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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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• General treatment of essential boundary conditions in reduced order models for non-linear problems

  A. Cosimo, A. Cardona, S. Idelsohn

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

  
  

  Abstract

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

  Abstract
  Inhomogeneous essential boundary conditions must be carefully treated in the formulation of Reduced Order Models (ROMs) for non-linear problems. In order to investigate this [...]

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• A semi-analytical model for droplet dynamics on the GDL surface of a PEFC electrode

  A. Jarauta, M. Secanell, J. Pons Prats, P. Ryzhakov, S. Idelsohn, E. Oñate

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

  
  

  Abstract

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

  Abstract
  Water management is one of the key factors in Proton Exchange Fuel Cell (PEFC) performance. The water produced within the fuel cell is evacuated through the gas channels, [...]

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• GPGPU implementation of the BFECC algorithm for pure advection equations

  S. Costarelli, M. Storti, R. Paz, L. Dalcin, S. Idelsohn

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

  
  

  Abstract

  In the present work an implementation of the Back and Forth Error Compensation and Correction (BFECC) algorithm specially suited for running on General-Purpose Graphics Processing Units (GPGPUs) through Nvidia’s Compute Unified Device Architecture (CUDA) is analyzed in order to solve transient pure advection equations. The objective is to compare it to a previous explicit version used in a Navier-Stokes solver fully written in CUDA. It turns out that BFECC could be implemented with unconditional stable stability using Semi-Lagrangian time integration allowing larger time steps than Eulerian ones.

  Abstract
  In the present work an implementation of the Back and Forth Error Compensation and Correction (BFECC) algorithm specially suited for running on General-Purpose Graphics Processing [...]

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• An assessment of the potential of PFEM-2 for solving long real-time industrial applications

  J. Gimenez, D. Ramajo, S. Damián, N. Nigro, S. Idelsohn

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

  
  

  Abstract

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

  Abstract
  The latest generation of the particle finite element method (PFEM-2) is a numerical method based on the Lagrangian formulation of the equations, which presents advantages [...]

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