Séminaire AA — Boundary conditions and entropy stability for nearshore wave models and their numerical discretization
Mathieu Rigal
Sorbonne Université
https://www.math.u-bordeaux.fr/~mrigal001/
Date(s) : 06/01/2026 iCal
11h00 - 12h00
This talk deals with several issues arising in the modelling and numerical approximation of water waves in the nearshore zone.
In the first part, we focus on boundary conditions for a dispersive Boussinesq-type model. We provide a rigorous analysis of boundary conditions that allow for wave generation and absorption without relying on artificial sponge layers. Based on this analysis, we propose a second-order accurate numerical scheme and illustrate its effectiveness.
The second part addresses wave breaking through a coupling between the dispersive model and the hyperbolic shallow water system. Numerical simulations are presented and compared with laboratory experiments, showing good agreement.
In the final part, we study a numerical discretization of the shallow water system based on a kinetic formulation. The resulting scheme is positive, well-balanced, and satisfies a fully discrete entropy inequality without sacrificing too much accuracy thanks to an adaptive time stepping procedure.
Emplacement
I2M Saint-Charles - Salle de séminaire
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