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Science China Mathematics 2012年第2期55卷 277-283页

作者： FERNANDEZ-NIETO Enrique D. NOBLE Pascal VILA Jean-Paul Departamento de Matemdtica Aplicada I Universidad de Sevilla 41012 Sevilla Spain Universite de Lyon Universitd Lyon1 Institut Camille Jordan UMR CNRS 520843 blvd du 11 novembre 1918 F-69622 ViUeurbanne Cedex France Institut de Mathdmatiques de Toulouse UMR CNRS 5219 INSA de Toulouse 135 avenue de Rangueil 31077 Toulouse Cedex 4 France

In this note, we provide a consistant thin layer theory for power law and Bingham incompressible fluids flowing down an inclined plane under the effect of gravity. The derivation of such equations is based on formal asymptotic expansions of solutions of Cauchy momentum equations in the shallow water scaling and in the neighbourhood of steady solutions so that we can close the average equations on the fluid height h and the total discharge rate q.

关键词： shallow water equations asymptotic analysis non-Newtonian fluids

A CHARACTERISTIC-BASED FINITE VOLUME SCHEME FOR shallow water equations

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Journal of Hydrodynamics 2009年第4期21卷 531-540页

作者： GUO Yan LIU Ru-xun DUAN Ya-li LI Yuan Department of Mathematics University of Science and Technology of China Hefei 230026 China Department of Mathematics China University of Mining and Technology XuZhou 221116 China

We propose a new characteristic-based finite volume scheme combined with the method of Central Weighted Essentially Non-Oscillatory （CWENO） reconstruction and characteristics, to solve shallow water equations. We apply the scheme to simulate dam-break problems. A number of challenging test cases are considered, such as large depth differences even wet/dry bed. The numerical solutions well agree with the analytical solutions. The results demonstrate the desired accuracy, high-resolution and robustness of the presented scheme.

关键词： shallow water equations finite volume method characteristic method Central Weighted Essentially Non-Oscillatory (CWENO) scheme HLLC flux

Urban Stormwater Modeling with Local Inertial Approximation Form of shallow water equations: A Comparative Study

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International Journal of Disaster Risk Science 2021年第5期12卷 745-763页

作者： Weiqi Wang Wenjie Chen Guoru Huang School of Civil Engineering and Transportation South China University of TechnologyGuangzhou 510640China State Key Laboratory of Subtropical Building Science School of Civil Engineering and TransportationSouth China University of TechnologyGuangzhou 510640China Guangdong Engineering Technology Research Center of Safety and Greenization for water Conservancy Project Guangzhou 510640China

This study focused on the performance and limitations of the local inertial approximation form model(LIM)of the shallow water equations(SWEs)when applied in urban flood modeling.A numerical scheme of the LIM equations was created using finite volume method with a first-order spatiotemporal Roe Riemann solver.A simplified urban stormwater model(SUSM)considering surface and underground dual drainage system was constructed based on LIM and the US Environmental Protection Agency Storm water Management ***,a complete urban stormwater model(USM)based on the SWEs with the same solution algorithm was used as the evaluation *** results of the SUSM and USM in a highly urbanized area under four rainfall return periods were analyzed and *** results reveal that the performance of the SUSM is highly consistent with that of the USM but with an improvement in computational efficiency of approximately 140%.In terms of the accuracy of the model,the SUSM slightly underestimates the water depth and velocity and is less accurate when dealing with supercritical flow in urban stormwater flood ***,the SUSM can produce comparable results to USM with higher computational efficiency,which provides a simplified and alternative method for urban flood modeling.

关键词： Comparative study Finite volume method Local inertial approximation form shallow water equations Urban stormwater model

A HIGH RESOLUTION FINITE VOLUME METHOD FOR SOLVING shallow water equations

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Journal of Hydrodynamics 2000年第1期12卷 35-41页

作者： Wang Jia song School of Civil Engineering and Mechanics, Shanghai Jiaotong University, Shanghai 200030, P.R.ChinaNi Hang gen Department of Civil and Structure Engineering, Dalian University of Technology, Dalian 116024, P.R.China Shanghai Jiaotong Univ Shanghai China

A high resolution finite volume numerical method for solving the shallow water equations is developed in this paper. In order to extend finite difference TVD scheme to finite volume method, a new geometry and topology of control bodies is defined by considering the corresponding relationships between nodes and elements. This solver is implemented on arbitrary quadrilateral meshes and their satellite elements, and based on a second order hybrid type of TVD scheme in space discretization and a two step Runge Kutta method in time discretization. Then it is used to deal with two typical dam break problems and very satisfactory results are obtained comparied with other numerical solutions. It can be considered as an efficient implement for the computation of shallow water problems, especially concerning those having discontinuities, subcritical and supercritical flows and complex geometries.

关键词： shallow water equations finite volume TVD scheme dam break bores

High-resolution central difference scheme for the shallow water equations

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Acta Oceanologica Sinica 2005年第5期24卷 39-45页

作者： CHEN Jianzhong SHI Zhongke HU Yanmei Northwestern Polytechnical University Xi＇an 710072 China College of Science Chang＇an University Xi＇an 710064 China

A two-dimensional nonoscillatory central difference scheme was extended to the shallow water equations. A high-resolution numerical method for solving the shallow water equations was presented. In order to prevent oscillation, the nonlinear limiter is employed to approximate the discrete slopes. The main advantage of the presented method is simplicity comparable with the upwind schemes. This method does not require Riemann solvers or some form of flux difference splitting methods. Furthermore, the discrete derivatives of flux can be approximated by the component-wise approach and thus the computation of Jacobian can be avoided. The method retains high resolution and high accuracy similar to the upwind results. It is applied to simulating several tests, including circular dam-break problem, shock focusing problem and partial dam-break problem. The results are in good agreement with the numerical results obtained by other methods. The simulated results also demonstrate that the presented method is stable and efficient.

