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Shallow Water Model (shallow + water_model)

Distribution by Scientific Domains

Engineering	50%

Selected Abstracts

Numerical simulation of a dam break for an actual river terrain environment

HYDROLOGICAL PROCESSES, Issue 4 2007
C. B. Liao
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 14·12 m s,1, which corresponds to the supercritical flow condition (Fr , 1·31). 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. Copyright © 2006 John Wiley & Sons, Ltd. [source]

Non-hydrostatic 3D free surface layer-structured finite volume model for short wave propagation

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2009
L. Cea
Abstract In this paper a layer-structured finite volume model for non-hydrostatic 3D environmental free surface flow is presented and applied to several test cases, which involve the computation of gravity waves. The 3D unsteady momentum and mass conservation equations are solved in a collocated grid made of polyhedrons, which are built from a 2D horizontal unstructured mesh, by just adding several horizontal layers. The mesh built in such a way is unstructured in the horizontal plane, but structured in the vertical direction. This procedure simplifies the mesh generation and at the same time it produces a well-oriented mesh for stratified flows, which are common in environmental problems. The model reduces to a 2D depth-averaged shallow water model when one single layer is defined in the mesh. Pressure,velocity coupling is achieved by the Semi-Implicit Method for Pressure-Linked Equations algorithm, using Rhie,Chow interpolation to stabilize the pressure field. An attractive property of the model proposed is the ability to compute the propagation of short waves with a rather coarse vertical discretization. Several test cases are solved in order to show the capabilities and numerical stability of the model, including a rectangular free oscillating basin, a radially symmetric wave, short wave propagation over a 1D bar, solitary wave runup on a vertical wall, and short wave refraction over a 2D shoal. In all the cases the numerical results are compared either with analytical or with experimental data. Copyright © 2008 John Wiley & Sons, Ltd. [source]

A new shallow water model with polynomial dependence on depth

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 5 2008
José M. Rodríguez
Abstract In this paper, we study two-dimensional Euler equations in a domain with small depth. With this aim, we introduce a small non-dimensional parameter , related to the depth and we use asymptotic analysis to study what happens when , becomes small. We obtain a model for , small that, after coming back to the original domain, gives us a shallow water model that considers the possibility of a non-constant bottom, and the horizontal velocity has a dependence on z introduced by the vorticity when it is not zero. This represents an interesting novelty with respect to shallow water models found in the literature. We stand out that we do not need to make a priori assumptions about velocity or pressure behaviour to obtain the model. The new model is able to approximate the solutions to Euler equations with dependence on z (reobtaining the same velocities profile), whereas the classic model just obtains the average velocity. Copyright © 2007 John Wiley & Sons, Ltd. [source]