Finite volume methods for unidirectional dispersive wave models

被引：38

作者：

Dutykh, D. ^{[1
]}

Katsaounis, Th. ^{[2
,3
]}

Mitsotakis, D. ^{[4
]}

机构：

[1] Univ Savoie, LAMA UMR 5127, CNRS, F-73376 Le Bourget Du Lac, France

[2] Univ Crete, Dept Appl Math, Iraklion 71409, Greece

[3] FORTH, IACM, Iraklion 71110, Greece

[4] Univ Minnesota, Inst Math & Applicat, Minneapolis, MN 55455 USA

来源：

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS | 2013年 / 71卷 / 06期

关键词：

finite volume method; nonlinear dispersive waves; unidirectional propagation; solitary waves; water waves; HYPERBOLIC CONSERVATION-LAWS; DISCONTINUOUS GALERKIN METHODS; TIME DISCRETIZATION METHODS; KDV-TYPE EQUATIONS; BOUSSINESQ EQUATIONS; LONG WAVES; NONOSCILLATORY SCHEMES; DIFFERENTIAL-EQUATIONS; NUMERICAL-SOLUTION; 2-WAY PROPAGATION;

D O I：

10.1002/fld.3681

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

We extend the framework of the finite volume method to dispersive unidirectional water wave propagation in one space dimension. In particular, we consider a KdVBBM-type equation. Explicit and implicitexplicit RungeKutta-type methods are used for time discretizations. The fully discrete schemes are validated by direct comparisons to analytic solutions. Invariants' conservation properties are also studied. Main applications include important nonlinear phenomena such as dispersive shock wave formation, solitary waves, and their various interactions. Copyright (C) 2012 John Wiley & Sons, Ltd.

引用

页码：717 / 736

页数：20

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