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Online ISSN 1552-4485; Print ISSN 0033-569X
Inviscid water-waves and interface modeling
Authors:
Emmanuel Dormy and Christophe Lacave
Journal:
Quart. Appl. Math. 82 (2024), 583-637
MSC (2020):
Primary 76B15, 65M22; Secondary 35R37, 35Q31
DOI:
https://doi.org/10.1090/qam/1685
Published electronically:
January 19, 2024
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: We present a rigorous mathematical analysis of the modeling of inviscid water waves. The free-surface is described as a parametrized curve. We introduce a numerically stable algorithm which accounts for its evolution with time. The method is shown to converge using approximate solutions, such as Stokes waves and Green-Naghdi solitary waves. It is finally tested on a wave breaking problem, for which an odd-even coupling suffices to achieve numerical convergence up to the splash without the need for additional filtering.
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Additional Information
Emmanuel Dormy
Affiliation:
Département de Mathématiques et Applications, UMR-8553, École Normale Supérieure, CNRS, PSL University, 75005 Paris, France
MR Author ID:
622868
ORCID:
0000-0002-9683-6173
Email:
Emmanuel.Dormy@ens.fr
Christophe Lacave
Affiliation:
Université de Grenoble Alpes, CNRS, IF, 38000 Grenoble, France
Address at time of publication:
(Christophe Lacave) Université Savoie Mont Blanc, CNRS, LAMA, 73000 Chambéry, France
MR Author ID:
878311
ORCID:
0000-0002-2488-4117
Email:
Christophe.Lacave@univ-smb.fr
Keywords:
Singular integral formulations,
vortex and dipole formulation,
overturning waves,
splash singularity
Received by editor(s):
July 5, 2023
Received by editor(s) in revised form:
September 1, 2023
Published electronically:
January 19, 2024
Additional Notes:
The authors were supported in part by the ANR project ‘SINGFLOWS’ (ANR-18-CE40-0027-01), the IMPT project ‘Ocean waves’, and the CNES-Tosca project ‘Maeva’.
Article copyright:
© Copyright 2024
Brown University