Proper Orthogonal Decomposition models are presented. The basic idea consists in splitting the full-order solution into the part [...]
- 12
- read
The extended Delaunay tessellation
N. Calvo, S. Idelsohn, E. Oñate

Engineering Computations (2003). Vol. 20 (5-6), pp. 583-600

Abstract
The extended Delaunay tessellation (EDT) is presented in this paper as the unique partition of a node set into polyhedral regions defined by nodes lying on the nearby Voronoï spheres. Until recently, all the FEM mesh generators were limited to the generation of tetrahedral or hexahedral elements (or triangular and quadrangular in 2D problems). The reason for this limitation was the lack of any acceptable shape function to be used in other kind of geometrical elements. Nowadays, there are several acceptable shape functions for a very large class of polyhedra. These new shape functions, together with the EDT, gives an optimal combination and a powerful tool to solve a large variety of physical problems by numerical methods. The domain partition into polyhedra presented here does not introduce any new node nor change any node position. This makes this process suitable for Lagrangian problems and meshless methods in which only the connectivity information is used and there is no need for any expensive smoothing process.
Abstract
The extended Delaunay tessellation (EDT) is presented in this paper as the unique partition of a node set into polyhedral regions defined by nodes lying on the nearby Voronoï [...]
- 12
- read
Interaction between an elastic structure and free-surface flows: experimental versus numerical comparisons using the PFEM
S. Idelsohn, J. Marti, A. Souto-Iglesias, E. Oñate

Computational Mechanics (2008). Vol. 43 (1), pp. 125-132

Abstract
The paper aims to introduce new fluid–structure interaction (FSI) tests to compare experimental results with numerical ones. The examples have been chosen for a particular case for which experimental results are not much reported. This is the case of FSI including free surface flows. The possibilities of the Particle Finite Element Method (PFEM) for the simulation of free surface flows is also tested. The simulations are run using the same scale as the experiment in order to minimize errors due to scale effects. Different scenarios are simulated by changing the boundary conditions for reproducing flows with the desired characteristics. Details of the input data for all the examples studied are given. The aim is to identifying benchmark problems for FSI including free surface flows for future comparisons between different numerical approaches.
Abstract
The paper aims to introduce new fluid–structure interaction (FSI) tests to compare experimental results with numerical ones. The examples have been chosen for a particular [...]
- 12
- read
Analysis of multifluid flows with large time steps using the particle finite element method
S. Idelsohn, J. Marti, P. Becker, E. Oñate

Int. J. Numer. Meth. Fluids (2014). Vol. 75 (9), pp. 621-644

Abstract
Multifluids are those fluids in which their physical properties (viscosity or density) vary internally and abruptly forming internal interfaces that introduce a large nonlinearity in the Navier–Stokes equations. For this reason, standard numerical methods require very small time steps in order to solve accurately the internal interface position. In a previous paper, the authors developed a particle‐based method (named particle finite element method (PFEM)) based on a Lagrangian formulation and FEM for solving the fluid mechanics equations for multifluids. PFEM was capable of achieving accurate results, but the limitation of small time steps was still present. In this work, a new strategy concerning the time integration for the analysis of multifluids is developed allowing time steps one order of magnitude larger than the previous method. The advantage of using a Lagrangian solution with PFEM is shown in several examples. All kind of heterogeneous fluids (with different densities or viscosities), multiphase flows with internal interfaces, breaking waves, and fluid separation may be easily solved with this methodology without the need of small time steps.
Abstract
Multifluids are those fluids in which their physical properties (viscosity or density) vary internally and abruptly forming internal interfaces that introduce a large nonlinearity [...]
- 12
- read
Global–Local ROM for the solution of parabolic problems with highly concentrated moving sources
A. Cosimo, A. Cardona, S. Idelsohn

Comput. Methods Appl. Mech. Engrg., (2017). Vol. 326, pp. 739-756

Abstract
Problems characterised by steep moving gradients are challenging for any numerical technique and even more for the successful formulation of Reduced Order Models (ROMs). The aim of this work is to study the numerical solution of problems with steep moving gradients, by placing the focus on parabolic problems with highly concentrated moving sources. More specifically, a Global–Local scheme well-suited for reduction methods is formulated. With this Global–Localscheme, the local nature of the steep moving gradients is exploited by modelling the neighbourhood of the heat source with a moving local domain. This domain is coupled to the global domain without requiring any re-mesh and preserving the meshes of both domains during the whole simulation. Then, a ROM based on the Proper Orthogonal Decomposition (POD) technique is developed for the moving local domain. The proposed technique establishes a valid approach for tackling the non-separability of the space and time dimensions of these problems. In order to assess the numerical performance of the proposed numerical techniques, several evaluation tests are performed.
Abstract
Problems characterised by steep moving gradients are challenging for any numerical technique and even more for the successful formulation of Reduced Order Models (ROMs). [...]
- 12
- read
A compressible Lagrangian framework for the simulation of the underwater implosion of large air bubbles
K. Kamran, R. Rossi, E. Oñate, S. Idelsohn

Comput. Methods Appl. Mech. Engrg., (2013). Vol. 255 (1), pp. 210-225

Abstract
A fully Lagrangian compressible numerical framework for the simulation of underwater implosion of a large air bubble is presented. Both air and water are considered compressible and the equations for the Lagrangian shock hydrodynamics are stabilized via a variationally consistent multiscale method. A nodally perfect matched definition of the interface is used and then the kinetic variables, pressure and density, are duplicated at the interface level. An adaptive mesh generation procedure, which respects the interface connectivities, is applied to provide enough refinement at the interface level. This framework is verified by several benchmarks which evaluate the behavior of the numerical scheme for severe compression and expansion cases. This model is then used to simulate the underwater implosion of a large cylindrical bubble, with a size in the order of cm. We observe that the conditions within the bubble are nearly uniform until the converging pressure wave is strong enough to create very large pressures near the center of the bubble. These bubble dynamics occur on very small spatial (0.3 mm), and time (0.1 ms) scales. During the final stage of the collapse Rayleigh–Taylor instabilities appear at the interface and then disappear when the rebounce starts. At the end of the rebounce phase the bubble radius reaches 50% of its initial value and the bubble recover its circular shape. It is when the second collapse starts, with higher mode shape instabilities excited at the bubble interface, that leads to the rupture of the bubble. Several graphs are presented and the pressure pulse detected in the water is compared by experiment.
Abstract
A fully Lagrangian compressible numerical framework for the simulation of underwater implosion of a large air bubble is presented. Both air and water are considered compressible [...]
- 11
- read
Improving the k-compressibility of Hyper Reduced Order Models with moving sources: Applications to welding and phase change problems
A. Cosimo, A. Cardona, S. Idelsohn

Comput. Methods Appl. Mech. Engrg., (2014). Vol. 274, pp. 237-263

Abstract
The simulation of engineering problems is quite often a complex task that can be time consuming. In this context, the use of Hyper Reduced Order Models (HROMs) is a promising alternative for real-time simulations. In this work, we study the design of HROMs for non-linear problems with a moving source. Applications to nonlinear phase change problems with temperature dependent thermophysical properties are particularly considered; however, the techniques developed can be applied in other fields as well. A basic assumption in the design of HROMs is that the quantities that will be hyper-reduced are k-compressible in a certain basis in the sense that these quantities have at most k non-zero significant entries when expressed in terms of that basis. To reach the computational speed required for a real-time application, k must be small. This work examines different strategies for addressing hyper-reduction of the nonlinear terms with the objective of obtaining k-compressible signals with a notably small k. To improve performance and robustness, it is proposed that the different contributing terms to the residual are separately hyper-reduced. Additionally, the use of moving reference frames is proposed to simulate and hyper-reduce cases that contain moving heat sources. Two application examples are presented: the solidification of a cube in which no heat source is present and the welding of a tube in which the problem posed by a moving heat source is analysed.
Abstract
The simulation of engineering problems is quite often a complex task that can be time consuming. In this context, the use of Hyper Reduced Order Models (HROMs) is a promising [...]
- 11
- read
Explicit reduced‐order models for the stabilized finite element approximation of the incompressible Navier–Stokes equations
J. Baiges, R. Codina, S. Idelsohn

