A general numerical procedure for solidification and melting in porous media and free fluids

A numerical model of the solid/liquid phase change problem in porous media and free fluids is presented in this paper for the first time by employing a modified version of the generalized porous medium model, in 2D and 3D, solved by means of the Characteristic-Based-Split (CBS) scheme. The proposed procedure is based on the solution of one set of equations to describe different phenomena: natural convection in porous media, solidification and melting both in porous media and in free fluids. The generalized model has been modified to incorporate the apparent heat capacity, source term and pseudo-viscosity methods in order to reproduce phase change phenomena.Two versions of the algorithm, the Semi-Implicit (SI) and the Quasi-Implicit (QI) schemes, have been developed to solve the governing equations, and validated against numerical and experimental data available in the literature. The two schemes have been compared in terms of accuracy and efficiency for the solution of the benchmark problems.