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AN UNSTRUCTURED FINITE-VOLUME ALGORITHM FOR NONLINEAR TWO-DIMENSIOAL SHALLOW WATER EQUATION

Journal of Hydrodynamics 2005年第3期17卷 306-312页

作者： WANGZhi-li GENGYan-fen JINSheng StateKeyLaboratoryofCoastalandoffshoreEngineering DalianUniversityofTechnologyDalian116024China

An unstructured finite-volume numerical algorithm was presented for solution of the two-dimensional shallow water equations, based on triangular or arbitrary quadrilateral meshes. The Roe type approximate Riemann solver was used to the system. A second-order TVD scheme with the van Leer limiter was used in the space discretization and a two-step Runge-Kutta approach was used in the time discretization. An upwind, as opposed to a pointwise, treatment of the slope source terms was adopted and the semi-implicit treatment was used for the friction source terms. Verification for two-dimension dam-break problems are carried out by comparing the present results with others and very good agreement is shown.

关键词： shallow water equation dam break Riemann solver finite-volume method source terms

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Efficient Modeling of an Axial Compressor with Swirl Distortion

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Journal of Thermal Science 2021年第4期30卷 1421-1434页

作者： GUO Jin HU Jun WANG Xuegao TU Baofeng College of Energy and Power Engineering Nanjing University of Aeronautics and AstronauticsJiangsu Province Key Laboratory of Aerospace Power SystemsNanjing 210016China

This paper presents a satisfactory numerical strategy to reliably evaluate the three-dimensional large-scale flow feature of multistage axial compressors in response to complex swirl distortion with acceptable computational cost. Under the theoretical framework of the body force method, the guide vanes of a swirl distortion generator and the multiple blade rows of a two-stage low-speed axial compressor are described by distributed source terms instead of a complex body-fitted grid approach. The key flow structure of the paired swirl generated by the swirl generator and the main distributions of flow angle at the rotor outlet of the first stage captured by the model agree well with experimental results, demonstrating the effectiveness of the numerical strategy. Additionally, the interaction process between the steady-state paired swirl and the compressor is clearly revealed by the study. The intensity of the swirl distortion can be greatly reduced after passing through the axial compressor. However, the swirl has a significant impact on the local blade loading of the first stage, which induces the mass flux nonuniformity as well as total pressure and total temperature distortion. The combined total pressure and total temperature distortion is significantly attenuated near tip and slightly enhanced near hub as it moves through the second stage.

关键词： axial compressor vane-based paired swirl source terms numerical simulation

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

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Communications in Computational Physics 2010年第5期7卷 1049-1075页

作者： Qiuhua Liang School of Civil Engineering and Geosciences Newcastle UniversityNewcastle upon TyneNE17RUEnglandUK

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.

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

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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 term.Our new scheme will be based on the FVEG methods presented in(Noelle and Kraft,J.Comp.Phys.,221(2007)),but adds the possibility to handle dry boundaries.The most important aspect is to preserve the positivity of the water height.We present a general approach to ensure this for arbitrary finite volume schemes.The main idea is to limit the outgoing fluxes of a cell whenever they would create negative water height.Physically,this corresponds to the absence of fluxes in the presence of vacuum.Wellbalancing is then re-established by splitting gravitational and gravity driven parts of the flux.Moreover,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

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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 role.We 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 equations.In 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 established.The 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.

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

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

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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 solver.The scheme solves the 1D shallow water equations with source terms using a Godunov-type finite volume method.The solver is robust,especially for the wetting/drying interface and complex terrain.The reconstruction with Superbee limiter and the two-step Runge-Kutta approach are applied in spatial and time,respectively,to get second-order TVD scheme.Comparisons 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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A New Approach on Simulating Two Dimensional Shallow-Water Flow with Uneven Bottom

A New Approach on Simulating Two Dimensional Shallow-Water F...

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第七届全国水动力学学术会议暨第十九届全国水动力学研讨会

作者： Andrew YT Leung Department of Building and Construction City University of Hong Kong Hong Kong

＜正＞Numerical simulation of 2D shallow-water flow over uneven bottom performed under a new form of shallow-water equations is reported in this paper. The original shallow water equations are rewritten so that it ensures the water units at the same water depth with the same potential energy. The balance between the flux gradient and the slope term is always matched so that the initial still water can keep static. The reformed equation set is also suitable for simulating the shallow water flow over sharply changed, uneven bottom. The numerical solution is based on the cell-centred finite-volume method and the advection terms in the shallow-water equations are treated by Harten, Lax and Van Leer’s approximating Riemann solver. Several test cases are performed to verify the accuracy, stability and reliability of the program.

关键词： shallow water equations finite volume method HLL approximate Riemann solver source terms

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