Multiscale Mortar Mixed Finite Elements for Multiphase Flow in Porous Media

We present a multiscale mortar mixed finite element method for multiphase flow in porous media. The method is based on a domain decomposition (or coarse grid). Mass balance equations in matching fine grids of scale h, while continuity of fluxes is imposed via mortar finite elements on a coarse scale H. Higher order mortar spaces on appropriately chosen coarse interface grids are used to provide optimal fine scale convergence. For example, for the lowest order Raviart-Thomas mixed method or cell-centered finite differences, a choice of H = O(sqrt h) and quadratic mortars gives O(h) convergence for both the pressure and the velocity. The nonlinear algebraic system in a fully implicit discretization is solved via a non- overlapping domain decomposition algorithm, which reduces the global problem to an interface problem for one pressure and one saturation. Computational experiments for oil-water displacement in highly heterogeneous media illustrate the efficiency of the multiscale mortar formulation versus the single-scale<br>approach.