Modified Multiscale Finite-Element Method for Solving Groundwater Flow Problem in Heterogeneous Porous Media

Abstract

The purpose of this paper is to modify the multiscale finite-element method (MSFEM) to solve groundwater flow problems in heterogeneous porous media, such as large-scale problems, long-term prediction problems, and nonlinear problems. The MSFEM has been developed to deal with flows in heterogeneous porous media. Many practical works and numerical simulations have been done to show its accuracy. However, for the large-scale or long-term prediction problems, the MSFEM needs a great amount of computational cost in constructing base functions, which is not efficiency. The primary feature of our modified MSFEM (MMSFEM) is to use a new coarse element subdivision to reduce the number of the interior nodes, thus to decrease the unknowns in the reduced elliptic problems to save much computational cost while ensuring computational accuracy. Some numerical experiments in this paper indicate that the MMSFEM can reduce more than 90% of CPU time of the MSFEM.