JOURNALS

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• Evolutionary methods for optimal shape design

  A. Fung, E. Pahl, G. Bugeda, E. Oñate

  (2005). Research Report, Nº PI270

  
  

  Abstract

  An optimization code called Optima has been developed at the International Centre for Numerical Methods in Engineering (CIMNE). This report validates two reputably robust Evolutionary Algorithms available in Optima and employs them on aerodynamic shape optimization problems. The two schemes, Differential Evolution Scheme 1 (DE1) and Evolution Strategy coupled with Covariance Matrix Adaptation (ES-CMA), were tested and verified on three standard parametric optimization objective functions through comparison against existing results. Analysis of the test data allowed trends to be established and from this, settings to enhance the performance of the algorithms were proposed and substantiated. The algorithms and their suggested settings were applied on an inverse and a direct constrained shape optimization problem involving NACA four digit airfoils. The inverse task involves the recovery of an airfoil profile through its pressure distribution combination of lift and drag coefficients. Simulation of the airfoil in turbulent flow was done using a Computational Fluid Dynamics (CFD) setup. Finally, the results are presented and the ES-CMA method, using the setting CMA-B proposed in this paper, was found to be most robust. Suggestions for improvements and further work in the optimization configuration and the problem simulation are also proposed.  

  Abstract
  An optimization code called Optima has been developed at the International Centre for Numerical Methods in Engineering (CIMNE). This report validates two reputably robust [...]

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• Modeling bed erosion in free surface flows by the particle finite element method

  E. Oñate, M. Celigueta, S. Idelsohn

  (2006). Research Report, Nº PI293

  
  

  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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• LES turbulence models. Relation with stabilized numerical methods

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

  (2006). Research Report, Nº PI288

  
  

  Abstract

  One of the aims of this text is to show some important results in LES modelling and to identify which are main mathematical problems for the development of a complete theory. A relevant aspect of LES theory, which we will consider in our work, is the close relationship between the mathematical properties of LES models and the numerical methods used for their implementation. In last years it is more and more common the idea in the scientific community, especially in the numerical community, that turbulence models and stabilization techniques play a very similar role. Methodologies used to simulate turbulent flows, RANS or LES approaches, are based on the same concept: unability to simulate a turbulent flow using a finite discretization in time and space. Turbulence models introduce additional information (impossible to be captured by the approximation technique used in the simulation) to obtain physically coherent solutions. On the other side, numerical methods used for the integration of partial differential equations (PDE) need to be modified in order to able to reproduce solutions that present very high localized gradients. These modifications, known as stabilization techniques, make possible to capture these sharp and localized changes of the solution. According with previous paragraphs, the following natural question appears: Is it possible to reinterpret stabilization methods as turbulence models? This question suggests a possible principle of duality between turbulence modelling and numerical stabilization. More than to share certain properties, actually, it is suggested that the numerical stabilization can be understood as turbulence. The opposite will occur if turbulence models are only necessary due to discretization limitations instead of a need for reproducing the physical behaviour of the flow. Finally: can turbulence models be understood as a component of a general stabilization method?

  Abstract
  One of the aims of this text is to show some important results in LES modelling and to identify which are main mathematical problems for the development of a complete theory. [...]

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• Variational formulation of the finite calculus equations in solid mechanics and diffusion-reaction problems

  E. Oñate, C. Felippa

  (2006). Research Report, Nº PI283

  
  

  Abstract

  We present a variational formulation of the finite calculus (FIC) equations for problems in mechanics governed by differential equations with symmetric operators. Applications considered include solid mechanics, diffusion-transport and diffusion-reaction problems. The key of the variational formulation is the identification of the FIC governing equations with the classical differential equations of mechanics written in terms of modified non-local variables. A total potential energy (TPE) functional is found in terms of the modified variables. The FIC equations in the domain and the boundary are recovered as the Euler-Lagrange equations and the natural boundary condition of the TPE functional, respectively. Symmetric finite element equations are obtained after discretization of the TPE functional, therefore preserving the symmetry of the governing infinitesimal equations. The variational FIC expression is reinterpreted as a Petrov Galerkin weighted residual form of the original FIC equations with non-local weighting functions. The analogy of the variational FIC-FEM formulation with a discontinuous Galerkin method is recognized. Extensions to multidimensional linear elastostatics and diffusion-reaction problems are presented.

  Abstract
  We present a variational formulation of the finite calculus (FIC) equations for problems in mechanics governed by differential equations with symmetric operators. Applications [...]

