On novel linear schemes for the Cahn-Hilliard equation based on an improved invariant energy quadratization approach

被引：7

作者：

Chen, Rui ^{[1
]}

Gu, Shuting ^{[2
]}

机构：

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

[2] Shenzhen Technol Univ, Coll Big Data & Internet, Shenzhen 518118, Peoples R China

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2022年 / 414卷

关键词：

Cahn-Hilliard equation; Energy stability; Improved invariant energy quadratization; PHASE-FIELD MODEL; 2-PHASE INCOMPRESSIBLE FLOWS; FINITE-DIFFERENCE SCHEME; STABLE NUMERICAL SCHEMES; BEAM EPITAXY MODEL; THIN-FILM MODEL; GROWTH-MODEL; ALLEN-CAHN; 2ND-ORDER; EFFICIENT;

D O I：

10.1016/j.cam.2022.114405

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we present two fully discrete time-marching schemes including the first order and the second order schemes for the Cahn-Hilliard equation. The proposed method is based on an improved "Invariant Energy Quadratization"method. Here are two distinct features: (i) the two schemes are linear and energy stable for the original energy; (ii) the well-posedness and energy stability of the discrete problems are proven. Extensive numerical experiments are carried out to verify the convergence, the robustness and the energy stability of such schemes. (c) 2022 Elsevier B.V. All rights reserved.

引用

页数：18

共 56 条

[1] Finite element approximation of nematic liquid crystal flows using a saddle-point structure [J].

Badia, Santiago ;

Guillen-Gonzalez, Francisco ;

Vicente Gutierrez-Santacreu, Juan .

JOURNAL OF COMPUTATIONAL PHYSICS, 2011, 230 (04) :1686-1706

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

CAHN, JW ;

HILLIARD, JE .

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

[3] Efficient numerical scheme for a dendritic solidification phase field model with melt convection [J].

Chen, Chuanjun ;

Yang, Xiaofeng .

JOURNAL OF COMPUTATIONAL PHYSICS, 2019, 388 :41-62

[4] A Novel Second-Order Scheme for the Molecular Beam Epitaxy Model with Slope Selection [J].

Chen, Lizhen ;

Zhao, Jia ;

Gong, Yuezheng .

COMMUNICATIONS IN COMPUTATIONAL PHYSICS, 2019, 25 (04) :1024-1044

[5] Regularized linear schemes for the molecular beam epitaxy model with slope selection [J].

Chen, Lizhen ;

Zhao, Jia ;

Yang, Xiaofeng .

APPLIED NUMERICAL MATHEMATICS, 2018, 128 :139-156

[6] DECOUPLED, ENERGY STABLE SCHEME FOR HYDRODYNAMIC ALLEN-CAHN PHASE FIELD MOVING CONTACT LINE MODEL [J].

Chen, Rui ;

Yang, Xiaofeng ;

Zhang, Hui .

JOURNAL OF COMPUTATIONAL MATHEMATICS, 2018, 36 (05) :661-681

[7] SECOND ORDER, LINEAR, AND UNCONDITIONALLY ENERGY STABLE SCHEMES FOR A HYDRODYNAMIC MODEL OF SMECTIC-A LIQUID CRYSTALS [J].

Chen, Rui ;

Yang, Xiaofeng ;

Zhang, Hui .

SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2017, 39 (06) :A2808-A2833

[8] Decoupled energy stable schemes for phase-field vesicle membrane model [J].

Chen, Rui ;

Ji, Guanghua ;

Yang, Xiaofeng ;

Zhang, Hui .

JOURNAL OF COMPUTATIONAL PHYSICS, 2015, 302 :509-523

[9] Energy stable higher-order linear ETD multi-step methods for gradient flows: application to thin film epitaxy [J].

Chen, Wenbin ;

Li, Weijia ;

Wang, Cheng ;

Wang, Shufen ;

Wang, Xiaoming .

RESEARCH IN THE MATHEMATICAL SCIENCES, 2020, 7 (03)

[10] A stabilized second order exponential time differencing multistep method for thin film growth model without slope selection [J].

Chen, Wenbin ;

Li, Weijia ;

Luo, Zhiwen ;

Wang, Cheng ;

Wang, Xiaoming .

ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 2020, 54 (03) :727-750

← 1 2 3 4 5 6 →