A Stable Arbitrarily High Order Time-Stepping Method for Thermal Phase Change Problems  

作　　者：Weiwen Wang Chuanju Xu 

机构地区：[1]School of Mathematical Sciences and Fujian Provincial Key Laboratory of MathematicalModeling and High Performance Scientific Computing,Xiamen University,Xiamen 361005,P.R.China.

出　　处：《Communications in Computational Physics》2023年第2期477-510,共34页计算物理通讯（英文）

基　　金：NSFC grant 11971408.

摘　　要：Thermal phase change problems are widespread in mathematics,nature,and science.They are particularly useful in simulating the phenomena of melting and solidification in materials science.In this paper we propose a novel class of arbitrarily high-order and unconditionally energy stable schemes for a thermal phase changemodel,which is the coupling of a heat transfer equation and a phase field equation.The unconditional energy stability and consistency error estimates are rigorously proved for the proposed schemes.A detailed implementation demonstrates that the proposed method requires only the solution of a system of linear elliptic equations at each time step,with an efficient scheme of sufficient accuracy to calculate the solution at the first step.It is observed from the comparison with the classical explicit Runge-Kutta method that the new schemes allow to use larger time steps.Adaptive time step size strategies can be applied to further benefit from this unconditional stability.Numerical experiments are presented to verify the theoretical claims and to illustrate the accuracy and effectiveness of our method.

关 键 词：Thermal phase change problem gradient flows unconditional energy stability auxiliary variable Runge-Kutta methods phase field 

分 类 号：O24[理学—计算数学]