Int. J. Numer. Meth. Fluids (2013). Vol. 72 (12), pp. 1219-1243

Abstract
In this paper, we present an explicit formulation for reduced‐order models of the stabilized finite element approximation of the incompressible Navier–Stokes equations. The basic idea is to build a reduced‐order model based on a proper orthogonal decomposition and a Galerkin projection and treat all the terms in an explicit way in the time integration scheme, including the pressure. This is possible because the reduced model snapshots do already fulfill the continuity equation. The pressure field is automatically recovered from the reduced‐order basis and solution coefficients. The main advantage of this explicit treatment of the incompressible Navier–Stokes equations is that it allows for the easy use of hyper‐reduced order models, because only the right‐hand side vector needs to be recovered by means of a gappy data reconstruction procedure. A method for choosing the optimal set of sampling points at the discrete level in the gappy procedure is also presented. Numerical examples show the performance of the proposed strategy
Abstract
In this paper, we present an explicit formulation for reduced‐order models of the stabilized finite element approximation of the incompressible Navier–Stokes equations. [...]
- 11
- read
A second-order in time and space particle-based method to solve flow problems on arbitrary meshes
J. Gimenez, H. Aguerre, S. Idelsohn, N. Nigro

Journal of Computational Physics (2018). Vol. 380, pp. 295-310

Abstract
This work presents a novel proposal of a second-order accurate (in time and space) particle-based method for solving transport equations including incompressible flows problems within a mixed Lagrangian–Eulerian formulation. This methodology consists of a symmetrical operator splitting, the use of high-order operators to transfer data between the particles and the background mesh, and an improved version of the eXplicit Integration Following the Streamlines (X–IVS) method. In the case of incompressible flows, a large time-step iterative solver is employed where the momentum equation is split to improve the numerical approximation of the convective term. New interpolation and projection operators are evaluated and quadratically accurate solutions of scalar transport tests are presented. Then, incompressible flow problems are solved where the rate of convergence of the method is assessed using both structured and unstructured background grids. The method is implemented in the open source platform OpenFOAM®allowing employing arbitrary meshes and obtaining reliable computing time comparisons with standardized solvers. The results obtained reveal that the current method is able to obtain a lower level of error than a fast Eulerian alternative, without increasing the total computing time.
Abstract
This work presents a novel proposal of a second-order accurate (in time and space) particle-based method for solving transport equations including incompressible [...]
- 11
- read
Multifluid flows with weak and strong discontinuous interfaces using an elemental enriched space
S. Idelsohn, J. Gimenez, N. Nigro

Int. J. Numer. Meth. Fluids (2018). Vol. 86 (12), pp. 750–769

Abstract
In a previous paper, the authors presented an elemental enriched space to be used in a finite‐element framework (EFEM) capable of reproducing kinks and jumps in an unknown function using a fixed mesh in which the jumps and kinks do not coincide with the interelement boundaries. In this previous publication, only scalar transport problems were solved (thermal problems). In the present work, these ideas are generalized to vectorial unknowns, in particular, the incompressible Navier‐Stokes equations for multifluid flows presenting internal moving interfaces. The advantage of the EFEM compared with global enrichment is the significant reduction in computing time when the internal interface is moving. In the EFEM, the matrix to be solved at each time step has not only the same amount of degrees of freedom (DOFs) but also the same connectivity between the DOFs. This frozen matrix graph enormously improves the efficiency of the solver. Another characteristic of the elemental enriched space presented here is that it allows a linear variation of the jump, thus improving the convergence rate, compared with other enriched spaces that have a constant variation of the jump. Furthermore, the implementation in any existing finite‐element code is extremely easy with the version presented here because the new shape functions are based on the usual finite‐element method shape functions for triangles or tetrahedrals, and once the internal DOFs are statically condensed, the resulting elements have exactly the same number of unknowns as the nonenriched finite elements.
Abstract
In a previous paper, the authors presented an elemental enriched space to be used in a finite‐element framework (EFEM) capable of reproducing kinks and jumps in an unknown [...]
- 11
- read
A semi-analytical model for droplet dynamics on the GDL surface of a PEFC electrode
A. Jarauta, M. Secanell, J. Pons Prats, P. Ryzhakov, S. Idelsohn, E. Oñate

Int. J. Hydrogen Energy (2015). Vol. 40 (15), pp. 5375-5383 (Preprint)

Abstract
Water management is one of the key factors in Proton Exchange Fuel Cell (PEFC) performance. The water produced within the fuel cell is evacuated through the gas channels, but at high current densities water can block the channel, thus limiting the current density generated in the fuel cell. A semi-analytical model of a water droplet emerging from a gas diffusion layer pore in a PEFC channel is developed. The transient model contains a detailed adhesion and drag force estimation model. Results show that the predicted values for both drag and surface tension force are higher than the results found in literature. The results for the detachment force are consistent with the experimental data available. Higher air velocity values lead to more deformation of the droplet and oscillation with lower frequency but higher amplitude. Similar effects have been identified when the liquid mass flow is increased, leading to faster detachment of the droplet.
Abstract
Water management is one of the key factors in Proton Exchange Fuel Cell (PEFC) performance. The water produced within the fuel cell is evacuated through the gas channels, [...]
- 11
- read
Petrov-Galerkin methods for the transient advective-diffusive equation with sharp gradients
S. Idelsohn, J. Heinrich, E. Oñate

Int. J. Numer. Meth. Engng. (1996). Vol. 39 (9), pp. 1455-1473

Abstract
A Petrov–Galerkin formulation based on two different perturbations to the weighting functions is presented. These perturbations stabilize the oscillations that are normally exhibited by the numerical solution of the transient advective–diffusive equation in the vicinity of sharp gradients produced by transient loads and boundary layers. The formulation may be written as a generalization of the Galerkin Least‐Square method.
Abstract
A Petrov–Galerkin formulation based on two different perturbations to the weighting functions is presented. These perturbations stabilize the oscillations that are normally [...]
- 10
- read
A monolithic Lagrangian approach for fluid–structure interaction problems
P. Ryzhakov, R. Rossi, S. Idelsohn, E. Oñate

Computational Mechanics (2010). Vol. 46 (6), pp. 883-899

Abstract
Current work presents a monolithic method for the solution of fluid–structure interaction problems involving flexible structures and free-surface flows. The technique presented is based upon the utilization of a Lagrangian description for both the fluid and the structure. A linear displacement–pressure interpolation pair is used for the fluid whereas the structure utilizes a standard displacement-based formulation. A slight fluid compressibility is assumed that allows to relate the mechanical pressure to the local volume variation. The method described features a global pressure condensation which in turn enables the definition of a purely displacement-based linear system of equations. A matrix-free technique is used for the solution of such linear system, leading to an efficient implementation. The result is a robust method which allows dealing with FSI problems involving arbitrary variations in the shape of the fluid domain. The method is completely free of spurious added-mass effects.
Abstract
Current work presents a monolithic method for the solution of fluid–structure interaction problems involving flexible structures and free-surface flows. The technique [...]
- 10
- read
Fractional step like schemes for free surface problems with thermal coupling using the Lagrangian PFEM
R. Aubry, E. Oñate, S. Idelsohn