关键词： shallow water equations central difference scheme high-resolution scheme

A NUMERICAL STUDY FOR THE PERFORMANCE OF THE WENO SCHEMES BASED ON DIFFERENT NUMERICAL FLUXES FOR THE shallow water equations

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Journal of Computational Mathematics 2010年第6期28卷 807-825页

作者： Changna Lu Jianxian Qiu Ruyun Wang College of Mathematics and Physics Nanjing University of Information Science and Technology Nanjing 210044 China Department of Mathematics Nanjing University Nanjing 210093 China College of Ocean Hohai University Nanjing Jiangsu 210098 P.R. China

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 property, and resolution of discontinuities. issues of CPU cost, accuracy, non-oscillatory

关键词： Numerical flux WENO finite volume scheme shallow water equations High order accuracy Approximate Riemann solver Runge-Kutta time discretization.

Implicit Parallel FEM Analysis of shallow water equations

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Tsinghua Science and Technology 2005年第3期10卷 364-371页

作者：江春波李凯刘宁张庆海 Department of Hydraulic and Hydropower Engineering Tsinghua University Beijing 100084 China Ministry of water Resources Beijing 100053 China

The velocity field in the Wu River at Chongqing was simulated using the shallow water equation implemented on clustered workstations. The parallel computing technique was used to increase the comput- ing power. The shallow water equation was discretized to a linear system of equations with a direct parallel generalized minimum residual algorithm (GMRES) used to solve the linear system. Unlike other parallel GMRES methods, the direct GMRES method does not alter the sequential algorithm, but bases the paral- lelization on basic operations such as the matrix-vector product. The computed results agree well with ob- served results. The parallel computing technique significantly increases the solution speed for this large- scale problem.

关键词： shallow water equations parallel computing generalized minimum residual algorithm (GMRES)

Finite Volume Evolution Galerkin Methods for the shallow water equations with Dry Beds

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Communications in Computational Physics 2011年第7期10卷 371-404页

作者： Andreas Bollermann Sebastian Noelle Maria Lukacova-Medvid’ova IGPM RWTH AachenTemplergraben 5552062 AachenGermany Institut fur Mathematik Universitat MainzStaudingerweg 955099 MainzGermany.

We present a new Finite Volume Evolution Galerkin(FVEG)scheme for the solution of the shallow water equations(SWE)with the bottom topography as a source *** new scheme will be based on the FVEG methods presented in(Noelle and Kraft,***.,221(2007)),but adds the possibility to handle dry *** most important aspect is to preserve the positivity of the water *** present a general approach to ensure this for arbitrary finite volume *** main idea is to limit the outgoing fluxes of a cell whenever they would create negative water ***,this corresponds to the absence of fluxes in the presence of *** is then re-established by splitting gravitational and gravity driven parts of the ***,a new entropy fix is introduced that improves the reproduction of sonic rarefaction waves.

关键词： Well-balanced schemes dry boundaries shallow water equations evolution Galerkin schemes source terms

Finite Volume Multilevel Approximation of the shallow water equations

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Chinese Annals of Mathematics,Series B 2013年第1期34卷 1-28页

作者： Arthur BOUSQUET Martine MARION Roger TEMAM The Institute for Scientific Computing and Applied Mathematics Indiana University Département Mathématique Informatique Université de LyonEcole Centrale de Lyon

The authors consider a simple transport equation in one-dimensional space and the linearized shallow water equations in two-dimensional space, and describe and implement a multilevel finite-volume discretization in the context of the utilization of the incremental unknowns. The numerical stability of the method is proved in both cases.

关键词： Finite-volume methods Multilevel methods shallow water equations Stability analysis

GPU Accelerated Discontinuous Galerkin Methods for shallow water equations

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Communications in Computational Physics 2015年第6期18卷 37-64页

作者： Rajesh Gandham David Medina Timothy Warburton Department of Computational and Applied Mathematics Rice University6100 Main StreetMS-134HoustonTX-77005USA

We discuss the development,verification,and performance of a GPU accelerated discontinuous Galerkin method for the solutions of two dimensional nonlinear shallow water *** shallow water equations are hyperbolic partial differential equations and are widely used in the simulation of tsunami wave *** algorithms are tailored to take advantage of the single instruction multiple data(SIMD)architecture of graphic processing *** time integration is accelerated by local time stepping based on a multi-rate Adams-Bashforth scheme.A total variational bounded limiter is adopted for nonlinear stability of the numerical *** limiter is coupled with a mass and momentum conserving positivity preserving limiter for the special treatment of a dry or partially wet element in the ***,robustness and performance are demonstrated with the aid of test ***,we developed a unified multi-threading model *** kernels expressed in OCCA model can be cross-compiled with multi-threading models OpenCL,CUDA,and *** compare the performance of the OCCA kernels when cross-compiled with these models.

关键词： shallow water equations discontinuous Galerkin positivity preserving slope limiting GPUs accelerators multi-threading