Geometrical interpretation of the multi-point flux approximationL-method

摘要

In this paper, we first investigate the influence of different Dirichlet boundary discretizations on the convergence rate of the multi-point flux approximation (MPFA) L-method by the numerical comparisons between the MPFA O- and L-method, and show how important it is for this new method to handle Dirichlet boundary conditions in a suitable way. A new Dirichlet boundary strategy is proposed, which in some sense can well recover the super-convergence rate of the normal velocity. In the second part of the work, the MPFA L-method with homogeneous media is studied. A systematic concept and geometrical interpretations of the L-method are given and illustrated, which yield more insight into the L-method. Finally, we apply the MPFA L-method for two-phase flow in porous media on different quadrilateral grids and compare its numerical results for the pressure and saturation with the results of the two-point flux approximation method.