Numerical resolution of well-balanced shallow water equations with complex source terms

被引：464

作者：

Liang, Qiuhua ^{[1
]}

Marche, Fabien ^{[2
]}

机构：

[1] Univ Newcastle, Sch Civil Engn & Geosci, Newcastle Upon Tyne NE1 7RU, Tyne & Wear, England

[2] Univ Montpellier 2, F-34090 Montpellier, France

来源：

ADVANCES IN WATER RESOURCES | 2009年 / 32卷 / 06期

基金：

英国工程与自然科学研究理事会;

关键词：

Shallow water equations; Well-balanced scheme; Wetting and drying; Source terms; Riemann solver; Bed friction; FINITE-VOLUME METHOD; HYPERBOLIC CONSERVATION-LAWS; SAINT-VENANT SYSTEM; GODUNOV-TYPE SCHEME; DAM-BREAK; UNSTRUCTURED MESHES; BED TOPOGRAPHY; FLUX GRADIENTS; UPWIND SCHEMES; FLOWS;

D O I：

10.1016/j.advwatres.2009.02.010

中图分类号：

TV21 [水资源调查与水利规划];

学科分类号：

081501 ;

摘要：

This paper presents a well-balanced numerical scheme for simulating frictional shallow flows over complex domains involving wetting and drying. The proposed scheme solves, in a finite volume Godunov-type framework, a set of pre-balanced shallow water equations derived by considering pressure balancing. Non-negative reconstruction of Riemann states and compatible discretization of slope source term produce stable and well-balanced solutions to shallow flow hydrodynamics over complex topography. The friction source term is discretized using a splitting implicit scheme. Limiting value of the friction force is derived to ensure stability. This new numerical scheme is validated against four theoretical benchmark tests and then applied to reproduce a laboratory dam break over a domain with irregular bed profile. (C) 2009 Elsevier Ltd. All rights reserved.

引用

页码：873 / 884

页数：12

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