A mass conservative, well balanced and positivity-preserving central scheme for shallow water equations

Ruifang Yan, Wei Tong and Guoxian Chen

Applied Mathematics and Computation, 2023, vol. 443, issue C

Abstract: Based on the invariant-region-preserving (IRP) reconstruction method introduced in [Yan, Tong and Chen, Appl. Math. Comput., 436 (2023) 127500], a second order unstaggered central scheme is proposed to solve the shallow water equations with bottom topography in the framework that the bottom is discretized by a continuous, piecewise linear approximation. The reconstruction applies a modification locally on a preliminary reconstructed surface gradient in every cell to yield a convexity property of the sampled point value in the forward and backward projections. The water mass conservation is proved by rewriting the scheme in a conservation form. The modification does not change the preliminary reconstructed slope of water surface for the lake-at-rest steady state and then keeps the well-balancing property of the surface gradient method. The convexity property ensures the nonnegativity of the updated water depth under a large CFL number which yields a considerable speed-up. The numerical experiments are shown to demonstrate the robustness of the scheme.

Keywords: Shallow water equations; Central scheme; Well-balancing property; Positivity-preserving property; Mass conservation (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:443:y:2023:i:c:s0096300322008463

DOI: 10.1016/j.amc.2022.127778

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