Numerical modeling of thermal stabilization of filter ground

We consider the numerical simulation of the thermal stabilization (artificial freezing) filter soil around the base of the mine. Mathematical model based on the classical model of Stephen, which describes the process of heat transfer with phase change with the filter in a porous medium, and the system of equations for the temperature and pressure. Fictitious domain method is used for numerical solution of the resulting problem. Discretization of the system of equations is the finite element method, which is implemented in a software package FEniCSon high performance computing clusters. The numerical results are given and discussed.