Second-order, fully decoupled, linearized, and unconditionally stable scalar auxiliary variable schemes for Cahn-Hilliard-Darcy system
Second-order, fully decoupled, linearized, and unconditionally stable scalar auxiliary variable schemes for Cahn-Hilliard-Darcy system
复制标题
Cahn-Hilliard-Darcy 系统的二阶、完全解耦、线性化、无条件稳定标量辅助变量格式
DOI：
10.1002/num.22829
复制
发表时间：
2021
影响因子：
3.9
通讯作者：
Yufeng Nie
中科院分区：
文献类型：
--
作者：
Yali Gao;Xiaoming He;Yufeng Nie
本文利用标量辅助变量法建立了求解Cahn-Hilliard-Darcy方程组的全解耦数值方法。我们利用算子分裂技术来解耦耦合系统和Galerkin有限元方法在空间上构造完全离散的提法。所发展的数值方法具有二阶精度、完全解耦、线性化和无条件能量稳定等特点。严格证明了这两个解耦数值格式的无条件稳定性。大量的数值结果验证了所提出的数值方法的准确性和有效性。
In this paper, we establish the fully decoupled numerical methods by utilizing scalar auxiliary variable approach for solving Cahn–Hilliard–Darcy system. We exploit the operator splitting technique to decouple the coupled system and Galerkin finite element method in space to construct the fully discrete formulation. The developed numerical methods have the features of second order accuracy, totally decoupling, linearization, and unconditional energy stability. The unconditionally stability of the two proposed decoupled numerical schemes are rigorously proved. Abundant numerical results are reported to verify the accuracy and effectiveness of proposed numerical methods.