Reports de recercahttp://hdl.handle.net/2117/53952021-07-30T22:23:52Z2021-07-30T22:23:52ZA general stabilized formulation for incompressible fluid flow using finite calculus and the finite element methodOñate Ibáñez de Navarra, EugenioGarcía Espinosa, JulioBugeda Castelltort, GabrielIdelsohn Barg, Sergio Rodolfohttp://hdl.handle.net/2117/1710292021-04-11T06:37:55Z2019-10-29T09:29:24ZA general stabilized formulation for incompressible fluid flow using finite calculus and the finite element method
Oñate Ibáñez de Navarra, Eugenio; García Espinosa, Julio; Bugeda Castelltort, Gabriel; Idelsohn Barg, Sergio Rodolfo
We present a general formulation for incompressible fluid flow analysis using the finite element method (FEM). The necessary stabilization for dealing with convective effects and the incompressibility condition are introduced via the so called finite calculus (FIC) method. The extension of the standard eulerian form of the equations to an arbitrary lagrangian-eulerian (ALE) frame adequate for treating fluid-structure interaction problems is presented. The fully lagrangian form is also discussed. Details of an effective mesh updating procedure are presented together with a method for dealing with free surface effects of importance for ship hydrodynamic analysis and many other fluid flow problems. Examples of application of the eulerian, the ALE and the fully lagrangian flow descriptions are presented.
CIMNE, Technical Report Nº PI-223, 38pp., Barcelona, Spain
2019-10-29T09:29:24ZOñate Ibáñez de Navarra, EugenioGarcía Espinosa, JulioBugeda Castelltort, GabrielIdelsohn Barg, Sergio RodolfoWe present a general formulation for incompressible fluid flow analysis using the finite element method (FEM). The necessary stabilization for dealing with convective effects and the incompressibility condition are introduced via the so called finite calculus (FIC) method. The extension of the standard eulerian form of the equations to an arbitrary lagrangian-eulerian (ALE) frame adequate for treating fluid-structure interaction problems is presented. The fully lagrangian form is also discussed. Details of an effective mesh updating procedure are presented together with a method for dealing with free surface effects of importance for ship hydrodynamic analysis and many other fluid flow problems. Examples of application of the eulerian, the ALE and the fully lagrangian flow descriptions are presented.An anisotropic elasto-plastic model based on an isotropic formulationOller Martínez, Sergio HoracioBotello Rionda, SalvadorMiquel, JoanOñate Ibáñez de Navarra, Eugeniohttp://hdl.handle.net/2117/1667242021-05-21T01:03:58Z2019-07-24T10:09:43ZAn anisotropic elasto-plastic model based on an isotropic formulation
Oller Martínez, Sergio Horacio; Botello Rionda, Salvador; Miquel, Joan; Oñate Ibáñez de Navarra, Eugenio
2019-07-24T10:09:43ZOller Martínez, Sergio HoracioBotello Rionda, SalvadorMiquel, JoanOñate Ibáñez de Navarra, EugenioSLAP: programa para modelado numérico de procesos de estereolitografía utilizando el método de los elementos finitosLombera, GuillermoBugeda Castelltort, GabrielCervera Ruiz, MiguelOñate Ibáñez de Navarra, Eugeniohttp://hdl.handle.net/2117/1667102020-07-23T21:34:23Z2019-07-24T09:45:43ZSLAP: programa para modelado numérico de procesos de estereolitografía utilizando el método de los elementos finitos
