Analyzing Finite Volume for Single-Phase Flow in Porous Media

Abstract

Two-point finite volume methods (2P-FVMs) are extensively used for understanding porous media flow because these methods are fast and simple. In this article, we present numerical analysis of the two-point finite volume discretization of a pressure equation of a single-phase flowing in porous media. We present numerical problems with discontinuous permeability and diagonal permeability, together with Neumann and Dirichlet boundary conditions. An analysis of the effect of boundary conditions on the conditioning of the discrete systems is presented. We also analyze convergence of the 2P-FVM in various norms (L2 convergence for pressure and Darcy velocity and L∞ convergence for pressure) for problems with regularity H1+γ, for γ = 0.1, 0.2, ..., 0.9, 0.99.