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Mandari, Mohamed; Rhoudaf, Mohamed; Soualhi, Ouafa

The generalized finite volume SUSHI scheme for the discretization of the Peaceman model. (English) Zbl 07332692

Appl. Math., Praha 66, No. 1, 115-143 (2021).
Summary: We demonstrate some a priori estimates of a scheme using stabilization and hybrid interfaces applying to partial differential equations describing miscible displacement in porous media. This system is made of two coupled equations: an anisotropic diffusion equation on the pressure and a convection-diffusion-dispersion equation on the concentration of invading fluid. The anisotropic diffusion operators in both equations require special care while discretizing by a finite volume method SUSHI. Later, we present some numerical experiments.

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
76M12 Finite volume methods applied to problems in fluid mechanics
76S05 Flows in porous media; filtration; seepage
76R99 Diffusion and convection
65M08 Finite volume methods for initial value and initial-boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs

Keywords:

porous medium; nonconforming grid; finite volume scheme; a priori estimate; miscible fluid flow
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\textit{M. Mandari} et al., Appl. Math., Praha 66, No. 1, 115--143 (2021; Zbl 07332692)
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References:

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