Cahn-Hilliard-Brinkman方程的二阶全解耦的线性格式

Fully-decoupled Linear BDF2 Scheme for the Cahn-Hilliard-Brinkman System

本文研究Cahn-Hilliard-Brinkman方程的数值求解方法.首先,基于二阶后向差分公式和标量辅助变量法,构造一个高效的,线性的,完全解耦的数值格式.其次,对新的方程在时间上采用二阶BDF格式离散.通过解耦技术,在每个时间步长上只需要求解一系列的常数系数方程.然后应用理论分析证明了二阶离散格式的无条件能量稳定.最后通过数值测试验证了理论部分的有效性和准确性.

In this paper,we study the numerical approximation of the Cahn-Hilliard-Brinkman model.Firstly,we construct an efficient,linear and fully-decoupled numerical scheme based on the second-order backward differentiation formula,which combines two types of scalar auxiliary variable approaches.Here,one of the variables is used to linearize the phase field function,and the other is added to the nonlinear and coupling terms which satisfy the so-called“zero-energy-contribution”property.Secondly,the process of detail implementation is given by using decoupling techniques,which only require solving a few constant-coefficient equations at each time step.Then,the solvability of the constructed scheme and its unconditional stability in energy are proved rigorously.Finally,numerical experiments are also carried out to demonstrate the accuracy and efficiency of the scheme.