Adaptive Mesh Refinement Based on Finite Analytical Method for Two‐Dimensional Flow in Heterogeneous Porous Media

Abstract

In this work, we improve the traditional adaptive mesh refinement (AMR) by combining it with the finite analytical method (FAM) to solve the multiphase flow in heterogeneous porous media numerically. The FAM can provide rather accurate internodal transmissibility, and it is employed to improve the accuracy of coarsening and refining processes in AMR. The high performance of the proposed AMR‐FAM is indicated through numerical tests for solving the two‐phase flow in 2D heterogeneous media. The numerical simulation results indicate that the proposed AMR‐FAM is more accurate than the traditional AMR‐FAM. Compared with the simulation in the original fine grids, the proposed AMR‐FAM can provide nearly the same results. Moreover, the computational cost in the AMR grids is only approximately one‐third of the cost in the original fine grids according to our numerical tests.