On a multigrid method for the coupled Stokes and porous media flow problem

Luo, P. ; Rodrigo, C. (Universidad de Zaragoza) ; Gaspar, F.J. (Universidad de Zaragoza) ; Oosterlee, C.W.

Resumen: The multigrid solution of coupled porous media and Stokes flow problems is considered. The Darcy equation as the saturated porous medium model is coupled to the Stokes equations by means of appropriate interface conditions. We focus on an efficient multigrid solution technique for the coupled problem, which is discretized by finite volumes on staggered grids, giving rise to a saddle point linear system. Special treatment is required regarding the discretization at the interface. An Uzawa smoother is employed in multigrid, which is a decoupled procedure based on symmetric Gauss-Seidel smoothing for velocity components and a simple Richardson iteration for the pressure field. Since a relaxation parameter is part of a Richardson iteration, Local Fourier Analysis (LFA) is applied to determine the optimal parameters. Highly satisfactory multigrid convergence is reported, and, moreover, the algorithm performs well for small values of the hydraulic conductivity and fluid viscosity, that are relevant for applications.

Idioma: Inglés

DOI: 10.1063/1.4992706

Año: 2017

Publicado en: AIP Conference Proceedings 1863, 1 (2017), 560023 [5 pp]
ISSN: 0094-243X

Tipo y forma: Artículo (Versión definitiva)

Área (Departamento): Área Matemática Aplicada (Dpto. Matemática Aplicada)