Documents published in 2019 : Scipedia

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 [...]
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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 [...]
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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 [...]
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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 [...]
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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 [...]
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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 [...]
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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 [...]
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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 [...]
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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 [...]
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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 [...]
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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. [...]
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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 [...]
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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 [...]
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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 [...]
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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 [...]
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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 [...]
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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 [...]
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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 [...]
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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 [...]
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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 [...]
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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 [...]
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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 [...]
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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. [...]
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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 [...]
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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 [...]
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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 [...]
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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 [...]
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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 [...]
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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 [...]
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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 [...]
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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. [...]
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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 [...]
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Fractures prediction in concrete structures combining the finite and discrete element methods
F. Zarate, E. Oñate

Hormigón y Acero (2018). (prepint) 69, Supl 1, pp. 53-69

Abstract
This paper presents the basic concepts and application of the strategy that combines finite element methods (FEM) and discrete elements (DEM)for the study of the propagation of fractures in concrete structures. The calculation of the structure, modeled as a continuum, begins with the FEMand the DEM is used to start and grow the cracks that may appear in the structure. This methodology has been proposed by the authors in two andthree dimensions. Recently, the use of one-dimensional steel elements embedded in the continuum has been added to model the reinforcement inconcrete structures. The work presents different examples of application to the study of the breakage of parts and structures of concrete in massand armed, as well as the multiple breakage of a historic structure of masonry due to an earthquake.
Abstract
This paper presents the basic concepts and application of the strategy that combines finite element methods (FEM) and discrete elements (DEM)for the study of the propagation [...]
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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 [...]
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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 [...]
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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 [...]
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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 [...]
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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 [...]
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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 [...]
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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 [...]
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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 [...]
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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 [...]
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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 [...]
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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 [...]
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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 [...]
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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 [...]
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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 [...]
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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 [...]
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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 [...]
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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. [...]
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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 [...]
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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 [...]
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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 [...]
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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 [...]
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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 [...]
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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 [...]
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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, [...]
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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 [...]
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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 [...]
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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 [...]
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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 [...]
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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 [...]
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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 [...]
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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 [...]
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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 [...]
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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 [...]
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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 [...]
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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). [...]
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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 [...]
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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 [...]
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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 [...]
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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 [...]
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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 [...]
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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 [...]
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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 [...]
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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 [...]
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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 [...]
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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 [...]
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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 [...]
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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 [...]
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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 [...]
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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 [...]
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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 [...]
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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 [...]
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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 [...]
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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 [...]
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A formulation for the study, by the method of finite elements, of the deformation of marine pipes during their installation
J. Oliver, E. Oñate

Revista de Obras Públicas (1983). Vol. 130 (3218), pp. 747-763

Abstract
La ejecución de emisarios submarinos para saneamiento y la instalación de tuberías para transporte de productos petrolíferos son ejemplos de la necesidad de conocer los esfuerzos y deformaciones que se producen en el tendido de tuberías submarinas, a cuyo estudio, mediante elementos finitos en diversas condiciones de instalación, se dedica este artículo, que permite la obtención de ábacos de cálculo o formulas sencillas aplicables en los distintos casos.
Abstract
La ejecución de emisarios submarinos para saneamiento y la instalación de tuberías para transporte de productos petrolíferos son ejemplos de la [...]
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Triangular element for two-dimensional elasticity with z stress and z strain constant and different from zero.
F. Zarate, N. Zarate

Revista Mexicana de Métodos Numéricos (2019). Vol. 3, 1

Abstract
This paper describes how to obtain a two-dimensional element of three nodes from a prismatic solid element of six nodes, assuming that the normal voltage to the triangular faces is constant and different from zero. A numerical example is also presented where the results obtained are compared with the developed element and with three-dimensional elements, showing the good behavior of the developed element.
Abstract
This paper describes how to obtain a two-dimensional element of three nodes from a prismatic solid element of six nodes, assuming that the normal voltage to the triangular [...]
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HPC-SHEAKS brief description
C. García

Collection of documents for the dissemination of the experiment "HPC-enabled system for enhanced seakeeping and station-keeping design (HPC-SHEAKS)" (2019). 5

Abstract
Compass IS is a consulting services company specialized in engineering design, as well as in development of software for engineering analysis and information management in technology. Civil and industrialengineering, naval architecture and ICT areas are the main focus of Compass IS activities. The HPC-Sheaks experiment aimed to increase the efficiency of the design, engineering and building processes of a marine structure, by offering to the market added-value tools that, thanks to high performance computing, can be used further down from the final design phase, and allowing its integration in the design cycle to develop more competitive designs.
Abstract
Compass IS is a consulting services company specialized in engineering design, as well as in development of software for engineering analysis and information management in [...]
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Presentation of HPC-SHEAKS in the Digital Innovation Hub Annual Event (Warsaw)
C. García

