On Heat Conduction with Phase Change: Accurate Explicit Numerical Method

The one phase Stefan problem is discussed using the Goodman HBI method and an explicit numerical method including modified boundary immobilization scheme. The main advantage of the HBI method lie in the remarkable association of simplicity, flexibility and acceptable accuracy which an error less than 2.5% in predicting the moving front location for Stefan number less than unity which covers most usual isothermal phase change material. An accurate explicit numerical model to track the moving front in Stefan-like problems is provided. The scheme is obtained using the variable space step method based on variable domain. The method is developed using central difference approximations to replace spatial and temporal derivatives. Furthermore, iterative procedure, in numerical calculation, is avoided by introducing simple assumptions. The numerical results show that the accuracy of the method has been considerably improved without additional computational cost.