Computational Mechanics (2006). Vol. 38 (4-5), pp. 294-309

Abstract
The method presented in Aubry et al. (Comput Struc 83:1459–1475, 2005) for the solution of an incompressible viscous fluid flow with heat transfer using a fully Lagrangian description of motion is extended to three dimensions (3D) with particular emphasis on mass conservation. A modified fractional step (FS) based on the pressure Schur complement (Turek 1999), and related to the class of algebraic splittings Quarteroni et al. (Comput Methods Appl Mech Eng 188:505–526, 2000), is used and a new advantage of the splittings of the equations compared with the classical FS is highlighted for free surface problems. The temperature is semi-coupled with the displacement, which is the main variable in a Lagrangian description. Comparisons for various mesh Reynolds numbers are performed with the classical FS, an algebraic splitting and a monolithic solution, in order to illustrate the behaviour of the Uzawa operator and the mass conservation. As the classical fractional step is equivalent to one iteration of the Uzawa algorithm performed with a standard Laplacian as a preconditioner, it will behave well only in a Reynold mesh number domain where the preconditioner is efficient. Numerical results are provided to assess the superiority of the modified algebraic splitting to the classical FS.
Abstract
The method presented in Aubry et al. (Comput Struc 83:1459–1475, 2005) for the solution of an incompressible viscous fluid flow with heat transfer using a fully Lagrangian [...]
- 10
- read
Numerical simulations of negatively buoyant jets in an immiscible fluid using the Particle Finite Element Method
M. Mier-Torrecilla, A. Geyer, J. Phillips, S. Idelsohn, E. Oñate

Int. J. Numer. Meth. Fluids (2012). Vol. 69 (5), pp. 1016-1030

Abstract
Negatively buoyant jets consist in a dense fluid injected vertically upward into a lighter ambient fluid. The numerical simulation of this kind of buoyancy‐driven flows is challenging as it involves multiple fluids with different physical properties. In the case of immiscible fluids, it requires, in addition, to track the motion of the interface between fluids and accurately represent the discontinuities of the flow variables. In this paper, we investigate numerically the injection of a negatively buoyant jet into a homogenous immiscible ambient fluid using the Particle Finite Element Method and compare the two‐dimensional numerical results with experiments on the injection of a jet of dyed water through a nozzle in the base of a cylindrical tank containing rapeseed oil. In both simulations and experiments, the fountain inlet flow velocity and nozzle diameter have been varied to cover a wide range of Froude Fr and Reynolds Re numbers ( 0.1 < Fr < 30, 8 < Re < 1350), reproducing both weak and strong laminar fountains. The flow behaviors observed for the different numerical simulations fit in the regime map based on the Re and Fr values of the experiments, and the maximum fountain height is in good agreement with the experimental observations, suggesting that particle finite element method is a useful tool for the study of immiscible two‐fluid systems.
Abstract
Negatively buoyant jets consist in a dense fluid injected vertically upward into a lighter ambient fluid. The numerical simulation of this kind of buoyancy‐driven flows [...]
- 10
- read
A FFT preconditioning technique for the solution of incompressible flow on GPUs
M. Storti, R. Paz, L. Dalcin, S. Costarelli, S. Idelsohn

Computers and Fluids (2013). Vol. 74, pp. 44-57

Abstract
Graphic processing units have received much attention in last years. Compute-intensive algorithms operating on multidimensional arrays that have nearest neighbor dependency and/or exploit data locality can achieve massive speedups. Simulation of problems modeled by time-dependent Partial Differential Equations by using explicit time-stepping methods on structured grids is an instance of such GPU-friendly algorithms. Solvers for transient incompressible fluid flow cannot be developed in a fully explicit manner due to the incompressibility constraint. Segregated algorithms like the fractional step method require the solution of a Poisson problem for the pressure field at each time level. This stage is usually the most time-consuming one. This work discuss a solver for the pressure problem in applications using immersed boundary techniques in order to account for moving solid bodies. This solver is based on standard Conjugate Gradients iterations and depends on the availability of a fast Poisson solver on the whole domain to define a preconditioner. We provide a theoretical and numerical evidence on the advantages of our approach versus classical techniques based on fixed point iterations such as the Iterated Orthogonal Projection method.
Abstract
Graphic processing units have received much attention in last years. Compute-intensive algorithms operating on multidimensional arrays that have nearest neighbor dependency [...]
- 10
- read
Reduced order models for thermally coupled low Mach flows
R. Reyes, R. Codina, J. Baiges, S. Idelsohn

Adv. Model. and Simul. in Eng. Sci. (2018). Vol. 5, art. 28

Abstract
In this paper we present a collection of techniques used to formulate a projection-based reduced order model (ROM) for zero Mach limit thermally coupled Navier–Stokes equations. The formulation derives from a standard proper orthogonal decomposition (POD) model reduction, and includes modifications to improve the drawbacks caused by the inherent non-linearity of the used Navier–Stokes equations: a hyper-ROM technique based on mesh coarsening; an implicit ROM subscales formulation based on a variational multi-scale (VMS) framework; and a Petrov–Galerkin projection necessary in the case of non-symmetric terms. At the end of the article, we test the proposed ROM formulation using 2D and 3D versions of the same example: a differentially heated cavity.
Abstract
In this paper we present a collection of techniques used to formulate a projection-based reduced order model (ROM) for zero Mach limit thermally coupled Navier–Stokes [...]
- 10
- read
A fast and accurate method to solve the incompressible Navier‐Stokes equations
S. Idelsohn, N. Nigro, J. Gimenez, R. Rossi, J. Marti

Engineering Computations (2013). Vol. 30 (2), pp. 197-222

Abstract
Purpose – The purpose of this paper is to highlight the possibilities of a novel Lagrangian formulation in dealing with the solution of the incompressible Navier‐Stokes equations with very large time steps. Design/methodology/approach – The design of the paper is based on introducing the origin of this novel numerical method, originally inspired on the Particle Finite Element Method (PFEM), summarizing the previously published theory in its moving mesh version. Afterwards its extension to fixed mesh version is introduced, showing some details about the implementation. Findings – The authors have found that even though this method was originally designed to deal with heterogeneous or free‐surface flows, it can be competitive with Eulerian alternatives, even in their range of optimal application in terms of accuracy, with an interesting robustness allowing to use large time steps in a stable way. Originality/value – With this objective in mind, the authors have chosen a number of benchmark examples and have proved that the proposed algorithm provides results which compare favourably, both in terms of solution time and accuracy achieved, with alternative approaches, implemented in in‐house and commercial codes.
Abstract
Purpose – The purpose of this paper is to highlight the possibilities of a novel Lagrangian formulation in dealing with the solution [...]
- 10
- read
Algebraic Discrete Nonlocal (DNL) Absorbing Boundary Condition for the Ship Wave Resistance Problem
M. Storti, J. D'ELIA, S. Idelsohn

Journal of Computational Physics (1998). Vol. 146 (2), pp 570-602

Abstract
An absorbing boundary condition for the ship wave resistance problem is presented. In contrast to the Dawson-like methods, it avoids the use of numerical viscosities in the discretization, so that a centered scheme can be used for the free surface operator. The absorbing boundary condition is “completely absorbing,” in the sense that the solution is independent of the position of the downstream boundary and is derived from straightforward analysis of the resulting constant-coefficients difference equations, assuming that the mesh is 1D-structured (in the longitudinal direction) and requires the eigen-decomposition of a matrix one dimension lower than the system matrix. The use of a centered scheme for the free surface operator allows a full finite element discretization. The drag is computed by a momentum flux balance. This method is more accurate and guarantees positive resistances.
Abstract
An absorbing boundary condition for the ship wave resistance problem is presented. In contrast to the Dawson-like methods, it avoids the use of numerical viscosities in the [...]
- 10
- read
Multi-fluid flows with the particle finite element method
S. Idelsohn, M. Mier-Torrecilla, E. Oñate