Collection of documents for the dissemination of the experiment "HPC-enabled system for enhanced seakeeping and station-keeping design (HPC-SHEAKS)" (2019). 6

Abstract
Presentation made during the DIH2018 Annual Event that took place in Warsaw, from November 27 to 28, 2018. During the DIH2018 Annual Event, Compass IS has been honored the I4MS Disruptors Award 2018, by the European Commissioner Mariya Gabriel and Jadwiga Emilewicz, Minister of Entrepreneurship and Technology of Poland. During the event, Compass had the opportunity to show a stand to present its technological capabilities and the solution of the experiment.
Abstract
Presentation made during the DIH2018 Annual Event that took place in Warsaw, from November 27 to 28, 2018. During the DIH2018 Annual Event, Compass IS has been honored the [...]
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HPC-SHEAKS in the Fortissimo Success Story Booklet (4th edition)
C. García

Collection of documents for the dissemination of the experiment "HPC-enabled system for enhanced seakeeping and station-keeping design (HPC-SHEAKS)" (2019). 2

Abstract
Seakeeping is the study of a ship or marine structure that is subject to the action of waves. WAVEC is a private non-profit association active in applied research and consulting. VICUSDT operates in the shipbuilding and shipping industries, providing hydrodynamic engineering services. It also provides hydrodynamic analysis capabilities to the offshore and marine energy sector, carrying out advanced simulations of structures for the oil and gas industry. COMPASSIS is an SME ISV which provides simulation software for a variety of different engineering fields including multiphysics simulations and structural and seakeeping analysis. In this experiment COMPASSIS will enable and evaluate simulations that require intense computational and data storage resources.
Abstract
Seakeeping is the study of a ship or marine structure that is subject to the action of waves. WAVEC is a private non-profit association active in applied research and consulting. [...]
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Presentation of HPC-SHEAKS Experiment in the kick-off meeting
C. García

Collection of documents for the dissemination of the experiment "HPC-enabled system for enhanced seakeeping and station-keeping design (HPC-SHEAKS)" (2019). 1

Abstract
Presentation of the "HPC-SHEAKS" experiment during the kick-off meeting which took place on July 2015, in the frame of the Fortissimo Forum in Amsterdam. The Forum was a platform for Independent Software Vendors (ISVs), Service Providers, Small & Medium Enterprises (SMEs) and technical experts around the theme of HPC applications in the cloud. The HPC-Sheaks experiment aimed to increase the efficiency of the design, engineering and building processes of a marine structure, by offering to the market added-value tools that, thanks to high performance computing, can be used further down from the final design phase, and allowing its integration in the design cycle to develop more competitive designs.
Abstract
Presentation of the "HPC-SHEAKS" experiment during the kick-off meeting which took place on July 2015, in the frame of the Fortissimo Forum in Amsterdam. The Forum [...]
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SeaFEM features and system requirements
Collection of documents for the dissemination of the experiment "HPC-enabled system for enhanced seakeeping and station-keeping design (HPC-SHEAKS)" (2019). 4

Abstract
SeaFEM is a suite of tools for the computational analysis of the effect of waves, wind and currents on naval and offshore structures, as well as for maneuvering studies. SeaFEM applications include ships, spar platforms, FPSO systems, semi- submersibles, TLPs, marine wind turbines and ocean energy harnessing devices. SeaFEM offers a state of the art solver developed for the most realistic seakeeping simulations of 3D multi-body radiation and diffraction problems, by solving potential flow equations in the time domain, using the finite element method on unstructured meshes. SeaFEM features the latest technology for solving first and second order diffraction-radiation equations with real sea spectra. SeaFEM has been developed in collaboration with the International Center for Numerical Methods in Engineering, and is completely integrated in the comprehensive simulation environment, Tdyn, developed by Compass.
Abstract
SeaFEM is a suite of tools for the computational analysis of the effect of waves, wind and currents on naval and offshore structures, as well as for maneuvering studies. SeaFEM [...]
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HPC-SHEAKS Success Story
C. García

Collection of documents for the dissemination of the experiment "HPC-enabled system for enhanced seakeeping and station-keeping design (HPC-SHEAKS)" (2019). 3

