Conservative scheme for the thermodiffusion Stefan problem

We suggest further development of the principle of conservation for problems with moving boundaries. Using the problem of phase transitions in binary compounds as an example, we demonstrate a technique for constructing divergence and nondivergence finite difference schemes guaranteeing that the energy and mass conservation laws hold in the discrete model. In a class of front tracking methods, we prove the equivalence of the approach based on the use of moving grids with that based on a dynamic change of variables which permits one to solve the problem on a fixed grid.