Boussinesq Systems of Bona-Smith Type on Plane Domains: Theory and Numerical Analysis

被引：19

作者：

Dougalis, V. A. ^{[2
,3
]}

Mitsotakis, D. E. ^{[1
]}

Saut, J. -C. ^{[1
]}

机构：

[1] Univ Paris 11, UMR Math, F-91405 Orsay, France

[2] Inst Appl & Computat Math FORTH, Iraklion 70013, Greece

[3] Univ Athens, Dept Math, Zografos 15784, Greece

来源：

JOURNAL OF SCIENTIFIC COMPUTING | 2010年 / 44卷 / 02期

关键词：

Boussinesq systems; Nonlinear dispersive wave equations; Initial-boundary-value problems; Galerkin-finite element methods for Boussinesq systems; NONLINEAR DISPERSIVE MEDIA; AMPLITUDE LONG WAVES; 2-WAY PROPAGATION; WATER-WAVES; EQUATIONS;

D O I：

10.1007/s10915-010-9368-z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider a class of Boussinesq systems of Bona-Smith type in two space dimensions approximating surface wave flows modelled by the three-dimensional Euler equations. We show that various initial-boundary-value problems for these systems, posed on a bounded plane domain are well posed locally in time. In the case of reflective boundary conditions, the systems are discretized by a modified Galerkin method which is proved to converge in L (2) at an optimal rate. Numerical experiments are presented with the aim of simulating two-dimensional surface waves in realistic (plane) domains with a variety of initial and boundary conditions, and comparing numerical solutions of Bona-Smith systems with analogous solutions of the BBM-BBM system.

引用

页码：109 / 135

页数：27

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