Efficient second-order, linear, decoupled and unconditionally energy stable schemes of the Cahn-Hilliard-Darcy equations for the Hele-Shaw flow

被引：1

作者：

Chen, Rui ^{[1
]}

Li, Yaxiang ^{[2
]}

Pan, Kejia ^{[3
]}

Yang, Xiaofeng ^{[4
]}

机构：

[1] Beijing Univ Posts & Telecommun, Sch Sci, Beijing 100876, Peoples R China

[2] Hunan First Normal Univ, Dept Math & Stat, Changsha 410205, Hunan, Peoples R China

[3] Cent South Univ, Sch Math & Stat, Changsha 410083, Peoples R China

[4] Univ South Carolina, Dept Math, Columbia, SC 29208 USA

来源：

NUMERICAL ALGORITHMS | 2023年 / 92卷 / 04期

基金：

中国国家自然科学基金; 美国国家科学基金会;

关键词：

Decoupled; Cahn-Hilliard-Darcy; Hele-Shaw; Invariant energy quadratization; Second-order; Unconditional energy stability; PHASE-FIELD MODEL; 2-PHASE INCOMPRESSIBLE FLOWS; DIFFUSE INTERFACE MODEL; NAVIER-STOKES EQUATIONS; TIME-STEPPING SCHEME; NUMERICAL SCHEMES; APPROXIMATIONS; RECONNECTION; SIMULATION; PINCHOFF;

D O I：

10.1007/s11075-022-01388-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider the numerical approximations for a hydrodynamical model of Cahn-Hilliard-Darcy equations. We develop two linear, decoupled, energy stable, and second-order time-marching schemes based on the "Invariant Energy Quadratization" method for nonlinear terms in the Cahn-Hilliard equation, and the projection method for the Darcy equations. Moreover, we prove the well-posedness of the linear system and their unconditional energy stabilities rigorously. We also construct a linear, decoupled, energy stable, and second-order time marching scheme by using the "Scalar Auxiliary Variable" method. Various numerical tests are presented to illustrate the stability and the accuracy of the numerical schemes and simulate the process of coarsening in binary fluid and investigate the effect of the rotating and the gravity on the Hele-Shaw cell in 2D and 3D.

引用

页码：2275 / 2306

页数：32

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