An Adaptive Hybrid Numerical Approach for Solving Two-Phase Flow in Rigid Porous Media

Multiphase flows in porous media are central to a wide range of natural and industrial processes.
The spatial discretization for transport problems in heterogeneous porous media requires local mass
conservative methods. Finite volume (FV) methods are often used for two-phase flow, but they
suffer from grid orientation effects and are unfavorable with discontinuous coefficients. On the
other hand, DG methods result in a larger linear system to solve at every time step but do not
suffer from grid orientation effects. DG methods are flexible for general geometry, hp adaptivity,
and resolve discontinuous coefficients to a higher degree of accuracy.