Lombera, Guillermo; Bugeda Castelltort, Gabriel; Cervera Ruiz, Miguel; Oñate Ibáñez de Navarra, Eugenio
PI 47
2019-07-24T09:45:43ZLombera, GuillermoBugeda Castelltort, GabrielCervera Ruiz, MiguelOñate Ibáñez de Navarra, EugenioA methodology for adaptive mesh refinement in optimum shape design problemsBugeda Castelltort, GabrielOñate Ibáñez de Navarra, Eugeniohttp://hdl.handle.net/2117/1666492020-07-23T22:54:58Z2019-07-24T06:39:30ZA methodology for adaptive mesh refinement in optimum shape design problems
Bugeda Castelltort, Gabriel; Oñate Ibáñez de Navarra, Eugenio
2019-07-24T06:39:30ZBugeda Castelltort, GabrielOñate Ibáñez de Navarra, EugenioAerodynamic shape optimization using automatic adaptive remeshingBugeda Castelltort, GabrielOñate Ibáñez de Navarra, EugenioJoannas, Dhttp://hdl.handle.net/2117/1666482020-07-23T20:56:47Z2019-07-24T06:26:05ZAerodynamic shape optimization using automatic adaptive remeshing
Bugeda Castelltort, Gabriel; Oñate Ibáñez de Navarra, Eugenio; Joannas, D
2019-07-24T06:26:05ZBugeda Castelltort, GabrielOñate Ibáñez de Navarra, EugenioJoannas, DBlock recursive LU preconditioners for the thermally coupled incompressible inductionless MHD problemBadia, SantiagoMartín Huertas, Alberto FranciscoPlanas Badenas, Ramonhttp://hdl.handle.net/2117/212292020-07-23T23:21:18Z2014-01-13T14:57:02ZBlock recursive LU preconditioners for the thermally coupled incompressible inductionless MHD problem
Badia, Santiago; Martín Huertas, Alberto Francisco; Planas Badenas, Ramon
The thermally coupled incompressible inductionless magnetohydrodynamics (MHD) problem models the ow of an electrically charged fuid under the in uence of an external electromagnetic eld with thermal coupling. This system of partial di erential equations is strongly coupled and highly nonlinear for real cases of interest. Therefore, fully implicit time integration schemes are very desirable in order to capture the di erent physical scales of the problem at hand. However, solving the multiphysics linear systems of equations resulting from such algorithms is a very challenging task
which requires e cient and scalable preconditioners. In this work, a new family of recursive block LU preconditioners is designed and tested for solving the thermally coupled inductionless MHD equations. These preconditioners are obtained after splitting the fully coupled matrix into one-physics problems for every variable (velocity, pressure,
current density, electric potential and temperature) that can be optimally solved, e.g., using preconditioned domain decomposition algorithms. The main idea is to arrange the original matrix into an (arbitrary) 2 2 block matrix, and consider a LU preconditioner obtained by approximating the corresponding Schur complement. For every one
of the diagonal blocks in the LU preconditioner, if it involves more than one type of unknown, we proceed the same way in a recursive fashion. This approach is stated in an abstract way, and can be straightforwardly applied to other multiphysics problems. Further, we precisely explain a fexible and general software design for the code implementation of this type of preconditioners.
