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Well-Balanced Unstaggered Central Scheme Based on the Continuous Approximation of the Bottom Topography

Jian Dong

Department of Mathematics, College of Liberal Arts and Science, National University of Defense Technology Changsha, Hunan 410073, P. R. China

E-mail Address: djmath@nudt.edu.cn

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https://doi.org/10.1142/S021987622250058XCited by:2 (Source: Crossref)

Abstract

A key difficulty of the conventional unstaggered central schemes for the shallow water equations (SWEs) is the well-balanced property that may be missed when the computational domain contains wet-dry fronts. To avoid the numerical difficulty caused by the nonconservative product, we construct a linear piecewise continuous bottom topography. We propose a new discretization of the source term on the staggered cells, and a novel “backward” step based on the water surface elevation. The core of this paper is that, we construct a map between the water surface elevation and the cell average of the free surface on the staggered cells to discretize the source term for maintaining the stationary solutions. The positivity-preserving property is obtained by using the “draining” time-step technique. A number of classical problems of the SWEs can be solved reasonably.

Keywords:

AMSC: 76M12, 35L65

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