A defect correction technique for the MPFA-H scheme in single-phase heterogeneous and anisotropic flow problems media

Resumo

The numerical simulation of fluid flow in porous media is a technical tool of fundamental importance in the oil industry and a significant challenge for numerical algorithms. Standard reservoir simulators use the classical Two-Point Flow Approximation (TPFA) technique to discretize diffusive fluxes. However, it fails to give proper results for complex reservoirs with highly anisotropic and heterogeneous media and does not allow the use of unstructured meshes. It is essential to adopt efficient numerical methods and computational strategies to overcome such limitations and optimize the numerical simulations of these flows. In this context, the cell-centered Multipoint Flux Approximation with Harmonic Points (MPFA-H) method is a robust and accurate alternative. Furthermore, enforcing the discrete maximum principle (DMP) is essential to avoid non-physical extremes, such as negative pressures or saturations. In our work, we investigated and implemented a slope limiting coupled with MPFA-H to impose these conditions. Finally, we evaluate benchmark problems extracted from the literature to verify our implementation.