2014-01-13T14:57:02ZBadia, SantiagoMartín Huertas, Alberto FranciscoPlanas Badenas, RamonThe thermally coupled incompressible inductionless magnetohydrodynamics (MHD) problem models the ow of an electrically charged fuid under the in uence of an external electromagnetic eld with thermal coupling. This system of partial di erential equations is strongly coupled and highly nonlinear for real cases of interest. Therefore, fully implicit time integration schemes are very desirable in order to capture the di erent physical scales of the problem at hand. However, solving the multiphysics linear systems of equations resulting from such algorithms is a very challenging task
which requires e cient and scalable preconditioners. In this work, a new family of recursive block LU preconditioners is designed and tested for solving the thermally coupled inductionless MHD equations. These preconditioners are obtained after splitting the fully coupled matrix into one-physics problems for every variable (velocity, pressure,
current density, electric potential and temperature) that can be optimally solved, e.g., using preconditioned domain decomposition algorithms. The main idea is to arrange the original matrix into an (arbitrary) 2 2 block matrix, and consider a LU preconditioner obtained by approximating the corresponding Schur complement. For every one
of the diagonal blocks in the LU preconditioner, if it involves more than one type of unknown, we proceed the same way in a recursive fashion. This approach is stated in an abstract way, and can be straightforwardly applied to other multiphysics problems. Further, we precisely explain a fexible and general software design for the code implementation of this type of preconditioners.Analysis of an unconditionally convergent stabilized finite element formulation for incompressible magnetohydrodynamicsBadia, SantiagoCodina, RamonPlanas Badenas, Ramonhttp://hdl.handle.net/2117/178022020-07-23T21:59:23Z2013-02-15T16:51:15ZAnalysis of an unconditionally convergent stabilized finite element formulation for incompressible magnetohydrodynamics
Badia, Santiago; Codina, Ramon; Planas Badenas, Ramon
In this work, we analyze a recently proposed stabilized finite element formulation for the approximation of the resistive magnetohydrodynamics equations. The novelty of this formulation with respect to existing ones is the fact that it always converges to the physical solution, even when it is singular. We have performed a detailed stability and convergence analysis of the formulation in a simplified setting. From the convergence analysis, we infer that a particular type of meshes with a macro-element structure is needed, which can be easily obtained after a straight modification of any original mesh.
2013-02-15T16:51:15ZBadia, SantiagoCodina, RamonPlanas Badenas, RamonIn this work, we analyze a recently proposed stabilized finite element formulation for the approximation of the resistive magnetohydrodynamics equations. The novelty of this formulation with respect to existing ones is the fact that it always converges to the physical solution, even when it is singular. We have performed a detailed stability and convergence analysis of the formulation in a simplified setting. From the convergence analysis, we infer that a particular type of meshes with a macro-element structure is needed, which can be easily obtained after a straight modification of any original mesh.Error analysis of discontinuous Galerkin methods for Stokes problem under minimal regularityBadia, SantiagoCodina, RamonGudi, ThirupathiGuzmán, Johnnyhttp://hdl.handle.net/2117/169222020-07-23T20:14:11Z2012-11-14T18:20:28ZError analysis of discontinuous Galerkin methods for Stokes problem under minimal regularity
Badia, Santiago; Codina, Ramon; Gudi, Thirupathi; Guzmán, Johnny
In this article, we analyze several discontinuous Galerkin methods (DG) for the
Stokes problem under the minimal regularity on the solution. We assume that the velocity
u belongs to [H1 0 ()]d and the pressure p 2 L2 0 (). First, we analyze standard DG methods assuming that the right hand side f belongs to [H¡1() \ L1()]d. A DG method that is well de¯ned for f belonging to [H¡1()]d is then investigated. The methods under study
include stabilized DG methods using equal order spaces and inf-sup stable ones where the pressure space is one polynomial degree less than the velocity space.
2012-11-14T18:20:28ZBadia, SantiagoCodina, RamonGudi, ThirupathiGuzmán, JohnnyIn this article, we analyze several discontinuous Galerkin methods (DG) for the
Stokes problem under the minimal regularity on the solution. We assume that the velocity
u belongs to [H1 0 ()]d and the pressure p 2 L2 0 (). First, we analyze standard DG methods assuming that the right hand side f belongs to [H¡1() \ L1()]d. A DG method that is well de¯ned for f belonging to [H¡1()]d is then investigated. The methods under study
include stabilized DG methods using equal order spaces and inf-sup stable ones where the pressure space is one polynomial degree less than the velocity space.On the design of discontinuous Galerkin methods for elliptic problems based on hybrid formulationsCodina, RamonBadia, Santiagohttp://hdl.handle.net/2117/169212020-07-23T22:47:15Z2012-11-14T18:01:39ZOn the design of discontinuous Galerkin methods for elliptic problems based on hybrid formulations
Codina, Ramon; Badia, Santiago
The objective of this paper is to present a framework for the design of discontinuous Galerkin (dG) methods for elliptic problems. The idea is to start from a hybrid formulation of the problem involving as unknowns the main field in the interior of the element domains and its fluxes and
traces on the element boundaries. Rather than working with this three-field formulation, fluxes are modeled using finite difference expressions and then the traces are determined by imposing continuity of fluxes, although other strategies could be devised. This procedure is applied to four
elliptic problems, namely, the convection-diffusion equation (in the diffusion dominated regime), the Stokes problem, the Darcy problem and the Maxwell problem. We justify some well known dG methods with some modifications that in fact allow to improve the performance of the original methods, particularly when the physical properties are discontinuous.
