Upwind WENO scheme for Shallow Water Equations in contravariant formulation

被引：18

作者：

Gallerano, F. ^{[1
]}

Cannata, G. ^{[1
]}

Tamburrino, M. ^{[1
]}

机构：

[1] Univ Roma La Sapienza, Dipartimento Ingn Civile Edile & Ambientale, I-00184 Rome, Italy

来源：

COMPUTERS & FLUIDS | 2012年 / 62卷

关键词：

2D Shallow Water Equations; Upwind WENO scheme; Contravariant formulation; Christoffel symbols; Freestream preservation; HYPERBOLIC CONSERVATION-LAWS; NAVIER-STOKES EQUATIONS; INVARIANT DISCRETIZATION; FINITE-DIFFERENCE; MODEL; SYSTEMS; FLOWS; JETS; FORM;

D O I：

10.1016/j.compfluid.2012.03.004

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

An Upwind Weighted Essentially Non-Oscillatory scheme for the solution of the Shallow Water Equations on generalized curvilinear coordinate systems is proposed. The Shallow Water Equations are expressed in a contravariant formulation in which Christoffel symbols are avoided. The equations are solved by using a high-resolution finite-volume method incorporated with an exact Riemann solver. A procedure developed in order to correct errors related to the difficulties of numerically satisfying the metric identities on generalized boundary-conforming grids is presented; this procedure allows the numerical scheme to satisfy the freestream preservation property on highly-distorted grids. The proposed scheme ensures the satisfaction of the C-property. The model is verified against several benchmark tests, and the results are compared with theoretical and alternative numerical solutions. (C) 2012 Elsevier Ltd. All rights reserved.

引用

页码：1 / 12

页数：12

共 64 条

[1] Aris R., 1989, Vectors, Tensors and the Basic Equations of Fluid Mechanics
[2] Nessyahu-Tadmor-type central finite volume methods without predictor for 3D Cartesian and unstructured tetrahedral grids
Arminjon, P
St-Cyr, A
[J]. APPLIED NUMERICAL MATHEMATICS, 2003, 46 (02) : 135 - 155
[3] A shock-capturing model based on flux-vector splitting method in boundary-fitted curvilinear coordinates
Baghlani, A.
Talebbeydokhti, N.
Abedini, M. J.
[J]. APPLIED MATHEMATICAL MODELLING, 2008, 32 (03) : 249 - 266
[4] High-order discontinuous Galerkin schemes on general 2D manifolds applied to the shallow water equations
Bernard, P-E.
Remacle, J. -F.
Comblen, R.
Legat, V.
Hillewaert, K.
[J]. JOURNAL OF COMPUTATIONAL PHYSICS, 2009, 228 (17) : 6514 - 6535
[5] An efficient solver for nearshore flows based on the WAF method
Brocchini, M
Bernetti, R
Mancinelli, A
Albertini, G
[J]. COASTAL ENGINEERING, 2001, 43 (02) : 105 - 129
[6] Cai X, 2008, 46 AIAA AER SCI M EX, P1
[7] Fourth-order balanced source term treatment in central WENO schemes for shallow water equations
Caleffi, V.
Valiani, A.
Bernini, A.
[J]. JOURNAL OF COMPUTATIONAL PHYSICS, 2006, 218 (01) : 228 - 245
[8] Well-balanced high-order centred schemes for non-conservative hyperbolic systems. Applications to shallow water equations with fixed and mobile bed
Canestrelli, Alberto
Siviglia, Annunziato
Dumbser, Michael
Toro, Eleuterio F.
[J]. ADVANCES IN WATER RESOURCES, 2009, 32 (06) : 834 - 844
[9] A central WENO scheme for solving hyperbolic conservation laws on non-uniform meshes
Capdeville, G.
[J]. JOURNAL OF COMPUTATIONAL PHYSICS, 2008, 227 (05) : 2977 - 3014
[10] SOLUTION OF 2D SHALLOW WATER EQUATIONS BY GENUINELY MULTIDIMENSIONAL SEMI-DISCRETE CENTRAL SCHEME
Chen Jian-zhong
Shi Zhong-ke
[J]. JOURNAL OF HYDRODYNAMICS, 2006, 18 (04) : 436 - 442

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