A free-energy stable nodal discontinuous Galerkin approximation with summation-by-parts property for the Cahn-Hilliard equation

被引：16

作者：

Manzanero, Juan ^{[1
,2
]}

Rubio, Gonzalo ^{[1
,2
]}

Kopriva, David A. ^{[3
,4
]}

Ferrer, Esteban ^{[1
,2
]}

Valero, Eusebio ^{[1
,2
]}

机构：

[1] Univ Politecn Madrid, Sch Aeronaut, ETSIAE, Plaza Cardenal Cisneros 3, E-28040 Madrid, Spain

[2] Univ Politecn Madrid, Ctr Computat Simulat, Campus Montegancedo, Madrid 28660, Spain

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

[4] San Diego State Univ, Computat Sci Res Ctr, San Diego, CA 92182 USA

来源：

JOURNAL OF COMPUTATIONAL PHYSICS | 2020年 / 403卷 / 403期

关键词：

Cahn-Hilliard; Summation-by-parts property; High-order methods; Discontinuous Galerkin; SPECTRAL ELEMENT DISCRETIZATION; SCHEMES;

D O I：

10.1016/j.jcp.2019.109072

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

We present a nodal Discontinuous Galerkin (DG) scheme for the Cahn-Hilliard equation that satisfies the summation-by-parts simultaneous-approximation-term (SBP-SAT) property. The latter permits us to show that the discrete free-energy is bounded, and as a result, the scheme is provably stable. The scheme and the stability proof are presented for general curvilinear three-dimensional hexahedral meshes. We use the Bassi-Rebay 1 (BR1) scheme to compute interface fluxes, and a first order IMplicit-EXplicit (IMEX) scheme to integrate in time. We provide a semi-discrete stability study, and a fully-discrete proof subject to a positivity condition on the solution. Lastly, we test the theoretical findings using numerical cases that include two and three-dimensional problems. (C) 2019 Elsevier Inc. All rights reserved.

引用

页数：25

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