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Implicit and implicit-explicit Lagrange-projection finite volume schemes exactly well-balanced for 1D shallow water system

Author

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  • Caballero-Cárdenas, C.
  • Castro, M.J.
  • Morales de Luna, T.
  • Muñoz-Ruiz, M.L.

Abstract

In this paper we consider the Lagrange-Projection technique in the framework of finite volume schemes applied to the shallow water system. We shall consider two versions of the scheme for the Lagrangian step: one fully implicit and one implicit-explicit, based on how the geometric source term is treated. First and second order well-balanced versions of the schemes are presented, in which the water at rest solutions are preserved. This allows to obtain efficient numerical schemes in low Froude number regimes, as the usual CFL restriction driven by the acoustic waves is avoided.

Suggested Citation

  • Caballero-Cárdenas, C. & Castro, M.J. & Morales de Luna, T. & Muñoz-Ruiz, M.L., 2023. "Implicit and implicit-explicit Lagrange-projection finite volume schemes exactly well-balanced for 1D shallow water system," Applied Mathematics and Computation, Elsevier, vol. 443(C).
    • Handle: RePEc:eee:apmaco:v:443:y:2023:i:c:s0096300322008529
    DOI: 10.1016/j.amc.2022.127784
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    References listed on IDEAS

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    1. Garres-Díaz, J. & Fernández-Nieto, E.D. & Narbona-Reina, G., 2022. "A semi-implicit approach for sediment transport models with gravitational effects," Applied Mathematics and Computation, Elsevier, vol. 421(C).
    2. Irene Gómez-Bueno & Manuel Jesús Castro Díaz & Carlos Parés & Giovanni Russo, 2021. "Collocation Methods for High-Order Well-Balanced Methods for Systems of Balance Laws," Mathematics, MDPI, vol. 9(15), pages 1-40, July.
    3. Michel-Dansac, Victor & Thomann, Andrea, 2022. "TVD-MOOD schemes based on implicit-explicit time integration," Applied Mathematics and Computation, Elsevier, vol. 433(C).
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