A precise time-domain expanding boundary element method based on enthalpy formulation for non-isothermal phase change problems

Abstract

A precise time-domain expanding boundary element method (PTEBEM) based on the enthalpy formulation is developed for solving non-isothermal phase change problems in this paper. Assume that temperature and enthalpy are independent field variables, and expand all variables over a time period. This allows the variation of variables to be described more accurately and the nonlinear governing equation to transform into a linear recursive form. Subsequently the boundary element method (BEM) is employed to solve recursive problems based on a fixed grid, and the radial integration method (RIM) is used to convert the resulting domain integrals into equivalent boundary integrals. In the recursive solution process, temperature and enthalpy are connected through the relationship between the two. Finally, a self-adaptive computation criterion is proposed to ensure sufficient computational accuracy. The phase change interfaces can be given by interpolation of the temperature field. No additional nonlinear iterations are required throughout the simulation. The calculation results are satisfactory and prove the accuracy and robustness of the proposed method.