COLLECTIONS

Documents published in Scipedia

• 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. [...]

  • 18
  •  read

• On some fluid-structure iterative algorithms using pressure segregation methods. Applications to aeroelasticity

  S. Badia, R. Codina

  (2006). Research Report, Nº PI287

  
  

  Abstract

  In this paper we suggest some algorithms for the fluid-structure interaction problem stated using a domain decomposition framework. These methods involve stabilized pressure segregation methods for the solution of the fluid problem and fixed point iterative algorithms for the fluid-structure coupling. These coupling algorithms are applied to the aeroelastic simulation of suspension bridges. We assess flexural and torsional frequencies for a given inflow velocity. Increasing this velocity we reach the value for which the flutter phenomenon appears.

  Abstract
  In this paper we suggest some algorithms for the fluid-structure interaction problem stated using a domain decomposition framework. These methods involve stabilized pressure [...]

  • 7
  •  read

• Velocity correction methods based on a discrete pressure Poisson equation an algebraic approach

  S. Badia, R. Codina

  (2006). Research Report, Nº PI286

  
  

  Abstract

  In this paper we introduce some pressure segregation methods obtained from a non-standard version of the discrete monolithic system, where the continuity equation has been replaced by a pressure Poisson equation obtained at the discrete level. In these methods it is the velocity instead of the pressure the extrapolated unknown. Moreover, predictor corrector schemes are suggested, again motivated by the new monolithic system. Key implementation aspects are discussed, and a complete stability analysis is performed. We end with a set of numerical examples in order to compare these methods with classical pressure correction schemes.

  Abstract
  In this paper we introduce some pressure segregation methods obtained from a non-standard version of the discrete monolithic system, where the continuity equation has been [...]

  • 5
  •  read

• Analysis of a stabilized finite element approximation of the transient convection-diffusion equation using an ale framework

  S. Badia, R. Codina

  (2006). Research Report, Nº PI285

  
  

  Abstract

  In this paper we analyze a stabilized finite element method to approximate the convection diffusion equation on moving domains using an ALE framework. As basic numerical strategy, we discretize the equation in time using first and second order backward differencing (BDF) schemes, whereas space is discretized using a stabilized finite element method (the orthogonal subgrid scale formulation) to deal with convection dominated flows. The semi-discrete problem (continuous in space) is first analyzed. In this situation it is easy to identify the error introduced by the ALE approach. After that, the fully discrete method is considered. We obtain optimal error estimates in both space and time in a mesh dependent norm. The analysis reveals that the ALE approach introduces an upper bound for the time step size for the results to hold. The results obtained for the fully discretized second order scheme (in time) are associated to a weaker norm than the one used for the first order method. Nevertheless, optimal convergence results have been proved. For fixed domains, we recover stability and convergence results with the strong norm for the second order scheme, stressing the aspects that make the analysis of this method much more involved.

  Abstract
  In this paper we analyze a stabilized finite element method to approximate the convection diffusion equation on moving domains using an ALE framework. As basic numerical strategy, [...]

  • 16
  •  read

• On some pressure segregation methods of fractional-step type for the finite element approximation of incompressible flow problems

  R. Codina, S. Badia

  (2006). Research Report, Nº PI284

  
  

  Abstract

  In this paper we treat several aspects related to time integration methods for the incompressible Navier-Stokes equations that allow to uncouple the calculation of the velocities and the pressure. The first family of schemes consists of classical fractional step methods, of which we discuss several possibilities for the pressure extrapolation and the time integration of first and second order. The second family consists of schemes based on an explicit treatment of the pressure in the momentum equation followed by a Poisson equation for the pressure. It turns out that this “staggered” treatment of the velocity and the pressure is stable. Finally, we present predictor-corrector methods based on the above schemes that aim to converge to the solution of the monolithic time integration method. Apart from presenting these schemes and check its numerical performance, we also present a complete set of stability results for the fractional step methods that are independent of the space stability of the velocity-pressure interpolation, that is, of the classical inf-sup condition.

  Abstract
  In this paper we treat several aspects related to time integration methods for the incompressible Navier-Stokes equations that allow to uncouple the calculation of the velocities [...]

  • 7
  •  read

• 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 [...]

  • 15
  •  read

• 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 [...]

  • 9
  •  read

• 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 [...]

  • 12
  •  read

• 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, [...]

  • 7
  •  read

• 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 [...]

  • 3
  •  read