A novel multislope MUSCL scheme for solving 2D shallow water equations on unstructured grids

Abstract

Within the framework of the two-dimensional cell-centered Godunov-type finite volume (CCFV) method, this paper presents a novel multislope scheme on the basis of the monotone upstream scheme for conservation law (MUSCL) for numerically solving nonlinear shallow water equations on two-dimensional triangular grids. The Riemann states of the considered edge are calculated by an edge-based reconstructing procedure, where a limited scalar slope is employed to prevent potential numerical oscillations. The novel aspect of the new scheme is that it takes advantage of the geometrical characteristics of triangular grids in the reconstructing and limiting procedures, which effectively reduces the cost of computation and provides higher resolution and accuracy compared with classical MUSCL schemes. Seven tests are adopted to verify the scheme, and the results indicate that this scheme is efficient, accurate, robust, and high-resolution, and can be an ideal alternative for solving shallow water problems over uneven and frictional topography.