Mathematical Simulation of a Heat Transfer Process in Phase Change Materials

Abstract

In the paper, we present a computational scheme for mathematical simulation of heat transfer processes in phase-changing multiscale media. In this problem, the correct approximation of heat flux jumps on phase transition boundaries is the main difficulty. Our approach is based on using a nonconforming multiscale finite element method to solve Stefan’s problem. We propose to divide a solution of Stefan’s problem into two components. A discontinuous component is determined in phase transition zones (fine level). The discontinuous component is approximated by a discontinuous Galerkin method. A continuous component is determined everywhere (coarse level). The continuous component is approximated by the classic finite element method. In this approach, a discrete analogue of Stefan’s problem can be solved in parallel. For the correct approximation of the heat flux jump on the phase transition boundary, we introduce a special lifting operator in the variational formulation of the multiscale discontinuous Galerkin method. Results of verification procedure for the developed computational scheme are shown using Stefan’s problem with the analytical solution. A validation procedure is performed using a comparative analysis of mathematical simulation results with physical experimental data. In the physical experiment, a phase change material sample was heated. At discrete time moments, the temperature was recorded using a sensor. We performed the mathematical simulation of the heat transfer process in the phase change material sample using experiment conditions. The difference between the calculated temperature field and physical experiment data was less than 5%.