Multiscale simulation of the heat and mass transfer with Brinkman model

Abstract

In this work, we consider a heat and mass transfer problem in heterogeneous media. Mathematical model is described by a system of equations for temperature, pressure and velocity. For simulations of the flow problem in domain with low permeable obstacles, we use a Brinkman model. Fine grid approximation is constructed based on the discontinuous Galerkin (IPDG) method for heat transfer and flow problems. For coarse grid approximation of the flow problem, we use a Generalized Multiscale Discontinuous Galerkin Method. Numerical results are presented for a two-dimensional model problem with different number of the multiscale basis functions.