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A Two-Layer Hydrostatic-Reconstruction Method for High-Resolution Solving of the Two-Layer Shallow-Water Equations over Uneven Bed Topography

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  • Jiang Lin
  • Bing Mao
  • Xinhua Lu

Abstract

In this study, attention is focused on numerically solving the two-dimensional, two-layer nonlinear shallow-water equations (2LSWEs) over uneven bed topography. A two-layer hydrostatic-reconstruction method (2LHRM) is proposed for face value reconstructions. A numerical model is then developed based on the 2LHRM in the framework of finite-volume methods using the slope-limited centered (SLIC) approximate Riemann solver for flux evaluations. The validations against various benchmark tests show that the 2LHRM by working with the SLIC scheme predicts robust solutions around large gradients and is able to simulate lake-at-rest solutions without using any ad-hoc techniques.

Suggested Citation

  • Jiang Lin & Bing Mao & Xinhua Lu, 2019. "A Two-Layer Hydrostatic-Reconstruction Method for High-Resolution Solving of the Two-Layer Shallow-Water Equations over Uneven Bed Topography," Mathematical Problems in Engineering, Hindawi, vol. 2019, pages 1-14, July.
    • Handle: RePEc:hin:jnlmpe:5064171
    DOI: 10.1155/2019/5064171
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    Cited by:

    1. Del Grosso, A. & Castro Díaz, M. & Chalons, C. & Morales de Luna, T., 2023. "On well-balanced implicit-explicit Lagrange-projection schemes for two-layer shallow water equations," Applied Mathematics and Computation, Elsevier, vol. 442(C).

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