A New High Order Mathematical Model for Calculating the Energy Conservation Equation

Abstract

The Explicit Finite Difference (EFD) method is used for calculating the energy conservation equation during solidification. In order to improve the computational efficiency, the equivalent specific heat method is adopted to calculate the latent heat and the high order Alternating Direction Implicit (ADI) method is also applied, which is fourth order in space and second order in time. The degree of similarity between the simulation results and experimental results is analyzed quantitatively by the Hamming Distance (HD) for the first time, and results show that this high order mathematical model based on the equivalent specific heat method and the high order ADI method is faster and more accurate than the EFD method.