On Numerical Methods Used in Mathematical Modeling of Phase Change in Liquid Metals

The work presents an analysis and comparative evaluation of different methods used for the numerical solution of heat conduction with phase change problems. Both freezing (melting) water as well as solidifying liquid metal problems are examined. Emphasis is placed on weak formulations as they tend to be simple to program and easily implemented in existing single-phase codes. A new method based on the apparent capacity technique is proposed. In this technique an “effective capacity” is computed, based on the integration of temperature profiles over the nodal volumes. This method shows significantly better performance when compared with other methods for the numerical analysis of solidifying metals.