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

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

Applied Mathematics and Computation, 2023, vol. 442, issue C

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.

Keywords: Hyperbolic partial differential equations; Lagrange-projection splitting; Two-layer shallow water; Implicit-explicit method; Well-balanced property (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:442:y:2023:i:c:s0096300322007706

DOI: 10.1016/j.amc.2022.127702

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