Mass Lumping for MHFEM in Two Phase Flow Problems in Porous Media

Abstract

This work deals with testing of the Mixed-Hybrid Finite Element Method (MHFEM) for solving two phase flow problems in porous media. We briefly describe the numerical method, it’s implementation, and benchmark problems. First, the method is verified using test problems in homogeneous porous media in 2D and 3D. Results show that the method is convergent and the experimental order of convergence is slightly less than one. However, for the problem in heterogeneous porous media, the method produces oscillations at the interface between different porous media and we demonstrate that these oscillations are not caused by the mesh resolution. To overcome these oscillations, we use the mass lumping technique which eliminates the oscillations at the interface. Tests on the problems in homogeneous porous media show that although the mass lumping technique slightly decreases the accuracy of the method, the experimental order of convergence remains the same.