Positivity-preserving DDFV scheme for compressible two-phase flow in porous media

Abstract

We propose a Positivity-Preserving Discrete Duality Finite Volume (PP-DDFV) to approximate solutions to immiscible compressible two-phase Darcy flow in porous media. This method allows us to treat the case with the volumetric mass depending on their own pressure, with no major limitations on the mesh and permeability tensor. The originality of our approach lies in the upwind mobility term in the normal discretization combined with minimum mobility in the tangential cross term. Using the mobility degeneracy we prove a bound preservation on the discrete saturations. In the second place, it gives us a coercivity-like property allowing retrieving energy estimates on the approximate solutions. We discuss the main ideas for the existence of solutions. Then, we present numerical tests to exhibit our scheme's efficiency and good behavior.