Abstract
The ultimate goal of the "HPC-enabled system for enhanced seakeeping and station-keeping design" (HPC-SHEAKS) experiment was the efficient and easy-to-use integration of available HPC infrastructures with the most advanced seakeeping software. As a result of the experiment, an effective interface between the end-user and the HPC resources was implemented. The relevant seakeeping software packages were ported to the HPC infrastructure and integrated into an overall simulation package. This solution enables the simulations to be run from a familiar desktop system whilst using the full capabilities of the HPC system.
Abstract
The ultimate goal of the "HPC-enabled system for enhanced seakeeping and station-keeping design" (HPC-SHEAKS) experiment was the efficient and easy-to-use integration [...]
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Decision support system for cardiovascular problems
E. Soudah, R. López, M. Bordone, E. Oñate

Monograph CIMNE (2008). M108

Abstract
The two main lines of medical research in this project are vascular anatomy (large vessels around the heart, coronaries and peripheral arteries) and heart chambers. Geometric models will be constructed to aid clinical diagnosis or multiphysical modelling and simulation. Two levels of complexity will be considered. For heart modelling, the first level will concentrate on models of the left and right ventricular cavities for robust and efficient extraction of simple clinical indexes of geometry, volume, mass, and wall kinetics. The second level will aim at more complex, fourchambered models, which will be important in developing comprehensive solid and fluid models to assist the design of medical devices.
Abstract
The two main lines of medical research in this project are vascular anatomy (large vessels around the heart, coronaries and peripheral arteries) and heart chambers. Geometric [...]
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A model of material failure for reinforced concrete via continuum strong discontinuity approach and mixing theory
D. Linero, J. Oliver, A. Huespe

Monograph CIMNE (2007). M106

Abstract
In this work a two-dimensional formulation describing the fracture process in reinforced concrete is developed, implemented and validated. The cracks in the material are captured by means of continuum strong discontinuity approach (CSDA) (Oliver 1996) and the constitutive model of composite material is defined through mixing theory (Truesdell & Toupin 1960). The composite material consists of one or two groups of long fibers or steel bars embedded within a concrete matrix. Likewise, each component is characterized by a constitutive model. The concrete is described by a damage model with degradation in tension and compression (Oliver, Cervera et al. 1990). A uniaxial plasticity model (Simó & Hughes 1998) is used for the steel. Also, phenomena as bond-slip and dowel action (Park & Paulay 1975) are included and represented by additional models of interaction between concrete and steel. The initiation and propagation of cracks are understood as a strain localization process described by means of CSDA. A bifurcation analysis of composite material is proposed to establish the bifurcation time and direction of the crack. The model has been implemented in a two-dimensional analysis program using the finite element method (FEM), where it is assumed material non-linearity and infinitesimal strains. An implicit-explicit integration scheme for the constitutive equation (Oliver, Huespe et al. 2004; Oliver, Huespe et al. 2006) ensures a positive defined stiffness matrix of the problem and increases the robustness and stability of the solution. On the other hand, a strategy to tracking discontinuity paths (Samaniego 2002; Oliver & Huespe 2004), allows that the discontinuity paths correspond among the elements. According to the proposed formulation, on each point of solid, the strain and stress fields of the reinforced concrete are described as a composite material. This has the following advantages: first, the model facilitates the implementation on the finite element method, since many ingredients of standard numerical process remain, and secondly, the macroscopic scale of analysis avoids the discretization of each component material and the interaction effects, and consequently the computational cost is reduced. The model can reproduce two different stages of cracking in the reinforced concrete. Initially, the steel capacity and the adherence in the interface produce a stable stage of distributed cracking, where appear many cracks with constant spacing and opening. Afterward, a localization cracking stage is characterized by few cracks while the structural response decreases. Reinforced concrete members subjected to tension, bending and shear are simulated. The numerical results, mainly the structural response and the crack pattern, are compared with experimental test (Leonhardt 1965; Collins, Vecchio et al. 1985; Ouyang & Shah 1994; Ruiz, Elices et al. 1998). The correlation between numerical results using the proposed formulation and actual results is quantitative and qualitatively satisfactory.
Abstract
In this work a two-dimensional formulation describing the fracture process in reinforced concrete is developed, implemented and validated. The cracks in the material are [...]
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Contribuciones a la simulación numérica del fallo material en medios tridimensionales mediante la metodología de discontinuidades fuertes de continuo
S. Blanco, J. Oliver, A. Huespe

