【摘要】 粘性Cahn-Hilliard方程被广泛应用于模拟自由界面运动,然而如何设计高效稳定的数值算法一直以来都是十分困难的.本文研究了粘性CahnHilliard方程的高效数值算法.通过引入标量辅助变量,本文提出了一系列新的数值算法.其次,针对方程的等价形式在时间离散上采用了一阶,二阶和高阶方法,并证明了数值格式是无条件能量稳定的.最后利用数值实验验证了该算法的准确性和有效性.更多还原

【Abstract】 In this paper, we consider numerical algorithms for the viscous Cahn-Hilliard equation. It has been well studied and broadly used to investigate the free interface motion. The main challenge is how to design efficient and stable numerical algorithms. By introducing scalar auxiliary variable, a new class of numerical algorithms are proposed to solve the viscous Cahn-Hilliard equation. The temporal discretizations are built upon the first-order, second-order and higher-order methods. All the proposed algorithms are rigorously proven to be unconditional energy stability. Various numerical simulations are presented to demonstrate the stability, accuracy, and efficiency of the proposed schemes.更多还原