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

JOURNAL OF COMPUTATIONAL PHYSICS

卷:374

Article

Liu, Xin¹  Albright, Jason²  Epshteyn, Yekaterina²  Kurganov, Alexander^1,3 

[1] Southern Univ Sci & Technol, Dept Math, Shenzhen 518055, Peoples R China

[2] Univ Utah, Dept Math, Salt Lake City, UT 84112 USA

[3] Tulane Univ, Math Dept, New Orleans, LA 70118 USA

关键词: Saint-Venant system of shallow water equations;    Central-upwind scheme;    Well-balanced scheme;    Positivity preserving scheme;    Wet/dry reconstruction;    Unstructured triangular grid;   

DOI  :  10.1016/j.jcp.2018.07.038

来源: Elsevier

【 摘 要 】

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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