A monotone finite volume scheme for single phase flow with reactive transport in anisotropic porous media

Abstract

This paper deals with development and analysis of a finite volume scheme for a nonlinear parabolic equation modeling a single phase flow with reactive solute transport, including equilibrium sorption, in heterogeneous porous media. We present a second-order, finite volume scheme by combining a nonlinear two point flux approximation for the diffusion term, and an upwind method for the advective term on unstructured meshes. It is shown that, under a CFL condition, this scheme ensures the non-negativity of the discrete solution, taking into account the anisotropy and heterogeneity of the domain. The existence of a solution for the discrete nonlinear system is studied, and the convergence of a fixed point method is proved. Our theoretical results are illustrated by numerical simulations in a bidimensional domain, in particular we show the second-order convergence rate for the numerical solution and confirm the monotonicity of the scheme.