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

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  • Yan, Ruifang
  • Tong, Wei
  • Chen, Guoxian

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.

Suggested Citation

  • Yan, Ruifang & Tong, Wei & Chen, Guoxian, 2023. "A mass conservative, well balanced and positivity-preserving central scheme for shallow water equations," Applied Mathematics and Computation, Elsevier, vol. 443(C).
    • Handle: RePEc:eee:apmaco:v:443:y:2023:i:c:s0096300322008463
    DOI: 10.1016/j.amc.2022.127778
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    References listed on IDEAS

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    1. Dong, Jian & Li, Ding Fang, 2020. "An effect non-staggered central scheme based on new hydrostatic reconstruction," Applied Mathematics and Computation, Elsevier, vol. 372(C).
    2. Yan, Ruifang & Tong, Wei & Chen, Guoxian, 2023. "An efficient invariant-region-preserving central scheme for hyperbolic conservation laws," Applied Mathematics and Computation, Elsevier, vol. 436(C).
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