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On well-balanced implicit-explicit Lagrange-projection schemes for two-layer shallow water equations

Author

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  • Del Grosso, A.
  • Castro Díaz, M.
  • Chalons, C.
  • Morales de Luna, T.

Abstract

This works concerns the study of well-balanced Lagrange-projection schemes applied to the two-layer shallow water system. In particular, a formulation of the mathematical model in Lagrangian coordinates is proposed. The HLL method is then applied to a simplified version of the resulting Lagrangian system. Furthermore, based on the acoustic-transport splitting interpretation, another approximate Riemann solver for the acoustic-Lagrangian step is described. Both an explicit and an implicit-explicit method are proposed, where the latter can allow very fast simulations in sub-critical regimes. Finally, we show numerical simulations in which the outputs are compared with the IFCP method’s results.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:apmaco:v:442:y:2023:i:c:s0096300322007706
    DOI: 10.1016/j.amc.2022.127702
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    References listed on IDEAS

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    1. 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.
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