Finite volume method for coupled subsurface flow problems, II: Poroelasticity

Abstract

The article introduces a cell-centered finite-volume method for the Biot problem in heterogeneous anisotropic media, characterized with full-tensor properties. We derive the expression for the coupled flux and the interpolation method across the discontinuity of the properties. The obtained flux expression consists of a two-point part, a transversal part and an additional contribution due to gravity. The interpolation method is the generalization of the harmonic averaging point concept to coupled problems. The method is stable despite collocation of both pressure and displacement at cell centers due to eigensplitting of the matrix coefficients in the flux expression and upstream approximation. A general type of boundary condition is integrated without introduction of auxiliary degrees of freedom. Our flux discretization method is a realization of our more general concept of stable flux discretization for saddle-point systems with vector of several unknowns. We demonstrate the applicability of the method on a set of challenging numerical benchmarks.