Comput. Methods Appl. Mech. Engrg., (2009). vol. 198, pp. 2750–2767

Abstract
Particle methods are those in which the problem is represented by a discrete number of particles. Each particle moves accordingly with its own mass and the external/internal forces applied on it. In this paper the Particle Finite Element Method based on finite element shape functions is used to solve the continuous fluid mechanics equations in the case of heterogeneous density. To evaluate the external applied forces to each particle, the incompressible Navier–Stokes equations are solved at each time step using a Lagrangian formulation. All the information in the fluid is transmitted via the particles. All kinds of density heterogeneous fluids and multiphase flows with internal interfaces including or not free-surfaces, breaking waves and fluid separations may be easily solved with this methodology.
Abstract
Particle methods are those in which the problem is represented by a discrete number of particles. Each particle moves accordingly with its own mass and the external/internal [...]
- 9
- read
An adaptive finite point method for the shallow water equations
E. Ortega, E. Oñate, S. Idelsohn, C. Buachart

Int. J. Numer. Meth. Engng. (2011). Vol. 88 (2), pp. 180-204

Abstract
An adaptive Finite Point Method (FPM) for solving shallow water problems is presented. The numerical methodology we propose, which is based on weighted‐least squares approximations on clouds of points, adopts an upwind‐biased discretization for dealing with the convective terms in the governing equations. The viscous and source terms are discretized in a pointwise manner and the semi‐discrete equations are integrated explicitly in time by means of a multi‐stage scheme. Moreover, with the aim of exploiting meshless capabilities, an adaptive h‐refinement technique is coupled to the described flow solver. The success of this approach in solving typical shallow water flows is illustrated by means of several numerical examples and special emphasis is placed on the adaptive technique performance. This has been assessed by carrying out a numerical simulation of the 26th December 2004 Indian Ocean tsunami with highly encouraging results. Overall, the adaptive FPM is presented as an accurate enough, cost‐effective tool for solving practical shallow water problems. Copyright © 2011 John Wiley & Sons, Ltd.
Abstract
An adaptive Finite Point Method (FPM) for solving shallow water problems is presented. The numerical methodology we propose, which is based on weighted‐least squares approximations [...]
- 9
- read
Fluid–structure interaction problems with strong added‐mass effect
S. Idelsohn, F. Del Pin, R. Rossi, E. Oñate

Int. J. Numer. Meth. Engng. (2009). Vol. 80, (10), pp. 1261-1294

Abstract
In this paper, the so‐called added‐mass effect is investigated from a different point of view of previous publications. The monolithic fluid–structure problem is partitioned using a static condensation of the velocity terms. Following this procedure the classical stabilized projection method for incompressible fluid flows is introduced. The procedure allows obtaining a new pressure segregated scheme for fluid–structure interaction problems, which has good convergent characteristics even for biomechanical application, where the added‐mass effect is strong. The procedure reveals its power when it is shown that the same projection technique must be implemented in staggered FSI methods. Copyright © 2009 John Wiley & Sons, Ltd.
Abstract
In this paper, the so‐called added‐mass effect is investigated from a different point of view of previous publications. The monolithic fluid–structure problem is [...]
- 9
- read
Finite element solution of free‐surface ship‐wave problems
S. Idelsohn, E. Oñate, C. Sacco

Int. J. Numer. Meth. Engng. (1999). Vol. 45 (5), pp. 503-528

Abstract
An unstructured finite element solver to evaluate the ship‐wave problem is presented. The scheme uses a non‐structured finite element algorithm for the Euler or Navier–Stokes flow as for the free‐surface boundary problem. The incompressible flow equations are solved via a fractional step method whereas the non‐linear free‐surface equation is solved via a reference surface which allows fixed and moving meshes. A new non‐structured stabilized approximation is used to eliminate spurious numerical oscillations of the free surface.
Abstract
An unstructured finite element solver to evaluate the ship‐wave problem is presented. The scheme uses a non‐structured finite element algorithm for the Euler or Navier–Stokes [...]
- 9
- read
The ALE/Lagrangian Particle Finite Element Method: A new approach to computation of free-surface flows and fluid–object interactions
F. Del Pin, S. Idelsohn, E. Oñate, R. Aubry

Computers and Fluids (2007). Vol. 36 (1), pp. 27-38

Abstract
The Particle Finite Element Method (PFEM) is a well established numerical method [Aubry R, Idelsohn SR, Oñate E, Particle finite element method in fluid mechanics including thermal convection–diffusion, Comput Struct 2004;83:1459–75; Idelsohn S, Oñate E, Del Pin F, A Lagrangian meshless finite element method applied to fluid–structure interaction problems, Comput Struct 2003;81:655–71; Idelsohn SR, Oñate E, Del Pin F, The particle finite element method a powerful tool to solve incompressible flows with free-surfaces and breaking waves, Int J Num Methods Eng 2004;61:964–84] where critical parts of the continuum are discretized into particles. The nodes treated as particles transport their momentum and physical properties in a Lagrangian way while the rest of the nodes may move in an Arbitrary Lagrangian–Eulerian (ALE) frame. In order to solve the governing equations that represent the continuum, the particles are connected by means of a Delaunay Triangulation [Idelsohn SR, Oñate E, Calvo N, Del Pin F, The meshless finite element method, Int J Num Methods Eng 2003;58(4)]. The resulting partition is a mesh where the Finite Element Method is applied to solve the equations of motion. The application of a fully Lagrangian formulation on the particles provides a natural and simple way to track free surfaces as well as to compute contacts in an accurate and robust fashion. Furthermore, the usage of an ALE formulation allows large mesh deformation with larger time steps than the full Lagrangian scheme.
Abstract
The Particle Finite Element Method (PFEM) is a well established numerical method [Aubry R, Idelsohn SR, Oñate E, Particle finite element method in fluid mechanics [...]
- 9
- read
An embedded strategy for the analysis of fluid structure interaction problems
S. Costarelli, L. Garelli, M. Cruchaga, M. Storti, R. Ausensi, S. Idelsohn

Comput. Methods Appl. Mech. Engrg., (2016). Vol. 300, pp. 106-128

Abstract
A Navier–Stokes solver based on Cartesian structured finite volume discretization with embedded bodies is presented. Fluid structure interaction with solid bodies is performed with an explicit partitioned strategy. The Navier–Stokes equations are solved in the whole domain via a Semi-Implicit Method for Pressure Linked Equations (SIMPLE) using a colocated finite volume scheme, stabilized via the Rhie–Chow discretization. As uniform Cartesian grids are used, the solid interface usually do not coincide with the mesh, and then a second order Immersed Boundary Method is proposed, in order to avoid the loss of precision due to the staircase representation of the surface. This fact also affects the computation of fluid forceson the solid wall and, accordingly, the results in the fluid–structure analysis. In the present work, first and second order approximations for computing the fluid forces at the interface are studied and compared. The solver is specially oriented to General Purpose Graphic Processing Units (GPGPU) hardware and the efficiency is discussed. Moreover, a novel submerged buoy experiment is also reported. The experiment consists of a sphere with positive buoyancy fully submerged in a cubic tank, subject to harmonic displacements imposed by a shake table. The sphere is attached to the bottom of the tank with a string. The position of the buoy is determined from video records with a Motion Capture algorithm. The obtained amplitude and phase curves allow a precise determination of the added mass and drag forces. Due to this aspect the experimental data can be of interest for comparison with other fluid–structure interaction codes. Finally, the numerical results are compared with the experiments, and allow the confirmation of the numerically predicted drag and added mass of the body.
Abstract
A Navier–Stokes solver based on Cartesian structured finite volume discretization with embedded bodies is presented. Fluid structure interaction with [...]
- 9
- read
A new enrichment space for the treatment of discontinuous pressures in multi‐fluid flows
R. Ausas, G. Buscaglia, S. Idelsohn

