A Well-Balanced and Non-Negative Numerical Scheme for Solving the Integrated Shallow Water and Solute Transport Equations

作     者：Qiuhua Liang 

作者机构：School of Civil Engineering and GeosciencesNewcastle UniversityNewcastle upon TyneNE17RUEnglandUK 

出 版 物：《Communications in Computational Physics》 (计算物理通讯（英文）)

年 卷 期：2010年第7卷第5期

页      面：1049-1075页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：This work is supported by the UK Engineering and Physical Sciences Research Council(EPSRC)through grant:EP/F030177/1 

主　　题：Solute transport shallow water equations advection-diffusion equation wellbalanced scheme wetting and drying source terms Riemann solver 

摘      要：Based on the recent development in shallow flow modelling, this paperpresents a finite volume Godunov-type model for solving a 4×4 hyperbolic matrixsystem of conservation laws that comprise the shallow water and depth-averaged solute transport equations. The adopted governing equations are derived to preserveexactly the solution of lake at rest so that no special numerical technique is necessaryin order to construct a well-balanced scheme. The HLLC approximate Riemann solveris used to evaluate the interface fluxes. Second-order accuracy is achieved using theMUSCL slope limited linear reconstruction together with a Runge-Kutta time integration method. The model is validated against several benchmark tests and the resultsare in excellent agreement with analytical solutions or other published numerical predictions.