Numerical analysis of a SUSHI scheme for an elliptic-parabolic system modeling miscible fluid flows in porous media - Soualhi, Ouafa; Mandari, Mohamed; Rhoudaf, Mohamed (European Journal of Computational Mechanics, 2020)
In this paper, we prove the convergence of a schema using stabilisation and hybrid interfaces of 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.