Int. J. Numer. Meth. Fluids (2011). Vol. 70 (7), pp. 829-850

Abstract
In this work, a new enrichment space to accommodate jumps in the pressure field at immersed interfaces in finite element formulations, is proposed. The new enrichment adds two degrees of freedom per element that can be eliminated by means of static condensation. The new space is tested and compared with the classical P1 space and to the space proposed by Ausas et al (Comp. Meth. Appl. Mech. Eng., Vol. 199, 1019–1031, 2010) in several problems involving jumps in the viscosity and/or the presence of singular forces at interfaces not conforming with the element edges. The combination of this enrichment space with another enrichment that accommodates discontinuities in the pressure gradient has also been explored, exhibiting excellent results in problems involving jumps in the density or the volume forces.
Abstract
In this work, a new enrichment space to accommodate jumps in the pressure field at immersed interfaces in finite element formulations, is proposed. The new enrichment adds [...]
- 9
- read
Parallel adaptive mesh refinement for incompressible flow problems
R. Rossi, J. Cotela, N. Lafontaine, P. Dadvand, S. Idelsohn

Computers and Fluids (2013). Vol. 80, pp. 342-355

Abstract
The present article describes a simple element-driven strategy for the conforming refinement of simplicial finite element meshes in a distributed environment. The proposed algorithm is effective both for local adaptive refinement and for the division of all the elements within an existing mesh. We aim to provide sufficient detail to allow the practical implementation of the algorithm, which can be coded with minimal effort provided that a distributed linear algebra library is available. The proposed refinement strategy is composed of three basic components: a global splitting strategy, an elemental splitting procedure and an error estimation technique, which are combined so to guarantee obtaining a conformant refined mesh. A number of benchmark examples show the capabilities of the proposed method. Error is estimated for the incompressible fluid-flow benchmarks using a novel indicator based on the computation of the sub-scale velocity.
Abstract
The present article describes a simple element-driven strategy for the conforming refinement of simplicial finite element meshes in a distributed environment. The proposed [...]
- 9
- read
Modeling bed erosion in free surface flows by the particle finite element method
E. Oñate, M. Celigueta, S. Idelsohn

Acta Geotechnica (2006). Vol. 1 (4), pp. 237-252

Abstract
We present a general formulation for modeling bed erosion in free surface flows using the particle finite element method (PFEM). The key feature of the PFEM is the use of an updated Lagrangian description to model the motion of nodes (particles) in domains containing fluid and solid subdomains. Nodes are viewed as material points (called particles) which can freely move and even separate from the fluid and solid subdomains representing, for instance, the effect of water drops or soil/rock particles. A mesh connects the nodes defining the discretized domain in the fluid and solid regions where the governing equations, expressed in an integral form, are solved as in the standard FEM. The necessary stabilization for dealing with the incompressibility of the fluid is introduced via the finite calculus (FIC) method. An incremental iterative scheme for the solution of the nonlinear transient coupled fluid-structure problem is described. The erosion mechanism is modeled by releasing the material adjacent to the bed surface according to the frictional work generated by the fluid shear stresses. The released bed material is subsequently transported by the fluid flow. Examples of application of the PFEM to solve a number of bed erosion problems involving large motions of the free surface and splashing of waves are presented.
Abstract
We present a general formulation for modeling bed erosion in free surface flows using the particle finite element method (PFEM). The key feature of the PFEM is the use of [...]
- 9
- read
A domain decomposition strategy for reduced order models. Application to the incompressible Navier–Stokes equations
J. Baiges, R. Codina, S. Idelsohn

Comput. Methods Appl. Mech. Engrg., (2013). Vol. 267, pp. 23-42

Abstract
In this work, a domain decomposition strategy for non-linear hyper-reduced-order models is presented. The basic idea consists of restricting the reduced-order basis functions to the nodes belonging to each of the subdomains into which the physical domain is partitioned. An extension of the proposed domain decomposition strategy to a hybrid full-order/reduced-order model is then described. The general domain decomposition approach is particularized for the reduced-order finite element approximation of the incompressible Navier–Stokes equations with hyper-reduction. When solving the reduced incompressible Navier–Stokes equations, instabilities in the form of large gradients of the recovered reduced-order unknown at the subdomain interfaces may appear, which is the motivation for the design of additional stability terms giving rise to penalty matrices. Numerical examples illustrate the behavior of the proposed method for the simulation of the reduced-order systems, showing the capability of the approach to adapt to configurations which are not present in the original snapshot set.
Abstract
In this work, a domain decomposition strategy for non-linear hyper-reduced-order models is presented. The basic idea consists of restricting the reduced-order basis functions [...]
- 9
- read
OpenCL‐based implementation of an unstructured edge‐based finite element convection‐diffusion solver on graphics hardware
F. Mossaiby, R. Rossi, P. Dadvand, S. Idelsohn

Int. J. Numer. Meth. Engng. (2012). Vol. 89 (13), pp. 1635-1651

Abstract
The solution of problems in computational fluid dynamics (CFD) represents a classical field for the application of advanced numerical methods. Many different approaches were developed over the years to address CFD applications. Good examples are finite volumes, finite differences (FD), and finite elements (FE) but also newer approaches such as the lattice‐Boltzmann (LB), smooth particle hydrodynamics or the particle finite element method. FD and LB methods on regular grids are known to be superior in terms of raw computing speed, but using such regular discretization represents an important limitation in dealing with complex geometries. Here, we concentrate on unstructured approaches which are less common in the GPU world. We employ a nonstandard FE approach which leverages an optimized edge‐based data structure allowing a highly parallel implementation. Such technique is applied to the ‘convection‐diffusion’ problem, which is often considered as a first step towards CFD because of similarities to the nonconservative form of the Navier–Stokes equations. In this regard, an existing highly optimized parallel OpenMP solver is ported to graphics hardware based on the OpenCL platform. The optimizations performed are discussed in detail. A number of benchmarks prove that the GPU‐accelerated OpenCL code consistently outperforms the OpenMP version.
Abstract
The solution of problems in computational fluid dynamics (CFD) represents a classical field for the application of advanced numerical methods. Many different approaches were [...]
- 9
- read
Foreword: special issue on particles finite element method in multi-physics problems
S. Idelsohn

Comp. Part. Mech (2017). Vol. 4 (3), pp. 249-249

Abstract
Particle-based methods in which each material particle is followed in a Lagrangian manner have been used successfully in the last years for different applications. One of the latest evolution of particle-based methods is the Particle Finite Element Method (PFEM). The PFEM combines the particle precept with the FEM shape functions using an auxiliary FE mesh. This mesh may be quickly rebuilt at each time step (PFEM with moving mesh) or may be a fixed mesh (PFEM with fixed mesh). In the last case, the results from the Lagrangian particles are projected at each time iteration on a fixed mesh. The idea of combining FMs with moving particles was originally used in the so-called Particle in Cell method and later in an extension called the Material Point Method (MPM), which uses an FE background mesh. Despite that both PFEM and MPM employ a fixed FE mesh and a set of Lagrangian particles, there are important differences in the way the particles are employed; in the MPM, all computations are performed on the mesh, while in the PFEM, the aim is to calculate as much as possible on the particles, leaving small corrections to be performed on the mesh. Furthermore, the most important difference is that in PFEM, the particles do not represent a fixed amount of mass but rather material points that transport only intrinsic properties. This allows using a variable number of particles and therefore simplifying refinement. The PFEM has been successfully used to solve the Navier–Stokes equations and fluid–structure interaction problems as well as solid mechanics problems. The advantages of the PFEM concerning the tracking of internal interfaces have also been explored and used to solve multi-fluid flows. The possibility to use PFEM to solve nonlinear problems with large time-steps in order to obtain an accurate and fast solution was also successfully presented for the solution of the homogeneous incompressible Navier–Stokes equations. This new strategy was named PFEM second generation (PFEM-2). The enhanced PFEM-2 version to solve multi-phase problems, preserves the large time-step goodnesses of the single-phase strategy, also includes enrichment strategies to capture discontinuities in the pressure gradient, i.e., pressure kinks. This special issue is a collection of nine technical papers presenting the state-of-the-art in modeling and simulations of solid and fluid mechanics problems at different scales involving the Particle Finite Element Method as well in his original version (PFEM) as in his new upgrade (PFEM-2).
Abstract
Particle-based methods in which each material particle is followed in a Lagrangian manner have been used successfully in the last years for different applications. One [...]
- 9
- read
Consistent pressure Laplacian stabilization for incompressible continua via higher‐order finite calculus
E. Oñate, S. Idelsohn, C. Felippa

