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Article Dans Une Revue Applied Mathematics and Computation Année : 2023

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

Manuel Jesús Castro Díaz
Tomás Morales de Luna

Résumé

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.
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Dates et versions

hal-04068544 , version 1 (14-04-2023)

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Alessia Del Grosso, Manuel Jesús Castro Díaz, Christophe Chalons, Tomás Morales de Luna. On well-balanced implicit-explicit Lagrange-projection schemes for two-layer shallow water equations. Applied Mathematics and Computation, 2023, 442, ⟨10.1016/j.amc.2022.127702⟩. ⟨hal-04068544⟩
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