Well-balanced high-order centered schemes on unstructured meshes for shallow water equations with fixed and mobile bed |
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| Authors: | Alberto Canestrelli Michael Dumbser Annunziato Siviglia Eleuterio F Toro |
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| Institution: | 1. Department IMAGE, University of Padova, Via Loredan 20, I-35131 Padova, Italy;2. Department of Civil and Environmental Engineering, University of Trento, Via Mesiano 77, I-38100 Trento, Italy |
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| Abstract: | In this paper, we study the numerical approximation of the two-dimensional morphodynamic model governed by the shallow water equations and bed-load transport following a coupled solution strategy. The resulting system of governing equations contains non-conservative products and it is solved simultaneously within each time step. The numerical solution is obtained using a new high-order accurate centered scheme of the finite volume type on unstructured meshes, which is an extension of the one-dimensional PRICE-C scheme recently proposed in Canestrelli et al. (2009) 5]. The resulting first-order accurate centered method is then extended to high order of accuracy in space via a high order WENO reconstruction technique and in time via a local continuous space–time Galerkin predictor method. The scheme is applied to the shallow water equations and the well-balanced properties of the method are investigated. Finally, we apply the new scheme to different test cases with both fixed and movable bed. An attractive future of the proposed method is that it is particularly suitable for engineering applications since it allows practitioners to adopt the most suitable sediment transport formula which better fits the field data. |
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| Keywords: | Non-conservative hyperbolic systems Centered schemes Unstructured mesh High-order WENO finite volume methods Shallow water equations with fixed and movable bed Sediment transport FORCE scheme |
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