2012-11-14T18:01:39ZCodina, RamonBadia, SantiagoThe objective of this paper is to present a framework for the design of discontinuous Galerkin (dG) methods for elliptic problems. The idea is to start from a hybrid formulation of the problem involving as unknowns the main field in the interior of the element domains and its fluxes and
traces on the element boundaries. Rather than working with this three-field formulation, fluxes are modeled using finite difference expressions and then the traces are determined by imposing continuity of fluxes, although other strategies could be devised. This procedure is applied to four
elliptic problems, namely, the convection-diffusion equation (in the diffusion dominated regime), the Stokes problem, the Darcy problem and the Maxwell problem. We justify some well known dG methods with some modifications that in fact allow to improve the performance of the original methods, particularly when the physical properties are discontinuous.Convergence towards weak solutions of the Navier-Stokes equations for a finite element approximation with numerical subgrid scale modelingBadia, SantiagoGutiérrez Santacreu, Juan Vicentehttp://hdl.handle.net/2117/169202020-07-23T21:53:36Z2012-11-14T17:48:02ZConvergence towards weak solutions of the Navier-Stokes equations for a finite element approximation with numerical subgrid scale modeling
Badia, Santiago; Gutiérrez Santacreu, Juan Vicente
Residual-based stabilized nite element techniques for the Navier-Stokes equations lead to numerical discretizations that provide convection stabilization as well as pressure stability without the need to satisfy an inf-sup condition. They can be motivated by using a variational multiscale framework, based on the decomposition of the
uid velocity into a resolvable nite element component plus a modeled subgrid scale
component. The subgrid closure acts as a large eddy simulation turbulence model, leading to accurate under-resolved simulations. However, even though variational multiscale formulations are increasingly used in the applied nite element community, their numerical analysis has been restricted to a priori estimates and convergence to smooth solutions only, via a priori error estimates. In this work we prove that some versions of these methods (based on dynamic and orthogonal closures)
also converge to weak (turbulent) solutions of the Navier-Stokes equations. These results are obtained by using compactness results in Bochner-Lebesgue spaces. Navier-Stokes equations; stability; convergence;
stabilized nite element methods; subgrid scales; variational multiscale methods.
2012-11-14T17:48:02ZBadia, SantiagoGutiérrez Santacreu, Juan VicenteResidual-based stabilized nite element techniques for the Navier-Stokes equations lead to numerical discretizations that provide convection stabilization as well as pressure stability without the need to satisfy an inf-sup condition. They can be motivated by using a variational multiscale framework, based on the decomposition of the
uid velocity into a resolvable nite element component plus a modeled subgrid scale
component. The subgrid closure acts as a large eddy simulation turbulence model, leading to accurate under-resolved simulations. However, even though variational multiscale formulations are increasingly used in the applied nite element community, their numerical analysis has been restricted to a priori estimates and convergence to smooth solutions only, via a priori error estimates. In this work we prove that some versions of these methods (based on dynamic and orthogonal closures)
also converge to weak (turbulent) solutions of the Navier-Stokes equations. These results are obtained by using compactness results in Bochner-Lebesgue spaces. Navier-Stokes equations; stability; convergence;
stabilized nite element methods; subgrid scales; variational multiscale methods.