A multi-scale discontinuous Galerkin method for mathematical modeling of heat conduction processes with phase transitions in heterogeneous media

We present results of mathematical modeling of the thermal conductivity process with phase transitions in heterogeneous media. For demonstrating the mathematical modeling results, we use a uniformly porous medium as an experimental sample. We suppose the sample matrix consists of sandstone and the pores are completely filled with a solid paraffin. When the sample is heated, the paraffin, in the pores, goes into the liquid phase. To solve the Stefan problem in a three-dimensional formulation, a computational scheme of a multi-scale discontinuous Galerkin method on tetrahedral finite elements is used. The algorithm for calculating the effective thermal conductivity is based on the solution of the thermal conductivity direct problem with phase transitions and Fourier's law. The effect of the molten paraffin volume concentration in the pores on the effective thermal conductivity is shown. (paper)