Well-balanced positivity preserving central-upwind scheme with a novel wet/dry reconstruction on triangular grids for the Saint-Venant system

Abstract

In this paper, we construct an improved well-balanced positivity preserving central-upwind scheme for the two-dimensional Saint-Venant system of shallow water equations. As in Bryson et al. (2011) [7], our scheme is based on a continuous piecewise linear discretization of the bottom topography over an unstructured triangular grid. The main new technique is a special reconstruction of the water surface in partially flooded cells. This reconstruction is an extension of the one-dimensional wet/dry reconstruction from Bollermann et al. (2013) [3]. The positivity of the computed water depth is enforced using the “draining” time-step technique introduced in Bollermann et al. (2011) [4]. The performance of the proposed central-upwind scheme is tested on a number of numerical experiments.