A NUMERICAL STUDY FOR THE PERFORMANCE OF THE WENO SCHEMES BASED ON DIFFERENT NUMERICAL FLUXES FOR THE SHALLOW WATER EQUATIONS

被引：10

作者：

Lu, Changna ^{[1
]}

Qiu, Jianxian ^{[2
]}

Wang, Ruyun ^{[3
]}

机构：

[1] Nanjing Univ Informat Sci & Technol, Coll Math & Phys, Nanjing 210044, Peoples R China

[2] Nanjing Univ, Dept Math, Nanjing 210093, Peoples R China

[3] Hohai Univ, Coll Ocean, Nanjing 210098, Jiangsu, Peoples R China

来源：

JOURNAL OF COMPUTATIONAL MATHEMATICS | 2010年 / 28卷 / 06期

关键词：

Numerical flux; WENO finite volume scheme; Shallow water equations; High order accuracy; Approximate Riemann solver; Runge-Kutta time discretization; ESSENTIALLY NONOSCILLATORY SCHEMES; FINITE-VOLUME METHOD; SOURCE TERMS; HYPERBOLIC SYSTEMS; TRIANGULAR MESHES; GALERKIN METHODS; RIEMANN SOLVER; IMPLEMENTATION; FLOWS; ORDER;

D O I：

10.4208/jcm.1001-m3122

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we investigate the performance of the weighted essential non-oscillatory (WENO) methods based on different numerical fluxes, with the objective of obtaining better performance for the shallow water equations by choosing suitable numerical fluxes. We consider six numerical fluxes, i.e., Lax-Friedrichs, local Lax-Friedrichs, Engquist-Osher, Harten-Lax-van Leer, HLLC and the first-order centered fluxes, with the WENO finite volume method and TVD Runge-Kutta time discretization for the shallow water equations. The detailed numerical study is performed for both one-dimensional and two-dimensional shallow water equations by addressing the issues of CPU cost, accuracy, non-oscillatory property, and resolution of discontinuities.

引用

页码：807 / 825

页数：19

共 28 条

[1]

Anastasiou K, 1997, INT J NUMER METH FL, V24, P1225, DOI 10.1002/(SICI)1097-0363(19970615)24:11<1225::AID-FLD540>3.0.CO

[2]

2-D

[3]

[Anonymous], 1997, 9765 ICASE BROWN U

[4]

[Anonymous], 2002, Cambridge Texts in Applied Mathematics, DOI [10.1017/CBO9780511791253, DOI 10.1017/CBO9780511791253]

[5] An HLLC scheme to solve the M1 model of radiative transfer in two space dimensions [J].

Berthon, Christophe ;

Charrier, Pierre ;

Dubroca, Bruno .

JOURNAL OF SCIENTIFIC COMPUTING, 2007, 31 (03) :347-389

[6] Fourth-order balanced source term treatment in central WENO schemes for shallow water equations [J].

Caleffi, V. ;

Valiani, A. ;

Bernini, A. .

JOURNAL OF COMPUTATIONAL PHYSICS, 2006, 218 (01) :228-245

[7] Finite volume method for simulating extreme flood events in natural channels [J].

Caleffi, V ;

Valiani, A ;

Zanni, A .

JOURNAL OF HYDRAULIC RESEARCH, 2003, 41 (02) :167-177

[8] Balanced finite volume WENO and central WENO schemes for the shallow water and the open-channel flow equations [J].

Crnjaric-Zic, N ;

Vukovic, S ;

Sopta, L .

JOURNAL OF COMPUTATIONAL PHYSICS, 2004, 200 (02) :512-548

[9] Weighted essentially non-oscillatory schemes for the interpolation of mean values on unstructured grids [J].

Friedrich, O .

JOURNAL OF COMPUTATIONAL PHYSICS, 1998, 144 (01) :194-212

[10]

Godunov S.K., 1959, Matematiceskij sbornik, V47, P271

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