Positivity-preserving DDFV scheme for the compressible two-phase Darcy flow in porous media - Thomas Crozon (Inria Lille)

I will  present a part of my work thesis. We are interested in making good approximations of solutions to the compressible two-phase Darcy flows in porous media. It usually describes the flow of gas/oil and water in sedimentary basins with a system of two coupled parabolic equations with degenerate mobilities. We propose a DDFV discretization in 2d, allowing the use of very general meshes. The proposed scheme guarantees the physical bounds of the approximated quantities and provides energy estimates such that one can benefit of compactness theorems to establish the convergence of the discrete solutions. Finally, we display our numerical results.