An efficient unstructured MUSCL scheme for solving the 2D shallow water equations. (April 2015) - Hou, Jingming; Liang, Qiuhua; Zhang, Hongbin; Hinkelmann, Reinhard
Abstract: The aim of this paper is to present a novel monotone upstream scheme for conservation law (MUSCL) on unstructured grids. The novel edge-based MUSCL scheme is devised to construct the required values at the midpoint of cell edges in a more straightforward and effective way compared to other conventional approaches, by making better use of the geometrical property of the triangular grids. The scheme is incorporated into a two-dimensional (2D) cell-centered Godunov-type finite volume model as proposed in Hou et al. (2013a, c) to solve the shallow water equations (SWEs). The MUSCL scheme renders the model to preserve the well-balanced property and achieve high accuracy and efficiency for shallow flow simulations over uneven terrains. Furthermore, the scheme is directly applicable to all triangular grids. Application to several numerical experiments verifies the efficiency and robustness of the current new MUSCL scheme. Highlights: A novel MUSCL scheme is developed to provide more efficient and accurate numerical solutions to the 2D shallow water equations. The scheme is flexible for implementation on all common 2D unstructured grids. The scheme satisfies the well-balanced property. It can be generalized into 3D tetrahedron grids and to solve other hyperbolic PDEs.