A second-order decoupled energy stable numerical scheme for Cahn-Hilliard-Hele-Shaw system

被引：17

作者：

Gao, Yali ^{[1
]}

Li, Rui ^{[2
]}

Mei, Liquan ^{[3
]}

Lin, Yanping ^{[4
]}

机构：

[1] Northwestern Polytech Univ, Sch Math & Stat, Xian 710129, Shaanxi, Peoples R China

[2] Shaanxi Normal Univ, Sch Math & Informat Sci, Xian 710119, Shaanxi, Peoples R China

[3] Xi An Jiao Tong Univ, Sch Math & Stat, Xian 710049, Shaanxi, Peoples R China

[4] Hong Kong Polytech Univ, Dept Appl Math, Hung Hom, Hong Kong, Peoples R China

来源：

APPLIED NUMERICAL MATHEMATICS | 2020年 / 157卷

基金：

中国国家自然科学基金;

关键词：

Cahn-Hilliard-Hele-Shaw system; Scalar auxiliary variable approach; Second order in time; Energy stability; Finite element method; PHASE-FIELD MODEL; DISCONTINUOUS GALERKIN METHOD; TUMOR-GROWTH; ERROR ANALYSIS; SAV APPROACH; DARCY MODEL; ALLEN-CAHN; EFFICIENT; SIMULATION; TIME;

D O I：

10.1016/j.apnum.2020.06.010

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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. (C) 2020 IMACS. Published by Elsevier B.V. All rights reserved.

引用

页码：338 / 355

页数：18

共 58 条

[1] ENERGY-DECAYING EXTRAPOLATED RK-SAV METHODS FOR THE ALLEN-CAHN AND CAHN-HILLIARD EQUATIONS [J].

Akrivis, Georgios ;

Li, Buyang ;

li, Dongfang .

SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2019, 41 (06) :A3703-A3727

[2]

Backofen R, 2019, INT J NUMER ANAL MOD, V16, P192

[3] ON SPINODAL DECOMPOSITION [J].

CAHN, JW .

ACTA METALLURGICA, 1961, 9 (09) :795-801

[4] FREE ENERGY OF A NONUNIFORM SYSTEM .1. INTERFACIAL FREE ENERGY [J].

CAHN, JW ;

HILLIARD, JE .

JOURNAL OF CHEMICAL PHYSICS, 1958, 28 (02) :258-267

[5] A SECOND ORDER ENERGY STABLE SCHEME FOR THE CAHN-HILLIARD-HELE-SHAW EQUATIONS [J].

Chen, Wenbin ;

Feng, Wenqiang ;

Liu, Yuan ;

Wang, Cheng ;

Wise, Steven M. .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2019, 24 (01) :149-182

[6] Highly Efficient and Accurate Numerical Schemes for the Epitaxial Thin Film Growth Models by Using the SAV Approach [J].

Cheng, Qing ;

Shen, Jie ;

Yang, Xiaofeng .

JOURNAL OF SCIENTIFIC COMPUTING, 2019, 78 (03) :1467-1487

[7] MULTIPLE SCALAR AUXILIARY VARIABLE (MSAV) APPROACH AND ITS APPLICATION TO THE PHASE-FIELD VESICLE MEMBRANE MODEL [J].

Cheng, Qing ;

Shen, Jie .

SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2018, 40 (06) :A3982-A4006

[8] Cahn-Hilliard modeling of particles suspended in two-phase flows [J].

Choi, Young Joon ;

Anderson, Patrick D. .

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, 2012, 69 (05) :995-1015

[9]

Christlieb A., 2014, J CHEM PHYS, V257, P192

[10]

Ciarlet P. G., 2002, Stud. Math. Appl.

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