Uzawa smoother in multigrid for the coupled porous medium and Stokes flow system

Luo, Peiyao ; Rodrigo, Carmen (Universidad de Zaragoza) ; Gaspar Lorenz, Francisco José (Universidad de Zaragoza) ; Oosterlee, Cornelis 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 is applied to determine the optimal parameters. Highly satisfactory multigrid convergence is reported, and, moreover, the algorithm performs very well for small values of the hydraulic conductivity and fluid viscosity, which are relevant for applications.

Idioma: Inglés

DOI: 10.1137/16M1076514

Año: 2017

Publicado en: SIAM JOURNAL ON SCIENTIFIC COMPUTING 39, 5 (2017), S633-S661
ISSN: 1064-8275

Factor impacto JCR: 2.046 (2017)

Categ. JCR: MATHEMATICS, APPLIED rank: 27 / 252 = 0.107 (2017) - Q1 - T1

Factor impacto SCIMAGO: 1.973 - Computational Mathematics (Q1) - Applied Mathematics (Q1)

Financiación: info:eu-repo/grantAgreement/ES/DGA/PDIE
Financiación: info:eu-repo/grantAgreement/EC/H2020/705402/EU/Efficient numerical methods for deformable porous media. Application to carbon dioxide storage./poro sos
Financiación: info:eu-repo/grantAgreement/ES/MICINN/MTM2013-40842-P

Tipo y forma: Artículo (Versión definitiva)

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