A second-order decoupled energy stable numerical scheme for Cahn-Hilliard-Hele-Shaw system
A second-order decoupled energy stable numerical scheme for Cahn-Hilliard-Hele-Shaw system
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DOI：
10.1016/j.apnum.2020.06.010
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发表时间：
2020-11
影响因子：
2.8
通讯作者：
Yali Gao;Rui Li;Liquan Mei;Yanping Lin
中科院分区：
文献类型：
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作者：
Yali Gao;Rui Li;Liquan Mei;Yanping Lin
本文针对Cahn-Hilliard-Hele-Shaw系统，提出了一种新的时间二阶、解耦、能量稳定的有限元格式。引入标量辅助变量法的思想来处理非线性整体问题。采用算子分裂策略对耦合的Cahn-Hilliard方程和Darcy方程进行完全解耦。在Galerkin有限元框架下建立了完全离散。严格建立了数值解的唯一可解性和能量守恒律。通过数值实验，说明了所设计的数值方法的特点，验证了理论结果，并进行了实际应用。
In this paper, we develop a novel second order in time, decoupled, energy stable finite element scheme for simulation of Cahn-Hilliard-Hele-Shaw system. The idea of scalar auxiliary variable approach is introduced to handle the nonlinear bulk. An operator-splitting strategy is utilized to fully decouple the coupled Cahn-Hilliard equation and Darcy equation. A full discretization is built in the framework of Galerkin finite element method. The unique solvability of numerical solution and preservation of energy law are rigorously established. Numerical experiences are recorded to illustrate the features of the designed numerical method, verify the theoretical results and conduct realistic applications.