Numerical simulation of melting in two-dimensional cavity using adaptive grid

This paper presents a numerical simulation of melting of chemically pure material in two-dimensional square cavity. A single-domain model is used which does not require interface tracking and allows the use of a fixed grid in order to solve governing transport equations. However, a fully conservative control volume method, using r-adaptive moving grid, is implemented to enhance the precision. Simple, user-defined function is introduced to control the density of the grid generated with a robust elliptic generator. The simulation is tested extensively on a one-dimensional phase change problem which enables the comparison of the results with a existing analytical solution. Finally, the method is assessed on cases corresponding to melting of tin and octadecane driven by natural convection.