Generalized multiscale discontinuous Galerkin method for solving the heat problem with phase change

In this work, we consider a numerical solution of a heat transfer problem with phase change in heterogeneous domains. For simulation of heat transfer processes with phase transitions, we use a classic Stefan model. Computational implementation is based on generalized multiscale discontinuous Galerkin method (GMsDGM). In this method the interior penalty discontinuous Galerkin method is used for the global coupling on a coarse grid. The main idea of these methods is to construct a small dimensional local solution space that can provide an efficient calculation on coarse grid level. We present numerical results for different geometries to demonstrate an accuracy of the method.