Journal
JOURNAL OF COMPUTATIONAL PHYSICS
Volume 374, Issue -, Pages 213-236Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2018.07.038
Keywords
Saint-Venant system of shallow water equations; Central-upwind scheme; Well-balanced scheme; Positivity preserving scheme; Wet/dry reconstruction; Unstructured triangular grid
Funding
- NSF [DMS-1521009]
- NSFC [11771201]
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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. (C) 2018 Elsevier Inc. All rights reserved.
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