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Solution of shallow-water equations using least-squares finite-element method

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Abstract

A least-squares finite-element method (LSFEM) for the non-conservative shallow-water equations is pre- sented. The model is capable of handling complex topography, steady and unsteady flows, subcritical and supercritical flows, and flows with smooth and sharp gradient changes. Advantages of the model include: (1) sources terms, such as the bottom slope, surface stresses and bed frictions, can be treated easily without any special treatment; (2) upwind scheme is no needed; (3) a single approximating space can be used for all variables, and its choice of approximating space is not subject to the Ladyzhenskaya-Babuska-Brezzi (LBB) condition; and (4) the resulting system of equations is symmetric and positive-definite (SPD) which can be solved efficiently with the preconditioned conjugate gradient method. The model is verified with flow over a bump, tide induced flow, and dam-break. Computed results are compared with analytic solutions or other numerical results, and show the model is conservative and accurate. The model is then used to simulate flow past a circular cylinder. Important flow characteristics, such as variation of water surface around the cylinder and vortex shedding behind the cylinder are investigated. Computed results compare well with experiment data and other numerical results.

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Authors and Affiliations

  1. Department of Marine Environmental Informatics, National Taiwan Ocean University, Keelung, 20224, Taiwan, China

    Shin-Jye Liang

  2. Department of Bioenvironmental Engineering, Chung-Yuan Christian University, Chung-Li, 32023, Taiwan, China

    Jyh-Haw Tang

  3. Department of Geographic Information Systems, Feng Chia University, Taichung, 40724, Taiwan, China

    Ming-Shun Wu

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  1. Shin-Jye Liang
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  2. Jyh-Haw Tang
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  3. Ming-Shun Wu
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Correspondence to Shin-Jye Liang.

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Liang, SJ., Tang, JH. & Wu, MS. Solution of shallow-water equations using least-squares finite-element method. Acta Mech Sin 24, 523–532 (2008). https://doi.org/10.1007/s10409-008-0151-4

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  • DOI: https://doi.org/10.1007/s10409-008-0151-4

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