Comptes Rendus
Partial Differential Equations, Numerical Analysis
Some quasi-analytical solutions for propagative waves in free surface Euler equations
Comptes Rendus. Mathématique, Volume 358 (2020) no. 11-12, pp. 1111-1118.

This note describes some quasi-analytical solutions for wave propagation in free surface Euler equations and linearized Euler equations. The obtained solutions vary from a sinusoidal form to a form with singularities. They allow a numerical validation of the free-surface Euler codes.

Solutions quasi-analytiques d’ondes propagatives dans les équations d’Euler à surface libre. Cette note décrit des solutions quasi-analytiques correspondant à la propagation d’ondes dans les équations d’Euler et d’Euler linéarisées à surface libre. Les solutions obtenues varient d’une forme sinusoïdale à une forme présentant des singularités. Elles permettent de valider numériquement les codes de simulation des équations d’Euler à surface libre.

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DOI: 10.5802/crmath.63

Marie-Odile Bristeau 1; Bernard Di Martino 2; Anne Mangeney 1, 3; Jacques Sainte-Marie 1; Fabien Souille 1

1 ANGE project-team, Inria Paris, 2 rue Simone Iff, CS 42112, 75589 Paris Cedex 12, France; Sorbonne Université, Lab. Jacques-Louis Lions, 4 Place Jussieu, F-75252 Paris cedex 05
2 UMR CNRS 6134 SPE, Université de Corse, Campus Grimaldi, BP 52, 20250 Corte, France
3 Université de Paris, Institut de Physique du Globe de Paris, Seismology Group, 1 rue Jussieu, Paris F-75005, France
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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     title = {Some quasi-analytical solutions for propagative waves in free surface {Euler} equations},
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Marie-Odile Bristeau; Bernard Di Martino; Anne Mangeney; Jacques Sainte-Marie; Fabien Souille. Some quasi-analytical solutions for propagative waves in free surface Euler equations. Comptes Rendus. Mathématique, Volume 358 (2020) no. 11-12, pp. 1111-1118. doi : 10.5802/crmath.63. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.63/

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