The Explicit-Implicit-Null method: Removing the numerical instability of PDEs

被引：37

作者：

Duchemin, Laurent ^{[1
]}

Eggers, Jens ^{[2
]}

机构：

[1] Aix Marseille Univ, CNRS, Cent Marseille, IRPHE UMR 7342, F-13384 Marseille, France

[2] Univ Bristol, Dept Math, Bristol BS8 1TW, Avon, England

来源：

JOURNAL OF COMPUTATIONAL PHYSICS | 2014年 / 263卷

关键词：

Stiff set of partial differential equations; Kuramoto-Sivashinsky; Hele-Shaw; Birkhoff-Rott integral; Surface tension; DIFFERENTIAL-EQUATIONS;

D O I：

10.1016/j.jcp.2014.01.013

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

A general method to remove the numerical instability of partial differential equations is presented. Two equal terms are added to and subtracted from the right-hand side of the PDE: the first is a damping term and is treated implicitly, the second is treated explicitly. A criterion for absolute stability is found and the scheme is shown to be convergent. The method is applied with success to the mean curvature flow equation, the Kuramoto-Sivashinsky equation, and to the Rayleigh-Taylor instability in a Hele-Shaw cell, including the effect of surface tension. (C) 2014 Elsevier Inc. All rights reserved.

引用

页码：37 / 52

页数：16

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