Solution to the Shallow Water Equation with FVM Based on Unstructured Grid

Jie He; Xin Sheng Zhao; He Yong Liu

doi:10.4028/www.scientific.net/AMM.212-213.1168

Paper Titles

Energy Loss during Density Current Flowing through Width Abrupt Changed Channel
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Effects of Water Temperature on Clinging Flow of Rectangular Sharp-Crested Weir
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Vertical Distribution of Turbulence Shear Stress During Tidal Period
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Specification of Turbulent Diffusion by Random Walk Method for Oil Dispersion Modeling
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Solution to the Shallow Water Equation with FVM Based on Unstructured Grid
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A Study on the Evolution Characteristics of the Large Structure of Turbulence in a Meander Channel
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Investigation of Apron Setting on the Main Deep Trough of River Bed by 2D Unsteady Flow Simulation
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Software Development of Hydraulic Design for Pump Suction Chambers
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HomeApplied Mechanics and MaterialsApplied Mechanics and Materials Vols. 212-213Solution to the Shallow Water Equation with FVM...

Solution to the Shallow Water Equation with FVM Based on Unstructured Grid

Abstract:

The diffusion motion is one of the important items in the shallow water equations, and it is a crucial factor for the stability to simulate the shallow water flow in the numerical model. In this paper, a 2D model for the simulation of shallow water flow by convection and diffusion over variable bottom is presented, which is based on the FVM (finite volume method) over triangular unstructured grids. The format of Reo’s approximate Riemann is adopted to solve the flux terms. And the bed slope source term is treated by split in the form of the flux eigenvector. For the diffusion terms, the divergence theorem is employed to obtain the derivatives of a scalar variable on each triangular cell. Then, the flow around a pillar is simulated, which flow pattern is similar with the actual flow. Thus it is proved that the model could be applied to simulate the complicated current structure in the water area around hydraulic construction.

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Periodical:

Applied Mechanics and Materials (Volumes 212-213)

Pages:

1168-1171

DOI:

https://doi.org/10.4028/www.scientific.net/AMM.212-213.1168

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Online since:

October 2012

Authors:

Jie He, Xin Sheng Zhao, He Yong Liu

Keywords:

Diffusion Motion, Finite Volume Method (FVM), Shallow Water Equation, Unstructured Grid

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References

[1] P.L. Roe. Approximate Riemann solvers, parameter vectors, and difference schemes[J]. Journal of Computational Physics, 1997, 135, pp.250-258.

DOI: 10.1006/jcph.1997.5705

Google Scholar

[2] A. Harten, P.D. Lax, B. van Leer. On upstream differencing and Godunov-type schemes for hyperbolic conservation laws[J]. SIAM Rev. 1983, 25, pp.35-61.

DOI: 10.1137/1025002

Google Scholar

[3] P. Brufau. Zero mass error using unsteady wetting–drying conditions in shallow flows over dry irregular topography[J]. Int. J. Numer. Meth. Fluids 2004, 45, pp.1047-1082.

DOI: 10.1002/fld.729

Google Scholar

[4] Benedict D. Rogers. Mathematical balancing of flux gradient and source terms prior to using Roe's approximate Riemann solver[J]. Journal of Computational Physics, 2003, 192, pp.422-451.

DOI: 10.1016/j.jcp.2003.07.020

Google Scholar

[5] P. Brufau. Two-dimensional dam break flow simulation[J]. International Journal for Numerical Methods in Fluids, 2000, 33, pp.35-57.

DOI: 10.1002/(sici)1097-0363(20000515)33:1<35::aid-fld999>3.0.co;2-d

Google Scholar