Special Session 108: New Developments in porous media

Some new approaches to simulating two-phase flow in porous media on hexahedral meshes

Todd Arbogast
University of Texas at Austin
Co-Author(s):    Maicon Correa, Chieh-Sen Huang, Zhen Tao, and Xikai Zhao
Subsurface geology often dictates that relatively general hexahedral computational meshes be used when simulating flow in porous media. The equations of two-phase flow divides into a parabolic pressure equation for the flow and a degenerate parabolic (convection-diffusion) saturation equation for the transport. We present three new approaches. (1) The elliptic part of both equations is often approximated using mixed finite elements, which are defined by mapping from a reference cube using the Piola transformation. This destroys the approximation properties of the method. We describe a new family of finite elements (AC elements) that overcomes the problem. (2) The saturation equation exhibits degeneracy in its elliptic diffusion term due to loss of capillarity when a phase is lost. We present a new mixed formulation that is stable when approximating degeneracies. It is suitable for approximation with the new AC elements. (3) The convection part of the saturation equation is often approximated, for example, using discontinuous Galerkin (DG) methods, since DG can handle general meshes. Traditional WENO methods are very accurate but restricted to rectangular meshes. We present a new approach using high order WENO reconstructions on logically rectangular meshes.