Numerical simulation of natural convection in a freezing soil

A mathematical model and a numerical method for solving the natural convection and crystallization of pore moisture were considered. The mathematical model contains partial differential equations for temperature, velocity, and pressure. The fluid flow, under the assumption of low velocities, was described by the Stokes equations, where the phase transition of the liquid into ice was taken into account using the fictitious domain method by introducing an additional term responsible for the flow in frozen ground with a low permeability coefficient. The discontinuous finite element method on unstructured computational meshes was used for the numerical solution of the problem of modeling a multiphysical process in complex geometric domains. The fictitious domain method for the flow problem enables to carry out calculations on a fixed computational grid. The results of the numerical solution of the two-dimensional problem for three test geometric domains were presented.