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• FIC/FEM formulation with matrix stabilizing terms for incompressible floes at low and high Reynolds numbers

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

  (2006). Research Report, Nº PI282

  
  

  Abstract

  We present a general formulation for incompressible fluid flow analysis using the finite element method. The necessary stabilization for dealing with convective effects and the incompressibility condition are introduced via the Finite Calculus method using a matrix form of the stabilization parameters. This allows to model a wide range of fluid flow problems for low and high Reynolds numbers flows without introducing a turbulence model. Examples of application to the analysis of incompressible flows with moderate and large Reynolds numbers are presented.

  Abstract
  We present a general formulation for incompressible fluid flow analysis using the finite element method. The necessary stabilization for dealing with convective effects and [...]

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• On the simulation of flows with violent free surface motion

  R. Löhner, C. Yang, E. Oñate

  (2006). Research Report, Nº PI281

  
  

  Abstract

  A volume of fluid (VOF) technique has been developed and coupled with an incompressible Euler/Navier–Stokes solver operating on adaptive, unstructured grids to simulate the interactions of extreme waves and three-dimensional structures. The present implementation follows the classic VOF implementation for the liquid–gas system, considering only the liquid phase. Extrapolation algorithms to obtain velocities and pressure in the gas region near the free surface have been implemented. The VOF technique is validated against the classic dam-break problem, as well as series of 2D sloshing experiments and results from smoothed particle hydrodynamics (SPH) calculations. These and a series of other examples demonstrate that the present CFD method is capable of simulating violent free surface flows with strong nonlinear behavior.

  Abstract
  A volume of fluid (VOF) technique has been developed and coupled with an incompressible Euler/Navier–Stokes solver operating on adaptive, unstructured grids to simulate [...]

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• Coupling of Feflo with Simpact

  J. Arteaga-Gomez, R. Löhner, J. Rojek, E. Oñate

  (2006). Research Report, Nº PI280

  
  

  Abstract

  This paper describes the coupling of FEFLO, a general purpose compressible and incompressible flow solver base on adaptive unstructured grids with SIMPACT, a general purpose, large deformation, explicit structural dynamics code developed at the Center for Numerical Methods in Engineering (CIMNE). Details on the codes, as well as the compiling strategy employed are given. Examples illustrate the possibilies the present fluid-structure capability offers.

  Abstract
  This paper describes the coupling of FEFLO, a general purpose compressible and incompressible flow solver base on adaptive unstructured grids with SIMPACT, a general purpose, [...]

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• Centre Internacional de Mètodes Numèrics en Enginyeria (CIMNE). Vint anys d'historia

  E. Oñate

  (2007). Research Report, Nº PI312

  
  

  Abstract

  El CIMNE (www.cimne.com), un centre de recerca consorci entre la Universitat Politècnica de Catalunya i la Generalitat de Catalunya, fa vint anys. El CIMNE està especialitzat en el desenvolupament i l’aplicació de mètodes numèrics avançats per a la solució d’un ampli ventall de problemes en enginyeria, que van des de la mecánica de sòlids i estructures, fins als processos de fabricació, passant per les TIC i els sistemes de suport a la decisió per a la prevenció i el tractament de catàstrofes naturals, com poden ser les inundacions o els vessaments de productes tòxics. El CIMNE es posiciona com un centre clau en el paper del desenvolupament d’idees originades en entorns de recerca bàsica i la seva transferència al sector industrial, per a la seva posterior industrialització i comercialització.

  Abstract
  El CIMNE (www.cimne.com), un centre de recerca consorci entre la Universitat Politècnica de Catalunya i la Generalitat de Catalunya, fa vint anys. El CIMNE està [...]

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• A finite point method for three-dimensional compressible flow

  E. Ortega, E. Oñate, S. Idelsohn

  (2007). Research Report, Nº PI310

  
  

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• Shape optimization in aeronautical applications using neural networks

  A. Daring, R. López, R. Flores, G. Bugeda, E. Oñate

  (2007). Research Report, Nº PI306

  
  

  Abstract

  An optimization methodology based on neural networks was developed for use in 2D optimal shape design problems. Neural networks were used as a parameterization scheme to represent the shape function, and an edge-based high-resolution scheme for the solution of the compressible Euler equations was used to model the flow around the shape. The global system incorporates neural networks and the Euler fluid solver into the C++ Flood optimization framework containing a library of optimization algorithms. The optimization scheme was applied to a minimal drag problem in an unconstrained optimization case and a constrained case in hypersonic flow using evolutionary training algorithms. The results indicate that the minimum drag problem is solved to a high degree of accuracy but at high computational cost. For more complex shapes, parallel computing methods are required to reduce computational time.

  Abstract
  An optimization methodology based on neural networks was developed for use in 2D optimal shape design problems. Neural networks were used as a parameterization scheme to represent [...]

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