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One higher order scheme for shallow water equations based on HLLE approximate riemann solver

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One higher order scheme for shallow water equations based on...

ANALYSIS OF WATER QUALITY IN SHALLOW LAKES WITH A TWO-DIMENSIONAL FLOW-SEDIMENT MODEL

第十四届中国海洋（岸）工程学术讨论会

作者： GENG Yan-fen1,WANG Zhi-li2 (1.Transportation College,Southeast University,Najing 210096,China 2.State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering,Nanjing Hydraulic Research Institute,Nanjing 210024,China)

The present work addresses the numerical scheme of shallow water flows with the application of the HLLE approximate riemann *** scheme solves the 1D shallow water equations with source terms using a Godunov-type finite volume *** solver is robust,especially for the wetting/drying interface and complex *** reconstruction with Superbee limiter and the two-step Runge-Kutta approach are applied in spatial and time,respectively,to get second-order TVD *** between model results and exact solutions show that the scheme is high-order accurate,robust conservative and highly in capturing strong gradients.

关键词： shallow water flow approximate riemann solver flux limiter source terms

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Journal of Hydrodynamics 2007年第4期19卷 501-508页

作者： JI Yong ZhANG Jie YAO ei ZHAO Di-hua Nanchang Institute of Technology Nanchang 330099 China College of Environmental Science and Engineering Hohai University Nanjing 210098 China Nanjing Hydraulic Research Institute Nanjing 210098 China

The governing equation for sediment pollutions was derived based on the turbulent diffusion of pollutants in shallow lakes. Coupled with shallow water equations, a depth-averaged 2-D flow and water quality model was developed. By means of the conservation law, a proposed differential equation for the change of sediment pollutants was linked to the 2-D equations. Under the framework of the finite volume method, the Osher approximate riemann solver was employed to solve the equations. An analytical resolution was used to examine the model capabilities. Simulated results matched the exact solutions especially well. As an example, the simulation of CODMn in the Wuli Lake, a part of the Taihu lake, was conducted, which led to reasonable results. This study provides a new approach and a practical tool for the simulation of flow and water quality in shallow lakes.

关键词： sediment falling velocity turbulence flow and water quality model finite volume method approximate riemann solver shallow water equation advection-dispersion equation

DIFFERENCE SCHEME FOR TWO-PHASE FLOW

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Applied Mathematics and Mechanics(English Edition) 2004年第5期25卷 536-545页

作者：李强封建湖蔡体敏胡春波 Box 164 Northwestern Polytechnical University College of Science Changan University

A numerical method for two-phase flow with hydrodynamics behavior was considered. The nonconservative hyperbolic governing equations proposed by Saurel and Gallout were adopted. Dissipative effects were neglected but they could be included in the model without major difficulties. Based on the opinion proposed by Abgrall that “a two phase system, uniform in velocity and pressure at t=0 will be uniform on the same variable during its temporal evolution", a simple accurate and fully Eulerian numerical method was presented for the simulation of multiphase compressible flows in hydrodynamic regime. The numerical method relies on Godunov-type scheme, with HLLC and Lax-Friedrichs type approximate riemann solvers for the resolution of conservation equations, and nonconservative equation. Speed relaxation and pressure relaxation processes were introduced to account for the interaction between the phases. Test problem was presented in one space dimension which illustrated that our scheme is accurate, stable and oscillation free.

关键词： compressible two-phase flow relaxation process approximate riemann solver

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.

A Godunov-Type solver for the Numerical Approximation of Gravitational Flows

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Communications in Computational Physics 2014年第1期15卷 46-75页

作者： J.Vides B.Braconnier E.Audit C.Berthon B.Nkonga Inria Maison de la SimulationUSR 3441Gif-sur-YvetteFrance IFP Energies Nouvelles 1-4 avenue de Bois-Préau92852 Rueil-MalmaisonFrance CEA Maison de la SimulationUSR 3441Gif-sur-YvetteFrance. Univ.of Nantes Lab.J.LerayUMR CNRS 6629NantesFrance. Univ.of Nice-Sophia Antipolis Lab.J.A.DieudonnéUMR CNRS 7351NiceFrance. Inria Sophia Antipolis BP.93F-06902 Sophia Antipolis CedexFrance.

We present a new numerical method to approximate the solutions of an Euler-Poisson model,which is inherent to astrophysical flows where gravity plays an important *** propose a discretization of gravity which ensures adequate coupling of the Poisson and Euler equations,paying particular attention to the gravity source term involved in the latter *** order to approximate this source term,its discretization is introduced into the approximate riemann solver used for the Euler equations.A relaxation scheme is involved and its robustness is *** method has been implemented in the software HERACLES[29]and several numerical experiments involving gravitational flows for astrophysics highlight the scheme.

关键词： Euler-Poisson equations approximate riemann solver relaxation scheme source terms gravitational effects.

On the Computations of Gas-Solid Mixture Two-Phase Flow

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Advances in Applied Mathematics and Mechanics 2014年第1期6卷 49-74页

作者： D.Zeidan R.Touma Department of Mathematics Al-Balqa Applied UniversityAl-SaltJordan Department of Computer Science&Mathematics Lebanese American UniversityBeirutLebanon

This paper presents high-resolution computations of a two-phase gas-solid mixture using a well-defined mathematical *** HLL riemann solver is applied to solve the riemann problem for the model *** solution is then employed in the construction of upwind Godunov methods to solve the general initial-boundary value problem for the two-phase gas-solid *** representative test cases have been carried out and numerical solutions are provided in comparison with existing numerical *** demonstrate the robustness,effectiveness and capability of these methods,the model results are compared with reference *** addition to that,these results are compared with the results of other simulations carried out for the same set of test cases using other numerical methods available in the *** diverse comparisons demonstrate that both the model equations and the numerical methods are clear in mathematical and physical concepts for two-phase fluid flow problems.

关键词： Hyperbolic conservative equations two-phase flows compressible gas-solid mixture conservation laws approximate riemann solver upwind Godunov methods numerical simulation.

Development and Comparison of Numerical Fluxes for LWDG Methods

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Numerical Mathematics(Theory,Methods and Applications) 2008年第4期1卷 435-459页

作者： Jianxian Qiu Department of Mathematics Nanjing University Nanjing Jiangsu 210093 China.

The discontinuous Galerkin （DO） or local discontinuous Galerkin （LDG） method is a spatial discretization procedure for convection-diffusion equations, which employs useful features from high resolution finite volume schemes, such as the exact or approximate riemann solvers serving as numerical fluxes and limiters. The Lax- Wendroff time discretization procedure is an altemative method for time discretization to the popular total variation diminishing （TVD） Runge-Kutta time discretizations. In this paper, we develop fluxes for the method of DG with Lax-Wendroff time discretization procedure （LWDG） based on different numerical fluxes for finite volume or finite difference schemes, including the first-order monotone fluxes such as the Lax-Friedfichs flux, Godunov flux, the Engquist-Osher flux etc. and the second-order TVD fluxes. We systematically investigate the performance of the LWDG methods based on these different numerical fluxes for convection terms with the objective of obtaining better performance by choosing suitable numerical fluxes. The detailed numerical study is mainly performed for the one-dimensional system case, addressing the issues of CPU cost, accuracy, non-oscillatory property, and resolution of discontinuities. Numerical tests are also performed for two dimensional systems.

关键词： Discontinuous Galerkin method Lax-Wendroff type time discretization numerical flux approximate riemann solver timiter WENO scheme high order accuracy.