Monograph CIMNE (2007). M105

Abstract
Esta monografía presenta una reformulación de la metodología de discontinuidades fuertes de continuo para la simulación numérica del fallo material de estructuras. Los objetivos buscados han sido mejorar la robustez de este tipo de análisis numérico y proporcionar una serie de herramientas que garanticen la confiabilidad de los resultados obtenidos. La metodología de discontinuidades fuertes de continuo [50]-[51] es una aproximación numérica al fenómeno de la localización de deformaciones por ablandamiento. Al contrario de las aproximaciones discretas, utiliza un formato continuo tensión-deformación para describir todo el proceso de agotamiento del material. Gracias a una regularización (reinterpretación) de la cinemática del problema y del módulo de ablandamiento se garantiza que la disipación del modelo venga dada por la densidad superficial de energía de fractura [52]. Adicionalmente, la utilización de un algoritmo tipo térmico de captura y gestión de las superficies de localización de deformaciones permite abordar el análisis de problemas con multifisuración [57]. La mejora en la robustez del análisis numérico se ha conseguido adoptando la formulación simétrica cinemáticamente consistente y formulando un nuevo esquema de integración, denominado IMPL-EX, que garantiza la definición positiva de los operadores algorítmicos que intervienen en el problema. La confiabilidad en el resultado numérico se asegura mediante un algoritmo de control del error cometido y mediante un nuevo esquema de limitación de la longitud de arco. Estos dos algoritmos han sido desarrollados específicamente para el esquema de integración IMPL-EX. La formulación así definida ha sido aplicada en el estudio de dos fenómenos propios de la mecánica de la fractura: el estudio de la influencia del tamaño de una estructura en su resistencia nominal (efecto tamaño) y el estudio/medición de la longitud de procesamiento de fractura. Por último se presentan una serie de ensayos numéricos del fallo material en estructuras tridimensionales. Estos ensayos se dividen en tres grupos: ensayos donde el modo de fallo predominante es en modo I, ensayos donde el modo de fallo predominante es de deslizamiento (análisis de taludes) y ensayos donde el modo de fallo moviliza mecanismos resistentes tridimensionales (análisis del efecto arco en presas con simple y doble curvatura).
Abstract
Esta monografía presenta una reformulación de la metodología de discontinuidades fuertes de continuo para la simulación numérica del fallo [...]
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A finite element method for solving the incompressible Navier-Stokes equations at low and high Reynolds numbers using finite calculus. Application to fluid-structure interaction
H. Lynga, E. Oñate

Monograph CIMNE (2007). M104

Abstract
The main objective of this monograph is to develop a stabilized finite element method (FEM) for solving the incompressible Navier-Stokes equations. Using Finite Calculus (FIC), which is a methodology developed by E. On˜ate and co-workers at CIMNE (International Center for Numerical Methods in Engineering), flows with a wide range of Reynolds numbers can be modeled. The secondary objective is to test the applicability of the FIC/FEM model to fluid-structure interaction (FSI) emphasizing aero-elasticity. The implementation of the model is carried out within KRATOS, a finite element code for solving multi-physics problems developed at CIMNE.
Abstract
The main objective of this monograph is to develop a stabilized finite element method (FEM) for solving the incompressible Navier-Stokes equations. Using Finite Calculus [...]
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Formulaciones tangentes y secantes en análisis no lineal de vigas Cosserat
R. Morán, E. Oñate, J. Miquel

Monograph CIMNE (2007). M103

Abstract
En este trabajo se han dedicado cinco capítulos a la exposición y discretización de un modelo clásico no lineal de viga Cosserat por medio del método de elementos finitos, utilizando las formulaciones Tangente y Secante.
Abstract
En este trabajo se han dedicado cinco capítulos a la exposición y discretización de un modelo clásico no lineal de viga Cosserat por medio del [...]
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Análisis estructural de edificios históricos mediante modelos localizados de fisuración
R. Clemente, M. Cervera, P. Roca

Monograph CIMNE (2007). M102

Abstract
En este trabajo se plantea un objetivo principal: formular un modelo numérico capaz de estudiar el comportamiento estructural de edificios históricos de obra de fábrica. Para ello se estudian en primer lugar las características de este material, así como las particularidades que presentan las construcciones antiguas. Como referencia se toma la Catedral de Mallorca, de la que se dispone de información proveniente de una campaña de monitorización llevada a cabo recientemente, así como de diversos análisis estructurales elaborados por diferentes autores.
Abstract
En este trabajo se plantea un objetivo principal: formular un modelo numérico capaz de estudiar el comportamiento estructural de edificios históricos de obra [...]
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