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A well-balanced FVC scheme for 2D Shallow Water Flows on Unstructured Triangular Meshes

Advances in Applied Mathematics and Mechanics 2023年第5期15卷 1335-1378页

作者： Moussa Ziggaf Imad Kissami Mohamed Boubekeur Fayssal Benkhaldoun ENSAO LMCSComplexe UniversitaireB.P.66960000 OujdaMorocco MSDA Mohammed VI Polytechnic UniversityLot 66043150 Ben GuerirMorocco Universit´eéSorbonne Paris Nord LAGACNRSUMR 7539F-93430VilletaneuseFrance

This paper aims to present a new well-balanced,accurate and fast finite volume scheme on unstructured grids to solve hyperbolic conservation *** is a scheme that combines both finite volume approach and characteristic *** this study,we consider a shallow water system with Coriolis effect and bottom friction stresses where this new Finite Volume Characteristics(FVC)scheme has been *** physical and mathematical properties of the system,including the C-property,have been well ***,we developed this approach by preserving the advantages of the finite volume discretization such as conservation property and the method of characteristics,in order to avoid Riemann solvers and to enhance the accuracy without any complexity of the MUSCL ***,a discretization was applied to the bottom source term that leads to a well-balanced scheme satisfying the steady-state condition of still water.A semi-implicit treatment will also be presented in this study to avoid stability problems due to source ***,the proposed finite volume method is verified on several benchmark tests and shows good agreement with analytical solutions and experimental results;moreover,it gives a noteworthy accuracy and rapidity improvement compared to the original approaches.

关键词： Shallow water model method of characteristics FVC scheme finite volume method well-balanced scheme

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MODELING DAM-BREAK FLOOD OVER NATURAL RIVERS USING DISCONTINUOUS GALERKIN METHOD

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Journal of Hydrodynamics 2012年第4期24卷 467-478页

作者： KHAN Abdul A. Glenn Department of Civil Engineering Clemson University

A well-balanced numerical model is presented for two-dimensional, depth-averaged, shallow water flows based on the Discontinuous Galerkin （DG） method. The model is applied to simulate dam-break flood in natural rivers with wet/dry bed and complex topography. To eliminate numerical imbalance, the pressure force and bed slope terms are combined in the shallow water flow equations. For partially wet/dry elements, a treatment of the source term that preserves the well-balanced property is presented. A treatment for modeling flow over initially dry bed is presented. Numerical results show that the time step used is related to the dry bed criterion. The intercell numerical flux in the DG method is computed by the Harten-Lax-van Contact （HLLC） approximate Riemann solver. A two-dimensional slope limiting procedure is employed to prevent spurious oscillation. The robustness and accuracy of the model are demonstrated through several test cases, including dam-break flow in a channel with three bumps, laboratory dam-break tests over a triangular bump and an L-shape bend, dam-break flood in the Paute River, and the Malpasset dam-break case. Numerical results show that the model is robust and accurate to simulate dam-break flood over natural rivers with complex geometry and wet/dry beds.

关键词： Discontinuous Galerkin (DG) method shallow water flows dam-break flood well-balanced scheme

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AN EFFICIENT METHOD FOR COMPUTING HYPERBOLIC SYSTEMS WITH GEOMETRICAL SOURCE TERMS HAVING CONCENTRATIONS

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Journal of Computational Mathematics 2004年第2期22卷 230-249页

作者： ShiJin XinWen DepartmentofMathematicalSciences TsinghuaUniversityBeijing100084China DepartmentofMathematicalScience TsinghuaUniversityBeijing100084P.R.China

We propose a simple numerical method for calculating both unsteady and steady state solution of hyperbolic system with geometrical source terms having concentrations. Physical problems under consideration include the shallow water equations with topography,and the quasi one-dimensional nozzle flows. We use the interface value, rather than the cell-averages, for the source terms, which results in a well-balanced scheme that can capture the steady state solution with a remarkable accuracy. This method approximates the source terms via the numerical fluxes produced by an (approximate) Riemann solver for the homogeneous hyperbolic systems with slight additional computation complexity using Newton's iterations and numerical integrations. This method solves well the subor super-critical flows, and with a transonic fix, also handles well the transonic flows over the concentration. Numerical examples provide strong evidence on the effectiveness of this new method for both unsteady and steady state calculations.

关键词： Discontinuous topography Shallow water equations Shock capturing well-balanced scheme

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well-balanced numerical modelling of non-uniform sediment transport in alluvial rivers

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International Journal of Sediment Research 2015年第2期30卷 117-130页

作者： Honglu Qian Zhixian Cao Gareth Pender Huaihan Liu Peng Hu State Key Laboratory of Water Resources and Hydropower Engineering Science Wuhan University Institute for Infrastructure and Environment Heriot-Watt University Yangtze River Waterway Bureau School of Ocean Science and Engineering Zhejiang University

The last two decades have witnessed the development and application of well-balanced numerical models for shallow flows in natural ***,until now there have been no such models for flows with non-uniform sediment *** paper presents a 1D well-balanced model to simulate flows and non-capacity transport of non-uniform sediment in alluvial *** active layer formulation is adopted to resolve the change of bed sediment *** the framework of the finite volume Slope Llmiter Centred(SLIC) scheme,a surface gradient method is incorporated to attain well-balanced solutions to the governing *** proposed model is tested against typical cases with irregular topography,including the refilling of dredged trenches,aggradation due to sediment overloading and flood flow due to landslide dam *** agreement between the computed results and measured data is *** to a non-well-balanced model,the well-balanced model features improved performance in reproducing stage,velocity and bed *** should find general applications for non-uniform sediment transport modelling in alluvial rivers,especially in mountain areas where the bed topography is mostly irregular.

关键词： Non-uniform:sediment transport well-balanced scheme Irregular topography Shallow flow Mathematical river modelling

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