Decoupled energy-law preserving numerical schemes for the Cahn-Hilliard-Darcy system

被引：25

作者：

Han, Daozhi ^{[1
]}

Wang, Xiaoming ^{[2
]}

机构：

[1] Indiana Univ, Dept Math, Bloomington, IN 47405 USA

[2] Florida State Univ, Dept Math, Tallahassee, FL 32306 USA

来源：

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS | 2016年 / 32卷 / 03期

基金：

美国国家科学基金会;

关键词：

Cahn-Hilliard-Darcy; convex-splitting; decoupling; energy-law; Hele-Shaw cell; long-time stability; porous medium; stability; two-phase flow; 2-PHASE INCOMPRESSIBLE FLOWS; DIFFUSE INTERFACE MODELS; LONG-TIME BEHAVIOR; HELE-SHAW CELL; STABLE SCHEMES; WELL-POSEDNESS; APPROXIMATION; RECONNECTION; SIMULATION; EQUATIONS;

D O I：

10.1002/num.22036

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study two novel decoupled energy-law preserving and mass-conservative numerical schemes for solving the Cahn-Hilliard-Darcy system which models two-phase flow in porous medium or in a Hele-Shaw cell. In the first scheme, the velocity in the Cahn-Hilliard equation is treated explicitly so that the Darcy equation is completely decoupled from the Cahn-Hilliard equation. In the second scheme, an intermediate velocity is used in the Cahn-Hilliard equation which allows for the decoupling. We show that the first scheme preserves a discrete energy law with a time-step constraint, while the second scheme satisfies an energy law without any constraint and is unconditionally stable. Ample numerical experiments are performed to gauge the efficiency and robustness of our scheme. (c) 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 936-954, 2016

引用

页码：936 / 954

页数：19

共 41 条

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