| Issue |
ESAIM: M2AN
Volume 59, Number 6, November-December 2025
|
|
|---|---|---|
| Page(s) | 2895 - 2931 | |
| DOI | https://doi.org/10.1051/m2an/2025075 | |
| Published online | 07 November 2025 | |
A numerical method for wave-structure interactions in the Boussinesq regime
1
Univ Rennes, Inria Bretagne Atlantique (MINGuS), IRMAR UMR 6625, Rennes, France
2
UMR 5251 IMB, CNRS, University of Bordeaux, Talence, France
3
Univ. Bordeaux, CNRS, INRIA, Bordeaux INP, IMB, UMR 5251, F-33400 Talence, France
* Corresponding author: lisl.weynans@math.u-bordeaux.fr
Received:
5
April
2024
Accepted:
4
September
2025
This work studies waves interacting with partially immersed objects moving freely in the vertical direction, and waves described by the one-dimensional Boussinesq-Abbott system. This problem can be reduced to a transmission problem, with transmission conditions involving the resolution of coupled forced ODEs satisfied by the vertical displacement of the object and the average discharge of the fluid under the object. We propose a new extended formulation of the problem that provides the value of the surface elevation at the two contact points. This formulation simplifies the numerical computation of transmission conditions and the discretization of the fluid equations in cells near the object. Based on this formulation, we propose a second order-scheme involving a generalization of the Mac-Cormack scheme with nonlocal flux and a source term. Several explicit solutions are derived to validate this scheme. They can serve as benchmark for future codes.
Mathematics Subject Classification: 35G61 / 35Q35 / 74F10 / 65M08
Key words: Wave-structure interactions / initial boundary value problems / Boussinesq system / numerical analysis
© The authors. Published by EDP Sciences, SMAI 2025
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