修正相场晶体(MPFC)模型的二阶无条件能量稳定数值格式

A Second-Order Unconditional Energy Stable Numerical Scheme for the MPFC Model

本文研究修正的相场晶体(MPFC)方程的二阶无条件能量稳定数值格式.首先,利用标量辅助变量(SAV)法和二阶向后欧拉(BDF2)公式,得到了一个数值格式;其次,给出了能量耗散定律,严格证明了该数值格式是质量守恒的,唯一可解的,无条件能量稳定的;最后,通过数值实例验证了格式的精度和稳定性.

In this paper,a second-order unconditional energy stable numerical scheme for MPFC model is studied.Firstly,a numerical scheme is obtained by using SAV approach and BDF2 formula.Secondly,the law of energy dissipation is given.The mass conservation,unique solvability and the unconditional energy stability of the numerical scheme are rigorously proved.Finally,the numerical accuracy and the energy stability of the scheme are verified by various numerical experiments.