Int. J. Numer. Meth. Engng. (2011). Vol. 87 (1-5), pp. 171-195

Abstract
We present a stabilized numerical formulation for incompressible continua based on a higher‐order Finite Calculus (FIC) approach and the finite element method. The focus of the paper is on the derivation of a stabilized form for the mass balance (incompressibility) equation. The simpler form of the momentum equations neglecting the non‐linear convective terms, which is typical for incompressible solids, Stokes flows and Lagrangian flows is used for the sake of clarity. The discretized stabilized mass balance equation adds to the standard divergence of velocity term a pressure Laplacian and an additional boundary term. The boundary term is relevant for the accuracy of the numerical solution, especially for free surface flow problems. The Laplacian and boundary stabilization terms are multiplied by non‐linear parameters that have an extremely simple expression in terms of element sizes, the pressure and the discrete residuals of the incompressibility equation and the momentum equations, thus ensuring the consistency of the method. The stabilized formulation allows solving the incompressible problem iteratively using an equal‐order interpolation for the velocities (or displacements) and the pressure, which are the only unknowns. The use of additional pressure gradient projection variables, typical of many stabilized methods, is unnecessary. The formulation is particularly useful for heterogeneous incompressible materials with discontinuous material properties, as it allows computing all the stabilization matrices at the element level. Details of the finite element formulation are given. The good behaviour of the new pressure Laplacian stabilization (PLS) technique is shown in simple but demonstrative examples of application. A very accurate solution was obtained in all cases in 2–3 iterations. Copyright © 2010 John Wiley & Sons, Ltd.
Abstract
We present a stabilized numerical formulation for incompressible continua based on a higher‐order Finite Calculus (FIC) approach and the finite element method. The focus [...]
- 8
- read
Improving mass conservation in simulation of incompressible flows
P. Ryzhakov, E. Oñate, R. Rossi, S. Idelsohn

Int. J. Numer. Meth. Engng. (2012). Vol. 90 (12), pp. 1435-1451

Abstract
We propose a technique for improving mass‐conservation features of fractional step schemes applied to incompressible flows. The method is illustrated by using a Lagrangian fluid formulation, where the mass loss effects are particularly apparent. However, the methodology is general and could be used for fixed grid approaches. The idea consists in reflecting the incompressibility condition already in the intermediate velocity. This is achieved by predicting the end‐of‐step pressure and using this prediction in the fractional momentum equation. The resulting intermediate velocity field is thus much closer to the final incompressible one than that of the standard fractional step scheme. In turn, the predicted pressure can be used as the boundary condition necessary for the solution of the pressure Poisson equation in case a continuous Laplacian matrix is employed. Using this approximation of the end‐of‐step incompressible pressure as the essential boundary condition considerably improves the conservation of mass, specially for the free surface flows of fluids with low viscosity. The pressure prediction does not require the resolution of any additional equations system. The efficiency of the method is shown in two examples. The first one shows the performance of the method with respect to mass conservation. The second one tests the method in a challenging fluid–structure interaction benchmark, which can be naturally resolved by using the presented approach.
Abstract
We propose a technique for improving mass‐conservation features of fractional step schemes applied to incompressible flows. The method is illustrated by using a Lagrangian [...]
- 8
- read
On the analysis of heterogeneous fluids with jumps in the viscosity using a discontinuous pressure field
S. Idelsohn, M. Mier-Torrecilla, N. Nigro, E. Oñate

Computational Mechanics (2010). Vol. 46 (1), pp. 115-124

Abstract
Heterogeneous incompressible fluid flows with jumps in the viscous properties are solved with the particle finite element method using continuous and discontinuous pressure fields. We show the importance of using discontinuous pressure fields to avoid errors in the incompressibility condition near the interface.
Abstract
Heterogeneous incompressible fluid flows with jumps in the viscous properties are solved with the particle finite element method using continuous and discontinuous pressure [...]
- 8
- read
Evaluating the performance of the particle finite element method in parallel architectures
J. Gimenez, N. Nigro, S. Idelsohn

Comp. Part. Mech. (2014). Vol. 1 (1), pp. 103-116

Abstract
This paper presents a high performance implementation for the particle-mesh based method called particle finite element method two (PFEM-2). It consists of a material derivative based formulation of the equations with a hybrid spatial discretization which uses an Eulerian mesh and Lagrangian particles. The main aim of PFEM-2 is to solve transport equations as fast as possible keeping some level of accuracy. The method was found to be competitive with classical Eulerian alternatives for these targets, even in their range of optimal application. To evaluate the goodness of the method with large simulations, it is imperative to use of parallel environments. Parallel strategies for Finite Element Method have been widely studied and many libraries can be used to solve Eulerian stages of PFEM-2. However, Lagrangian stages, such as streamline integration, must be developed considering the parallel strategy selected. The main drawback of PFEM-2 is the large amount of memory needed, which limits its application to large problems with only one computer. Therefore, a distributed-memory implementation is urgently needed. Unlike a shared-memory approach, using domain decomposition the memory is automatically isolated, thus avoiding race conditions; however new issues appear due to data distribution over the processes. Thus, a domain decomposition strategy for both particle and mesh is adopted, which minimizes the communication between processes. Finally, performance analysis running over multicore and multinode architectures are presented. The Courant–Friedrichs–Lewy number used influences the efficiency of the parallelization and, in some cases, a weighted partitioning can be used to improve the speed-up. However the total cputime for cases presented is lower than that obtained when using classical Eulerian strategies.
Abstract
This paper presents a high performance implementation for the particle-mesh based method called particle finite element method two (PFEM-2). It consists of a material derivative [...]
- 8
- read
Application of the finite point method to high‐Reynolds number compressible flow problems
R. Ortega, E. Oñate, S. Idelsohn, R. Flores

Int. J. Numer. Meth. Fluids (2014). Vol. 74 (10), pp. 732-748

Abstract
In this work, the finite point method is applied to the solution of high‐Reynolds compressible viscous flows. The aim is to explore this important field of applications focusing on two main aspects: the easiness and automation of the meshless discretization of viscous layers and the construction of a robust numerical approximation in the highly stretched clouds of points resulting in such domain areas. The flow solution scheme adopts an upwind‐biased scheme to solve the averaged Navier–Stokes equations in conjunction with an algebraic turbulence model. The numerical applications presented involve different attached boundary layer flows and are intended to show the performance of the numerical technique. The results obtained are satisfactory and indicative of the possibilities to extend the present meshless technique to more complex flow problems.
Abstract
In this work, the finite point method is applied to the solution of high‐Reynolds compressible viscous flows. The aim is to explore this important field of applications [...]
- 8
- read
Validation of the particle finite element method (PFEM) for simulation of free surface flows
A. LARESE, R. Rossi, E. Oñate, S. Idelsohn

