A local-global multiscale mortar mixed finite element method for multiphase transport in heterogeneous media

Abstract

In this paper, we propose a local-global multiscale mortar mixed finite element method (MMMFEM) for multiphase transport in heterogeneous media. It is known that, in the efficient numerical simulations of this problem, one important step is a fast solution of the pressure equation, which is required to be solved in each time step. Thus, some types of efficient numerical methods, such as multiscale methods, are crucial for this problem. To present our main concepts, we take the two-phase flow system as an example. In our proposed method, the pressure equation is solved via the multiscale mortar mixed finite element method. Using this approach, a mass conservative velocity field can be obtained. Next, we use an explicit finite volume method to solve the saturation equation. The key ingredient of our proposed method is the choice of mortar space for the MMMFEM. We will use both polynomials and multiscale basis functions to form the coarse mortar space. The multiscale basis functions used are the restriction of the global pressure field obtained at the previous time step on the coarse interface. To initialize the simulations, we solve the pressure equation on the fine grid. We will present several numerical experiments on some benchmark 2D and 3D heterogeneous models to show the excellent performance of our method.