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• Foreword: special issue on particles finite element method in multi-physics problems

  S. Idelsohn

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

  
  

  Abstract

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

  Abstract
  Particle-based methods in which each material particle is followed in a Lagrangian manner have been used successfully in the last years for different applications. One [...]

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• On load interaction in the non linear buckling analysis of cylindrical shells

  L. Godoy, S. Idelsohn, E. Barbero

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

  
  

  Abstract

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

  Abstract
  The elastic stability of shells or shell-like structures under two independent load parameters is considered. One of the loads is associated to a limit point form of buckling, [...]

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• Upwind parameters for the numerical solution of the compressible flow Euler equations

  S. Idelsohn

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

  
  

  Abstract

  The present work generalises the earlier work in which a variational principle technique was presented in order to evaluate the magnitude of upwind required to solve the compressible flow equations. The technique proposed allows the choice of nodes where upwind is required in each of the relevant equations. It is a simple and mathematically consistent way of evaluating the amount of upwind or artificial viscosity to be introduced at every node and every equation involved.

  Abstract
  The present work generalises the earlier work in which a variational principle technique was presented in order to evaluate the magnitude of upwind required to solve the compressible [...]

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• Numerical implementation of a discontinuous finite element algorithm for phase-change problems

  M. Storti, L. Crivelli, S. Idelsohn

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

  
  

  Abstract

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

  Abstract
  This paper is devoted to the numerical solution of phase-change problems in two dimensions. The technique of finite elements is employed. The discretization is carried out [...]

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• A simple hidden line algorithm for a structural model of planar elements

  E. Laitano, S. Idelsohn

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

  
  

  Abstract

  A simple and efficient hidden line algorithm for finite element models is described here. The algorithm runs quickly, it has low computer storage and core size requirements. The method does not require any calculation of trigonometric functions and is able to treat planar quadrilateral polygons without subdividing them into triangles. Detailed flowcharts are presented for a better understanding.

  Abstract
  A simple and efficient hidden line algorithm for finite element models is described here. The algorithm runs quickly, it has low computer storage and core size requirements. [...]

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• Reduction methods and explicit time integration technique in structural dynamics

  S. Idelsohn, A. Cardona

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

  
  

  Abstract

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

  Abstract
  A computer procedure for economically time-integrating large structural dynamics problems is presented. The main process is described as a two-step discretisation, the first [...]

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• A Finite Element Model for the Simulation of the UL-94 Burning Test

  J. Marti, S. Idelsohn, E. Oñate

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

  
  

  Abstract

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

  Abstract
  The tendency of the polymers to melt and drip when they are exposed to external heat source play a very important role in the ignition and the spread of fire. Numerical simulation [...]

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• Global-local HROM for non-linear thermal problems with irreversible changes of material states

  A. Cosimo, A. Cardona, S. Idelsohn

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

  
  

  Abstract

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

  Abstract
  Highly concentrated moving nonlinearities are extremely difficult to solve numerically. The Selective Laser Melting Additive Manufacturing process [...]

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• Reduced order models for thermally coupled low Mach flows

  R. Reyes, R. Codina, J. Baiges, S. Idelsohn

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

  
  

  Abstract

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

  Abstract
  In this paper we present a collection of techniques used to formulate a projection-based reduced order model (ROM) for zero Mach limit thermally coupled Navier–Stokes [...]

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• On the issue that Finite Element discretizations violate, nodally, Clausius’s postulate of the second law of thermodynamics

  A. Limache, S. Idelsohn

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

  
  

  Abstract

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

  Abstract
  Discretization processes leading to numerical schemes sometimes produce undesirable effects. One potentially serious problem is that a discretization may produce the loss [...]

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