Precise integration boundary element method for solving dual phase change problems based on the effective heat capacity model

Abstract

Abstract A precise integration boundary element method based on the effective heat capacity model is proposed to solve dual phase change problems in this paper. The effective heat capacity model treated the entire domain of the phase change problem as one continuous medium. Therefore a unified governing equation can be established in the entire domain which includes the solid phase and the liquid phase. Then, the radial integration method is applied to transform the domain integrals into the boundary integrals to obtain the integral equation where only boundary integrals are involved. Since the effective heat capacity is dependent on temperature the differential equations obtained by the boundary element method are nonlinear. In order to solve these nonlinear differential equations and to determine the temperature field, the predictor-corrector precise integration method is needed. Finally, the phase change interface positions are obtained by interpolation of the temperature field. Several numerical examples are presented to verify the validity and accuracy of the proposed method.