A NUMERICAL-METHOD FOR PHASE-CHANGE PROBLEMS WITH CONVECTION AND DIFFUSION

An existing finite-difference formulation, which uses immobilization of the moving interface while preserving the conservative form of the equations, is extended here to include convection and volume change. In this two-dimensional treatment, the physical boundaries are allowed to move in both coordinate directions. This is done by using a novel technique that discretizes the pseudo-velocities (arising from the immobilization) according to the geometrical relation associated with the moving control-volumes. As a result, the pseudo-velocity fields independently satisfy the mass continuity. This makes the present numerical method suitable for both diffusion- and convection/diffusion-controlled moving boundary problems. In the solution of the momentum equations, the physical covariant velocity components are selected as the dependent variables and the SIMPLER algorithm is employed for the coupling between the continuity and the momentum equations. The method is applicable to problems with multiple, moving interfaces. As an illustrative example, melting in a two-dimensional cavity is considered. The predictions are then compared with the available experimental results and good agreements are found.