COLLECTIONS

JOURNALS

Documents published in Scipedia

• 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 [...]

  • 18
  •  read

• Iterative solution of panel method discretizations for potential flow problems. The modal multipolar preconditioning

  J. D'ELIA, M. Storti, S. Idelsohn

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

  
  

  Abstract

  The iterative solution of linear systems arising from panel method discretization of three‐dimensional (3D) exterior potential problems coming mainly from aero‐hydrodynamic engineering problems, is discussed. An original preconditioning based on an approximate eigenspace decomposition is proposed, which corrects bad conditioning arising from a pair of surfaces that are very close to each other, which is a very common situation in slender wings and other aerodynamic profiles. This preconditioning has been tested with the standard Bi‐conjugate gradient (Bi‐CG) and conjugate gradient squared (CGS) iterative methods.

  Abstract
  The iterative solution of linear systems arising from panel method discretization of three‐dimensional (3D) exterior potential problems coming mainly from aero‐hydrodynamic [...]

  • 0
  •  read

• Discrete non‐local absorbing boundary condition for exterior problems governed by Helmholtz equation

  R. Bonet Chaple, N. Nigro, M. Storti, S. Idelsohn

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

  
  

  Abstract

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

  Abstract
  The finite element method is employed to approximate the solutions of the Helmholtz equation for water wave radiation and scattering in an unbounded domain. A discrete, non‐local [...]

  • 6
  •  read

• GMRES physics‐based preconditioner for all Reynolds and Mach numbers: numerical examples

  N. Nigro, M. Storti, S. Idelsohn

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

  
  

  Abstract

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

  Abstract
  This paper presents several numerical results using a vectorized version of a 3D finite element compressible and nearly incompressible Euler and Navier–Stokes code. [...]

  • 4
  •  read

• Stability analysis of mixed finite element formulations with special mention of equal‐order interpolations

  S. Idelsohn, M. Storti, N. Nigro

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

  
  

  Abstract

  We present a method to assess the stability of pairs of interpolation spaces for mixed formulations. The method is based on a straightforward calculation of the eigenvalues of the discrete matrices through Fourier decomposition in plane waves and is intended to give, via straightforward numerical computations, a sharper determination of stability than the well‐known ‘patch test’ of Zienkiewicz et al. Special attention is devoted to the study of stability and accuracy of equal‐order interpolations

  Abstract
  We present a method to assess the stability of pairs of interpolation spaces for mixed formulations. The method is based on a straightforward calculation of the eigenvalues [...]

  • 8
  •  read

• Two‐phase flow modelling in gas‐stirred liquid vessels with SUPG‐stabilized equal‐order interpolations

  N. Nigro, M. Storti, S. Idelsohn

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

  
  

  Abstract

  The modelling of liquid flow in gas‐stirred vessels is described. A simple two‐phase model accounts for the buoyancy effect of bubbles. Friction between liquid and gas is modelled with the hypothesis of independent bubbles. The resulting PDE system is discretized with an original version of the SUPG‐FEM technique which stabilizes both the convection term and equal‐order interpolations for velocity and pressure, which are known to be unstable for incompressible flows. The resulting steady state discrete system is solved via pseudotemporal explicit iteration with a local time step and a preconditioning to homogenize the temporal scales for liquid and gas.

  Abstract
  The modelling of liquid flow in gas‐stirred vessels is described. A simple two‐phase model accounts for the buoyancy effect of bubbles. Friction between liquid and gas [...]

  • 8
  •  read

• Adaptive refinement criterion for elliptic problems discretized by FEM

  M. Storti, N. Nigro, S. Idelsohn

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

  
  

  Abstract

  In a recent paper we presented a data structure to be used with multigrid techniques on non‐homogeneously refined FEM meshes. This paper focuses on the adaptive refinement techniques used there. The error estimate is obtained from standard Taylor series. For each element we compute its efficiency in terms of the size, the norm of the second derivatives of the unknown and the parameter p, where Lp is the chosen norm. The way the norm influences the optimal mesh is studied. The number of elements to be refined at each step is such to produce a fast convergence to the optimal mesh, followed by successive homogeneous refinements. We hope that the analysis of these two subjects could be of value for people working with other (perhaps very dissimilar) adaptive refinement techniques (error estimate and data structure, for instance).

  Abstract
  In a recent paper we presented a data structure to be used with multigrid techniques on non‐homogeneously refined FEM meshes. This paper focuses on the adaptive refinement [...]

  • 11
  •  read

• A fast and accurate method to solve the incompressible Navier‐Stokes equations

  S. Idelsohn, N. Nigro, J. Gimenez, R. Rossi, J. Marti

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

  
  

  Abstract

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

  Abstract
  Purpose   – The purpose of this paper is to highlight the possibilities of a novel Lagrangian formulation in dealing with the solution [...]

  • 10
  •  read

• 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 [...]

  • 7
  •  read

• Fracture analysis of a surface-coated ceramic by speckle photography and finite elements

  E. Barbero, G. Kaufmann, S. Idelsohn

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

  
  

  Abstract

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

  Abstract
  The fracture behaviour of a four-point bend surface-coated ceramic specimen with a through-the-thickness crack was experimentally investigated. Speckle photography was used [...]

  • 5
  •  read