Abstract:A two-dimensional (2D) finite-difference shallow water model based on a second-order hybrid type of total variation diminishing (TVD) approximate solver with a MUSCL limiter function was developed to model flooding and inundation problems where the evolution of the drying and wetting interface is numerically challenging. Both a minimum positive depth (MPD) scheme and a non-MPD scheme were employed to handle the advancement of drying and wetting fronts. We used several model problems to verify the model, including a dam break in a slope channel, a dam break flooding over a triangular obstacle, an idealized circular dam-break, and a tide flow over a mound. Computed results agreed well with the experiment data and other numerical results available. The model was then applied to simulate the dam breaking and flooding of Hsindien Creek, Taiwan, with the detailed river basin topography. Computed flooding scenarios show reasonable flow characteristics. Though the average speed of flooding is 6-7 m s 1 , which corresponds to the subcritical flow condition (Fr < 1), the local maximum speed of flooding is 14Ð12 m s 1 , which corresponds to the supercritical flow condition (Fr ³ 1Ð31). It is necessary to conduct some kind of comparison of the numerical results with measurements/experiments in further studies. Nevertheless, the model exhibits its capability to capture the essential features of dam-break flows with drying and wetting fronts. It also exhibits the potential to provide the basis for computationally efficient flood routing and warning information.
A least-squares finite-element method (LSFEM) for the non-conservative shallow-water equations is presented. 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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