Engineering Computations (2008). Vol. 25 (3-4), pp. 385-425

Abstract
Purpose – The purpose of this paper is to evaluate the possibilities of the particle finite element method for simulation of free surface flows. Design/methodology/approach – A numerical simulation of a number of examples for which experimental data are available is performed. The simulations are run using the same scale as the experiment in order to minimize errors due to scale effects. Some examples are chosen from the civil engineering field: a study of the flow over a flip bucket is analyzed for both 2D and 3D models, and the flow under a planar sluice gate is studied in 2D. Other examples, such as a 2D and 3D “dam break” with an obstacle are taken from the smooth particle hydrodynamics literature. Findings – Different scenarios are simulated by changing the boundary conditions for reproducing flows with the desired characteristics. Different mesh sizes are considered for evaluating their influence on the final solution. Originality/value – Details of the input data for all the examples studied are given. The aim is to identify benchmark problems for future comparisons between different numerical approaches for free surface flows.
Abstract
Purpose – The purpose of this paper is to evaluate the possibilities of the particle finite element method for simulation of free surface flows. Design/methodology/approach [...]
- 7
- read
Comparative accuracy and performance assessment of the finite point method in compressible flow problems
E. Ortega, E. Oñate, S. Idelsohn, R. Flores

Computers and Fluids (2014). Vol. 89, pp. 53-65

Abstract
A comparative assessment of the Finite Point Method (FPM) is presented. Using a wing-fuselage configuration under transonic inviscid flow conditions as reference test case, the performance of the FPM flow solver is compared with an equivalent edge-based Finite Element (FEM) implementation. Efficiency issues have discouraged practical application of meshless methods in the past. Thus, a simplification of the basic FPM technique is proposed in order to reduce the performance gap with respect to classical grid-based algorithms. A comparative evaluation of the accuracy, computational cost and parallel performance of the meshless implementation is carried out with the objective to assess the level of maturity of the technique and identify improvements still required to tackle practical applications. The results obtained show accuracy and performance of the core algorithm comparable to a conventional FEM implementation, thus removing a major obstacle for further developments of the FPM.
Abstract
A comparative assessment of the Finite Point Method (FPM) is presented. Using a wing-fuselage configuration under transonic inviscid flow conditions as reference test case, [...]
- 7
- read
General treatment of essential boundary conditions in reduced order models for non-linear problems
A. Cosimo, A. Cardona, S. Idelsohn

Adv. Model. and Simul. in Eng. Sci. (2016). Vol. 3, art 7

Abstract
Inhomogeneous essential boundary conditions must be carefully treated in the formulation of Reduced Order Models (ROMs) for non-linear problems. In order to investigate this issue, two methods are analysed: one in which the boundary conditions are imposed in an strong way, and a second one in which a weak imposition of boundary conditions is made. The ideas presented in this work apply to the big realm of a posteriori ROMs. Nevertheless, an a posteriori hyper-reduction method is specifically considered in order to deal with the cost associated to the non-linearity of the problems. Applications to nonlinear transient heat conduction problems with temperature dependent thermophysical properties and time dependent essential boundary conditions are studied. However, the strategies introduced in this work are of general application.
Abstract
Inhomogeneous essential boundary conditions must be carefully treated in the formulation of Reduced Order Models (ROMs) for non-linear problems. In order to investigate this [...]
- 7
- read
An unstructured grid-based, parallel free surface solver
R. Löhner, C. Yang, E. Oñate, S. Idelsohn

Applied Numerical Mathematics (1999). Vol. 31 (3), pp. 271-293

Abstract
An unstructured grid-based, parallel-free surface solver is presented. The overall scheme combines a finite-element, equal-order, projection-type 3-D incompressible flow solver with a finite element, 2-D advection equation solver for the free surface equation. For steady-state applications, the mesh is not moved every timestep, in order to reduce the cost of geometry recalculations and surface repositioning. A number of modifications required for efficient processing on shared-memory, cache-based parallel machines are discussed, and timings are shown that indicate scalability to a modest number of processors. The results show good quantitative comparison with experiments and the results of other techniques. The present combination of unstructured grids (enhanced geometrical flexibility) and good parallel performance (rapid turnaround) should make the present approach attractive to hydrodynamic design simulations.
Abstract
An unstructured grid-based, parallel-free surface solver is presented. The overall scheme combines a finite-element, equal-order, projection-type 3-D incompressible flow solver [...]
- 7
- read
On the issue that Finite Element discretizations violate, nodally, Clausius’s postulate of the second law of thermodynamics
A. Limache, S. Idelsohn

Adv. Model. and Simul. in Eng. Sci. (2016). Vol. 3, art 13

Abstract
Discretization processes leading to numerical schemes sometimes produce undesirable effects. One potentially serious problem is that a discretization may produce the loss of validity of some of the physical principles or mathematical properties originally present in the continuous equation. Such loss may lead to uncertain results such as numerical instabilities or unexpected non-physical solutions. As a consequence, the compatibility of a discrete formulation with respect to intrinsic physical principles might be essential for the success of a numerical scheme. This paper addresses such type of issue. Its main objective is to demonstrate that standard Finite Element discretizations of the heat conduction equation violate Clausius’s postulate of the second law of thermodynamics, at nodal level. The problem occurs because non-physical, reversed nodal heat-fluxes arise in such discretizations. Conditions for compatibility of discrete nodal heat-fluxes with respect to Clausius’s postulate are derived here and named discrete thermodynamic compatibility conditions (DTCC). Simple numerical examples are presented to show the undesirable consequences of such failure. It must be pointed out that such DTCCs have previously appeared in the context of the study of the conditions that make discrete solutions to satisfy the discrete maximum principle (DMP). However, the present article does not put attention on such mathematical principle but on the satisfaction of a fundamental physical one: the second law of thermodynamics. Of course, from the presented point of view, it is clear that the violation of such fundamental law will cause, among different problems, the violation of the DMP.
Abstract
Discretization processes leading to numerical schemes sometimes produce undesirable effects. One potentially serious problem is that a discretization may produce the loss [...]
- 7
- read
Analysis of the melting, burning and flame spread of polymers with the Particle Finite Element Method
E. Oñate, J. Marti, P. Ryzhakov, R. Rossi, S. Idelsohn

(2013). Research Report, Nº PI395

Abstract
A computational procedure for analysis of the melting, burning and flame spread of polymers under fire conditions is presented. The method, termed Particle Finite Element Method (PFEM), combines concepts from particle-based techniques with those of the standard finite element method (FEM). The key feature of the PFEM is the use of an updated Lagrangian description to model the motion of nodes (particles) in the thermoplastic material. Nodes are viewed as material points which can freely move and even separate from the main analysis domain representing, for instance, the effect of melting and dripping of polymer particles. A mesh connects the nodes defining the discretized domain where the governing equations are solved using the FEM. An incremental iterative scheme for the solution of the nonlinear transient coupled thermal-flow problem, including radiation, loss of mass by gasification and combustion is used. Examples of the possibilities of the PFEM for the modelling and simulation of the melting, burning and flame spread of polymers under different fire conditions are described.
Abstract
A computational procedure for analysis of the melting, burning and flame spread of polymers under fire conditions is presented. The method, termed Particle Finite Element [...]
- 6
- 5/5
- read
Combined Eulerian–PFEM approach for analysis of polymers in fire situations
J. Marti, P. Ryzhakov, S. Idelsohn, E. Oñate

