A well‐balanced upstream flux‐splitting finite‐volume scheme for shallow‐water flow simulations with irregular bed topography |
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| Authors: | Jihn‐Sung Lai Wen‐Dar Guo Gwo‐Fong Lin Yih‐Chi Tan |
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| Institution: | 1. Hydrotech Research Institute, National Taiwan University, Taipei 10617, Taiwan;2. Department of Civil Engineering, National Taiwan University, Taipei 10617, Taiwan;3. Department of Bioenvironmental Systems Engineering, National Taiwan University, Taipei 10617, Taiwan |
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| Abstract: | This study extends the upstream flux‐splitting finite‐volume (UFF) scheme to shallow water equations with source terms. Coupling the hydrostatic reconstruction method (HRM) with the UFF scheme achieves a resultant numerical scheme that adequately balances flux gradients and source terms. The proposed scheme is validated in three benchmark problems and applied to flood flows in the natural/irregular river with bridge pier obstructions. The results of the simulations are in satisfactory agreement with the available analytical solutions, experimental data and field measurements. Comparisons of the present results with those obtained by the surface gradient method (SGM) demonstrate the superior stability and higher accuracy of the HRM. The stability test results also show that the HRM requires less CPU time (up to 60%) than the SGM. The proposed well‐balanced UFF scheme is accurate, stable and efficient to solve flow problems involving irregular bed topography. Copyright © 2009 John Wiley & Sons, Ltd. |
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| Keywords: | upstream flux‐splitting finite‐volume scheme shallow water equations hydrostatic reconstruction method surface gradient method bridge pier obstructions well balanced |
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