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An effect non-staggered central scheme based on new hydrostatic reconstruction

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  • Dong, Jian
  • Li, Ding Fang

Abstract

A non-staggered second-order accurate central scheme based on new hydrostatic reconstruction (HR) for the shallow water equation (SWE) with dry–wet fronts is presented. The well-balanced property maybe missed if the discretization of the source term based on an invariable water surface level on the staggered cell. We propose a novel discretization of the source term based on new hydrostatic reconstruction to ensure the well-balanced property on the staggered cell. To evolve the numerical solutions on a single grid and satisfy the well-balanced property, we construct a map between the water surface level and its cell average on the staggered cell. The positivity preserving property is achieved by providing an appropriate CFL condition. A number of classical problems for the SWE are successfully solved.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:apmaco:v:372:y:2020:i:c:s0096300319309841
    DOI: 10.1016/j.amc.2019.124992
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    Cited by:

    1. 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).

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