Geodesic
The generalized finite volume SUSHI scheme for the discretization of the peaceman model
Applications of Mathematics, Tome 66 (2021) no. 1, pp. 115-143.

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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.
DOI : 10.21136/AM.2020.0122-19
Classification : 65M08, 65N30, 76M10, 76M12, 76R99, 76S05
Keywords: porous medium; nonconforming grid; finite volume scheme; a priori estimate; miscible fluid flow 
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Mandari, Mohamed; Rhoudaf, Mohamed; Soualhi, Ouafa. The generalized finite volume SUSHI scheme for the discretization of the peaceman model. Applications of Mathematics, Tome 66 (2021) no. 1, pp. 115-143. doi : 10.21136/AM.2020.0122-19. http://geodesic.mathdoc.fr/articles/10.21136/AM.2020.0122-19/

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