Int. J. Numer. Meth. Engng. (2012). Vol. 92 (9), pp. 782-801

Abstract
In this paper, we present a computational algorithm for solving an important practical problem, namely, the thermoplastic polymer melting under fire conditions. We propose here a technique that aims at minimizing the computational cost. This is basically achieved by using the immersed boundary‐like approach, combining the particle finite element method for the polymer with an Eulerian formulation for the ambience. The polymer and ambience domains interact over the interface boundary. The boundary is explicitly defined by the position of the Lagrangian domain (polymer) within the background Eulerian mesh (ambience). This allows to solve the energy equation for both subdomains on the Eulerian mesh with different thermal properties. Radiative transport equation is exclusively considered for the ambience, and the heat exchange at the interface is modeled by calculating the radiant heat flux and imposing it as a natural boundary condition.
Abstract
In this paper, we present a computational algorithm for solving an important practical problem, namely, the thermoplastic polymer melting under fire conditions. We propose [...]
- 6
- read
An improved finite point method for tridimensional potential flows
E. Ortega, E. Oñate, S. Idelsohn

Computational Mechanics (2007). Vol. 40 (6), pp. 949-963

Abstract
At the local level, successful meshless techniques such as the Finite Point Method must have two main characteristics: a suitable geometrical support and a robust numerical approximation built on the former. In this article we develop the second condition and present an alternative procedure to obtain shape functions and their derivatives from a given cloud of points regardless of its geometrical features. This procedure, based on a QR factorization and an iterative adjust of local approximation parameters, allows obtaining a satisfactory minimization problem solution, even in the most difficult cases where usual approaches fail. It is known that high-order meshless constructions need to include a large number of points in the local support zone and this fact turns the approximation more dependent on the size, shape and spatial distribution of the local cloud of points. The proposed procedure also facilitates the construction of high-order approximations on generic geometries reducing their dependence on the geometrical support where they are based. Apart from the alternative solution to the minimization problem, the behaviour of high-order Finite Point approximations and the overall performance of the proposed methodology are shown by means of several numerical tests.
Abstract
At the local level, successful meshless techniques such as the Finite Point Method must have two main characteristics: a suitable geometrical support and a robust numerical [...]
- 6
- read
Smoothed surface gradients for panel methods
J. D'Elía, M. Storti, S. Idelsohn

Advances in Engineering Software (2000). Vol. 31 (5), pp. 339-346

Abstract
A weak form to compute the dipolar and monopolar surface gradients, related to a low-order panel method, is shown. The flow problem is formulated by means of a three-dimensional potential model and the discretization is based on Morino's formulation for the perturbation velocity potential. On the body surface, this representation reduces to a boundary integral equation with the source (or monopolar) and the doublet (or dipolar) densities. The first of the two is found by application of the boundary flow condition, and the second one is the unknown over the body surface. A lower panel method is used for the analytic integrations of both the monopolar and dipolar influence coefficients. The surface velocity field is computed after solving the linear system, with a strong and a weak form of the Stokes theorem, which is oriented to fairly non-structured panel meshes. The proposed method is validated by comparing the numerical results with analytical ones for an isolated sphere and includes a prediction over a car-like configuration.
Abstract
A weak form to compute the dipolar and monopolar surface gradients, related to a low-order panel method, is shown. The flow problem is formulated by means of a three-dimensional [...]
- 6
- read
An improved enrichment method for weak discontinuities for thermal problems
J. Marti, E. Ortega, S. Idelsohn

Int. J. of Num. Meths. for Heat and Fluid Flow (2017). Vol. 27 (8), pp.1748-1764

Abstract
Purpose The purpose of this paper is to propose a new elemental enrichment technique to improve the accuracy of the simulations of thermal problems containing weak discontinuities. Design/methodology/approach The enrichment is introduced in the elements cut by the materials interface by means of adding additional shape functions. The weak form of the problem is obtained using Galerkin approach and subsequently integrating the diffusion term by parts. To enforce the continuity of the fluxes in the “cut” elements, a contour integral must be added. These contour integrals named here the “inter-elemental heat fluxes” are usually neglected in the existing enrichment approaches. The proposed approach takes these fluxes into account. Findings It has been shown that the inter-elemental heat fluxes cannot be generally neglected and must be included. The corresponding method can be easily implemented in any existing finite element method (FEM) code, as the new degrees of freedom corresponding to the enrichment are local to the elements. This allows for their static condensation, thus not affecting the size and structure of the global system of governing equations. The resulting elements have exactly the same number of unknowns as the non-enriched finite element (FE). Originality/value It is the first work where the necessity of including inter-elemental heat fluxes has been demonstrated. Moreover, numerical tests solved have proven the importance of these findings. It has been shown that the proposed enrichment leads to an improved accuracy in comparison with the former approaches where inter-elemental heat fluxes were neglected.
Abstract
Purpose The purpose of this paper is to propose a new elemental enrichment technique to improve the accuracy of the simulations of thermal problems [...]
- 6
- read
Modèle d'ordre hyper-réduit (HROM) global-local pour des problèmes thermiques non linéaires avec changements d'état irréversibles
A. Cosimo, A. Cardona, S. Idelsohn

C. R. Mecanique (2018). Vol. 346 (7), pp. 539-555

Abstract
Highly concentrated moving nonlinearities are extremely difficult to solve numerically. The Selective Laser Melting Additive Manufacturing process is a problem of this kind. A material global-local scheme is proposed, which consists in describing the neighbourhood of the heat source by a moving local domain while the material phase fractions are represented in a global domain. The equations of the non-linear thermal problem are defined on the local domain only, assuming that the local domain is large enough to capture the most important variations of the temperature field. Additionally, a Hyper-Reduced-Order Model (HROM) is proposed for the local domain problem. The performance is studied by solving a SLM problem taken from the literature.
Abstract
Highly concentrated moving nonlinearities are extremely difficult to solve numerically. The Selective Laser Melting Additive Manufacturing process [...]
- 6
- read
A closed form for low-order panel methods
J. D'Elía, M. Storti, S. Idelsohn

Advances in Engineering Software (2000). Vol. 31 (5), pp. 347-353

Abstract
A closed form for the computation of the dipolar and monopolar influence coefficients related to a low-order panel method is shown. The flow problem is formulated by means of a three-dimensional potential model; the method of discretization is based on the Morino formulation for the perturbation velocity potential. On the body surface this representation reduces to an integral equation with the source (or monopolar) and the doublet (or dipolar) densities. The former is found by application of the boundary condition, and the latter is the unknown over the surface of the body. The lower panel method is used for the analytical integrations of the monopolar and dipolar influence coefficients, with special attention to avoid a logarithmic singularity in the monopolar matrix when flat fairly structured meshes that are common in ship-wave calculations are used.
Abstract
A closed form for the computation of the dipolar and monopolar influence coefficients related to a low-order panel method is shown. The flow problem is formulated by means [...]
- 0
- read
A Lagrangian Panel Method in the Time Domain for Moving Free-surface Potential Flows
J. D'ELIA, M. Storti, E. Oñate, S. Idelsohn

Int. J. Computational Fluid Dynamics (2002). Vol. 16 (4), pp. 263-275

Abstract
A Lagrangian-type panel method in the time domain is proposed for potential flows with a moving free surface. After a spatial semi-discretization with a low-order scheme, the instantaneous velocity-potential and normal displacement on the moving free surface are obtained by means of a time-marching scheme. The kinematic and dynamic boundary conditions at the free surface are non-linear restrictions over the related Ordinary Differential Equation (ODE) system and, in order to handle them, an alternative Steklov-Poincaré operator technique is proposed. The method is applied to sloshing like flow problems.
Abstract
A Lagrangian-type panel method in the time domain is proposed for potential flows with a moving free surface. After a spatial semi-discretization with a low-order scheme, [...]
- 0
- read

editors

Idelsohn, Sergio 162
International Centre for Numerical...

information

How to submit

Open access

Contact