Author(s): Francesca Aureli; Andrea Maranzoni; Paolo Mignosa; Chiara Ziveri
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Keywords: Shallow water equations; Finite volume scheme; Surface Gradient Method; Irregular topography; C-property
Abstract: In this paper a finite volume MUSCL-Hancock scheme for the integration of the 2D shallow water equations is proposed. It estimates the numerical water depth at cell interfaces through a suitable weighted average of the boundary extrapolated values deriving from SGM and DGM reconstructions. The Surface Gradient Method (SGM) computes water depth at the intercells from the extrapolation of the water surface level: it can maintain the static condition of a quiescent fluid over an irregular topography (C-property), but it is not completely efficient in tracking wetting and drying fronts. On the other hand, other schemes that evaluate water depth at the cell boundaries through the extrapolation of the same conserved variable (Depth Gradient Method, DGM) do not satisfy the C-property, but are robust and stable near moving boundaries. The proposed Weighted Surface-Depth Gradient Method is able to preserve the good capabilities of both the mentioned approaches. The efficiency and robustness of the numerical scheme is validated through the application to some reference test cases whose exact solution is available in literature.
Year: 2007