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• Analysis of a consistency recovery method for the 1D convection–diffusion equation using linear finite elements

  P. Nadukandi, E. Oñate, J. García-Espinosa

  International Journal for Numerical Methods in Fluids (2008). 57 (9), 1291-1320, 2008

  
  

  Abstract

  For residual-based stabilization methods such as streamline-upwind Petrov–Galerkin (SUPG) and finite calculus (FIC), the higher-order derivatives of the residual that appear in the stabilization term vanish when simplicial elements are used. The sub-grid scale method using orthogonal sub-scales (OSS) attempts to recover the lost consistency by using a fine-scale projected residual in the stabilization term. The FIC method may also be cast into an OSS form with very little manipulation using an auxiliary convective projection equation. This paper discusses the gain/loss by recovering the consistency of the discrete residual in the stabilization terms via the form that includes the convective projection (as in the OSS method). We present the von Neumann analysis of the FIC method with recovered consistency (FIC RC) for the 1D convection–diffusion problem and we compare it with the standard Bubnov–Galerkin linear finite element method and FIC/SUPG methods. The transient analysis is done by examining the discrete dispersion relation of the stabilization methods. The spectral results for the semi-discrete and fully discrete problem are presented with time integration done by the trapezoidal and second-order backward differencing formula schemes. The effect of lumping the effective mass matrix T is considered relative to using a consistent form. The effect of refinement in space and time is also discussed. Finally, an optimal expression for the stabilization parameter for the FIC RC method on a uniform grid and for the steady state is given and its performance in the transient mode is discussed. 

  Abstract
  For residual-based stabilization methods such as streamline-upwind Petrov–Galerkin (SUPG) and finite calculus (FIC), the higher-order derivatives of the residual that [...]

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• Computation of turbulent flows using a finite calculus–finite element formulation

  E. Oñate, A. Valls, J. García-Espinosa

  International journal for numerical methods in fluids (2007). 54 (6‐8), 609-637, 2007

  
  

  Abstract

  We present a formulation for analysis of turbulent incompressible flows using a stabilized finite element method (FEM) based on the finite calculus (FIC) procedure. The stabilization terms introduced by the FIC approach allow to solve a wide range of fluid flow problems at different Reynolds numbers, including turbulent flows, without the need of a turbulence model. Examples of application of the FIC/FEM formulation to the analysis of 2D and 3D incompressible flows at large Reynolds numbers exhibiting turbulence features are presented.

  Abstract
  We present a formulation for analysis of turbulent incompressible flows using a stabilized finite element method (FEM) based on the finite calculus (FIC) procedure. The stabilization [...]

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• Modeling incompressible flows at low and high Reynolds numbers via a finite calculus–finite element approach

  E. Oñate, A. Valls, J. García-Espinosa

  Journal of Computational Physics (2007). 224 (1), 332-351

  
  

  Abstract

  We present a formulation for incompressible flows analysis using the finite element method (FEM). The necessary stabilization for dealing with convective effects and the incompressibility condition is modeled via the finite calculus (FIC) method. The stabilization terms introduced by the FIC formulation allow to solve a wide range of fluid flow problems for low and high Reynolds numbers flows without the need for a turbulence model. Examples of application of the FIC/FEM formulation to the analysis of 2D and 3D incompressible flows with moderate and large Reynolds numbers are presented.

  Abstract
  We present a formulation for incompressible flows analysis using the finite element method (FEM). The necessary stabilization for dealing with convective effects and the [...]

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• An unstructured finite element solver for ship hydrodynamics problems

  J. García-Espinosa, E. Oñate

  Journal of Applied Mechanics (2003). 70(1): 18-26

  
  

  Abstract

  A stabilized semi-implicit fractional step algorithm based on the finite element method for solving ship wave problems using unstructured meshes is presented. The stabilized gov-erning equations for the viscous incompressible fluid and the free surface are derived at a differential level via a finite calculus procedure. This allows us to obtain a stabilized numerical solution scheme. Some particular aspects of the problem solution, such as the mesh updating procedure and the transom stern treatment, are presented. Examples of the efficiency of the semi-implicit algorithm for the analysis of ship hydrodynamics problems are presented.

  Abstract
  A stabilized semi-implicit fractional step algorithm based on the finite element method for solving ship wave problems using unstructured meshes is presented. The stabilized [...]

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• A finite element method for fluid-structure interaction with surface waves using a finite calculus formulation

  E. Oñate, J. García-Espinosa

  Comput. Methods Appl. Mech. Engrg. (2001). 191, 635-660

  
  

  Abstract

  A stabilized semi-implicit fractional step finite element method (FEM) for solving coupled fluid-structure interaction problems involving free surface waves is presented. The stabilized governing equations for the viscous incompressible fluid and the free surface are derived at a differential level via a finite calculus (FIC) procedure. A mesh updating technique based on solving a fictitious elastic problem on the moving mesh is described. Examples of the efficiency of the stabilized semi-implicit algorithm for the analysis of fluid-structure interaction problems in totally or partially submerged bodies is presented.

  Abstract
  A stabilized semi-implicit fractional step finite element method (FEM) for solving coupled fluid-structure interaction problems involving free surface waves is presented. [...]

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• Estudio de la distribución transitoria del gas en redes urbanas por el método de los elementos finitos

  B. Suárez, E. Oñate

  Anales de Ingeniería Mecánica (1984). Vol. 2 (1), pp. 59-68

  
  

  Abstract

  Se representa una formulación por elementos finitos que permite simular la distribución transitoria de presiones y caudales del gas en redes urbanas. Esta formulación, que parte de las ecuaciones básicas que proporciona la mecánica de fluidos para la circulación de un gas en régimen variable por conductos cilíndricos, utiliza elementos finitos unidimensionales parabólicos para discretizar los distintos tramos de la red y un esquema paso a paso de integración en el tiempo que supone una variación lineal de la presión del gas en cada intervalo de tiempo. La formulación se aplica al caso real de la red media presión de la ciudad de Barcelona utilizando algunos resultados experimentales para confirmar su eficiencia y aproximación. 

  Abstract
  Se representa una formulación por elementos finitos que permite simular la distribución transitoria de presiones y caudales del gas en redes urbanas. Esta formulación, [...]

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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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• 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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• A compressible Lagrangian framework for modeling the fluid-structure interaction in the underwater implosion of an aluminum cylinder

  K. Kamran, R. Rossi, E. Oñate, S. Idelsohn

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

  
  

  Abstract

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

  Abstract
  We propose a fully Lagrangian monolithic system for the simulation of the underwater implosion of cylindrical aluminum containers. A variationally stabilized form of the Lagrangian [...]

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• Flow behaviour of negatively buoyant jets in immiscible ambient fluid

  A. Geyer, J. Phillips, M. Mier-Torrecilla, S. Idelsohn, E. Oñate

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

  
  

  Abstract

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

  Abstract
  In this paper we investigate experimentally the injection of a negatively buoyant jet into a homogenous immiscible ambient fluid. Experiments are carried out by injecting [...]

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