A multilevel method for finite volume discretization of the two-dimensional nonlinear shallow-water equations

被引：13

作者：

Adamy, K. ^{[1
]}

Bousquet, A. ^{[2
]}

Faure, S. ^{[1
]}

Laminie, J. ^{[3
]}

Temam, R. ^{[2
]}

机构：

[1] Univ Paris Sud, CNRS, Math Lab, UMR 8628, Batiment 425, F-91405 Orsay, France

[2] Indiana Univ, Inst Appl Math & Sci Comp, Bloomington, IN 47405 USA

[3] Univ Antilles Guyane, GRIMAAG Guadeloupe, F-97157 Pointe A Pitre, Guadeloupe, France

来源：

OCEAN MODELLING | 2010年 / 33卷 / 3-4期

基金：

美国国家科学基金会;

关键词：

Finite volume methods; Multilevel methods; Shallow-water problem; Incremental unknowns; HYPERBOLIC CONSERVATION-LAWS; CENTRAL-UPWIND SCHEMES; INCREMENTAL UNKNOWNS; SIMULATION;

D O I：

10.1016/j.ocemod.2010.02.006

中图分类号：

P4 [大气科学（气象学）];

学科分类号：

0706 ; 070601 ;

摘要：

In this article we propose and implement a multilevel method to simulate the solution of the two-dimensional nonlinear shallow-water equations. The multilevel method is based on a central-upwind finite volume scheme and uses new incremental unknowns which enable to preserve the numerical conservation of the scheme. The method is tested and analyzed on two and three levels of discretization on different test cases and turns out to furnish a good solution of the problems while saving CPU time. (C) 2010 Elsevier Ltd. All rights reserved.

引用

页码：235 / 256

页数：22

共 24 条

[1] A fast and stable well-balanced scheme with hydrostatic reconstruction for shallow water flows [J].

Audusse, E ;

Bouchut, F ;

Bristeau, MO ;

Klein, R ;

Perthame, B .

SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2004, 25 (06) :2050-2065

[2]

AUDUSSE E, 2000, RR3989 INRIA

[3]

BENZONIGAVAGE S, 2007, OXFORD MATH MONOGRAP, V26

[4] Dynamical multilevel schemes for the solution of evolution equations by hierarchical finite element discretization [J].

Calgaro, C ;

Laminie, J ;

Temam, R .

APPLIED NUMERICAL MATHEMATICS, 1997, 23 (04) :403-442

[5]

Chehab JP, 1998, RAIRO-MATH MODEL NUM, V32, P51

[6] INCREMENTAL UNKNOWNS FOR SOLVING PARTIAL-DIFFERENTIAL EQUATIONS [J].

CHEN, M ;

TEMAM, R .

NUMERISCHE MATHEMATIK, 1991, 59 (03) :255-271

[7] INCREMENTAL UNKNOWNS IN FINITE-DIFFERENCES - CONDITION NUMBER OF THE MATRIX [J].

CHEN, M ;

TEMAM, R .

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 1993, 14 (02) :432-455

[8] Two-way embedding algorithms: a review [J].

Debreu, Laurent ;

Blayo, Eric .

OCEAN DYNAMICS, 2008, 58 (5-6) :415-428

[9] A Dynamical Multi-level scheme for the Burgers equation: Wavelet and hierarchical finite element [J].

Debussche, A ;

Laminie, J ;

Zahrouni, E .

JOURNAL OF SCIENTIFIC COMPUTING, 2005, 25 (03) :445-497

[10] Incremental unknowns, multilevel methods and the numerical simulation of turbulence [J].

Dubois, T ;

Jauberteau, F ;

Temam, R .

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 1998, 159 (1-2) :123-189

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