Numerical simulation of convection/diffusion phase change problems - a review

A review of numerical techniques for the solution of heat and mass transfer problems with solid/liquid phase change is presented. The mathematical model for a description of a thermal field is based on the conventional Stefan approximation for the evaluation of phase change and the Navier-Stokes equations in the Boussinesq approximation for convective flows of a melt. Two basic approaches for the solution of these problems with a free boundary (phase change interface) are considered. The first approach is connected with interface-fitting algorithms (referred to in the work as variable grid methods), the second one with interface-smearing (fixed grid) methods. Fixed grid methods for the investigation of hydrodynamical phenomena in a varying calculation domain are constructed using various modifications of a penalty method.