Imagen de Portada

Analysis of the HDG method for the stokes–darcy coupling

In this article, we introduce and analyze a hybridizable discontinuous Galerkin (HDG) method for numerically solving the coupling of fluid flow with porous media flow. Flows are governed by the Stokes and Darcy equations, respectively, and the corresponding transmission conditions are given by mass...

Descripción completa

Autores Principales: Sequeira, Filander, Gática, Gabriel N.
Formato: Artículo
Idioma: Inglés
Publicado: Numerical Methods for Partial Differential Equations 2020
Materias:
COUPLING
STOKES EQUATIONS
DARCY EQUATIONS
DISCONTINUOUS GALERKIN METHOD
Acceso en línea: http://hdl.handle.net/11056/17560
id RepoUNACR17560
recordtype dspace
spelling RepoUNACR175602021-06-14T19:30:02Z Analysis of the HDG method for the stokes–darcy coupling Sequeira, Filander Gática, Gabriel N. COUPLING STOKES EQUATIONS DARCY EQUATIONS DISCONTINUOUS GALERKIN METHOD In this article, we introduce and analyze a hybridizable discontinuous Galerkin (HDG) method for numerically solving the coupling of fluid flow with porous media flow. Flows are governed by the Stokes and Darcy equations, respectively, and the corresponding transmission conditions are given by mass conservation, balance of normal forces, and the Beavers‐Joseph‐Saffman law. We consider a fully‐mixed formulation in which the main unknowns in the fluid are given by the stress, the vorticity, the velocity, and the trace of the velocity, whereas the velocity, the pressure, and the trace of the pressure are the unknowns in the porous medium. In addition, a suitable enrichment of the finite dimensional subspace for the stress yields optimally convergent approximations for all unknowns, as well as a superconvergent approximation of the trace variables. To do that, similarly as in previous articles dealing with development of the a priori error estimates, we use the projection‐based error analysis to simplify the corresponding study. Finally, we provide several numerical results illustrating the good performance of the proposed scheme and confirming the optimal order of convergence provided by the HDG approximation. © 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 885–917, 2017 En este artículo, presentamos y analizamos un método de Galerkin discontinuo hibridable (HDG) para resolver numéricamente el acoplamiento del flujo de fluido con el flujo de medios porosos. Los flujos se rigen por las ecuaciones de Stokes y Darcy, respectivamente, y las condiciones de transmisión correspondientes están dadas por la conservación en masa, el equilibrio de las fuerzas normales y la ley de Beavers-Joseph-Saffman. Consideramos una formulación completamente mezclada en la cual las principales incógnitas en el fluido están dadas por el estrés, la vorticidad, la velocidad y el rastro de la velocidad, mientras que la velocidad, la presión y el rastro de la presión son las incógnitas. en el medio poroso Además, un enriquecimiento adecuado del subespacio de dimensión finita para el esfuerzo produce aproximaciones óptimamente convergentes para todas las incógnitas, así como una aproximación superconvergente de las variables de traza. Para hacer eso, de manera similar a como en los artículos anteriores relacionados con el desarrollo de las estimaciones de error a priori, utilizamos el análisis de error basado en la proyección para simplificar el estudio correspondiente. Finalmente, proporcionamos varios resultados numéricos que ilustran el buen desempeño del esquema propuesto y confirman el orden óptimo de convergencia proporcionado por la aproximación HDG. © 2017 Wiley Periodicals, Inc. Métodos numéricos Ecual diferencial parcial, 2017 Universidad Nacional, Costa Rica Escuela de Matemática 2020-06-11T18:23:48Z 2020-06-11T18:23:48Z 2017-02-03 http://purl.org/coar/resource_type/c_6501 http://hdl.handle.net/11056/17560 eng Acceso abierto application/pdf Numerical Methods for Partial Differential Equations Gatica, Gabriel & Sequeira, Filánder. (2017). Analysis of the HDG method for the stokes-darcy coupling: Hdg For Stokes-Darcy. Numerical Methods for Partial Differential Equations. Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 885–917, 2017
institution Universidad Nacional de Costa Rica
collection Repositorio UNA-Costa Rica
language Inglés
topic COUPLING
STOKES EQUATIONS
DARCY EQUATIONS
DISCONTINUOUS GALERKIN METHOD
spellingShingle COUPLING
STOKES EQUATIONS
DARCY EQUATIONS
DISCONTINUOUS GALERKIN METHOD
Sequeira, Filander
Gática, Gabriel N.
Analysis of the HDG method for the stokes–darcy coupling
description In this article, we introduce and analyze a hybridizable discontinuous Galerkin (HDG) method for numerically solving the coupling of fluid flow with porous media flow. Flows are governed by the Stokes and Darcy equations, respectively, and the corresponding transmission conditions are given by mass conservation, balance of normal forces, and the Beavers‐Joseph‐Saffman law. We consider a fully‐mixed formulation in which the main unknowns in the fluid are given by the stress, the vorticity, the velocity, and the trace of the velocity, whereas the velocity, the pressure, and the trace of the pressure are the unknowns in the porous medium. In addition, a suitable enrichment of the finite dimensional subspace for the stress yields optimally convergent approximations for all unknowns, as well as a superconvergent approximation of the trace variables. To do that, similarly as in previous articles dealing with development of the a priori error estimates, we use the projection‐based error analysis to simplify the corresponding study. Finally, we provide several numerical results illustrating the good performance of the proposed scheme and confirming the optimal order of convergence provided by the HDG approximation. © 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 885–917, 2017
format Artículo
author Sequeira, Filander
Gática, Gabriel N.
author_sort Sequeira, Filander
title Analysis of the HDG method for the stokes–darcy coupling
title_short Analysis of the HDG method for the stokes–darcy coupling
title_full Analysis of the HDG method for the stokes–darcy coupling
title_fullStr Analysis of the HDG method for the stokes–darcy coupling
title_full_unstemmed Analysis of the HDG method for the stokes–darcy coupling
title_sort analysis of the hdg method for the stokes–darcy coupling
publisher Numerical Methods for Partial Differential Equations
publishDate 2020
url http://hdl.handle.net/11056/17560
_version_ 1796096425531015168
score 12.232074

Ejemplares similares