Monolithic multigrid method for the coupled stokes flow and deformable porous medium system
Resumen: The interaction between fluid flow and a deformable porous medium is a complicated multi-physics problem, which can be described by a coupled model based on the Stokes and poroelastic equations. A monolithic multigrid method together with either a coupled Vanka smoother or a decoupled Uzawa smoother is employed as an efficient numerical technique for the linear discrete system obtained by finite volumes on staggered grids. A specialty in our modeling approach is that at the interface of the fluid and poroelastic medium, two unknowns from the different subsystems are defined at the same grid point. We propose a special discretization at and near the points on the interface, which combines the approximation of the governing equations and the considered interface conditions. In the decoupled Uzawa smoother, Local Fourier Analysis (LFA) helps us to select optimal values of the relaxation parameter appearing. To implement the monolithic multigrid method, grid partitioning is used to deal with the interface updates when communication is required between two subdomains. Numerical experiments show that the proposed numerical method has an excellent convergence rate. The efficiency and robustness of the method are confirmed in numerical experiments with typically small realistic values of the physical coefficients.
Idioma: Inglés
DOI: 10.1016/j.jcp.2017.09.062
Año: 2018
Publicado en: JOURNAL OF COMPUTATIONAL PHYSICS 353 (2018), 148-168
ISSN: 0021-9991

Financiación: info:eu-repo/grantAgreement/ES/DGA/PDIE
Financiación: info:eu-repo/grantAgreement/EUR/H2020/Marie Sklodowska-Curie-705402-POROSOS
Financiación: This project has received funding from the European Union’s Horizon 2020 research and innovation program under grant agreement No H2020 Marie Sklodowska-Curie-705402-POROSOS
Financiación: info:eu-repo/grantAgreement/ES/MICINN/MTM2016-75139-R
Tipo y forma: Artículo (PostPrint)
Área (Departamento): Área Matemática Aplicada (Dpto. Matemática Aplicada)

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