Adaptive simulations of two-phase flow by discontinuous Galerkin methods

In this paper we present and compare primal discontinuous Galerkin formulations of the two-phase flow equations. The wetting phase pressure and saturation equations are decoupled and solved sequentially. Proposed adaptivity in space and time techniques yield accurate and efficient solutions. Slope limiters valid on non-conforming meshes are also presented. Numerical examples of homogeneous and heterogeneous media are considered.