no. 11-12
Équations aux dérivées partielles, Analyse numérique
Some quasi-analytical solutions for propagative waves in free surface Euler equations
Bristeau, Marie-Odile1 ; Di Martino, Bernard2   ; Mangeney, Anne1, 3  ; Sainte-Marie, Jacques1  ; Souille, Fabien1
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
Comptes Rendus. Mathématique, Tome 358 (2020) no. 11-12, pp. 1111-1118.

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.

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.

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DOI : 10.5802/crmath.63
Bristeau, Marie-Odile 1 ; Di Martino, Bernard 2 ; Mangeney, Anne 1, 3 ; Sainte-Marie, Jacques 1 ; Souille, Fabien 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 
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     title = {Some quasi-analytical solutions for propagative waves in free surface {Euler} equations},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1111--1118},
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Bristeau, Marie-Odile; Di Martino, Bernard; Mangeney, Anne; Sainte-Marie, Jacques; Souille, Fabien. Some quasi-analytical solutions for propagative waves in free surface Euler equations. Comptes Rendus. Mathématique, Tome 358 (2020) no. 11-12, pp. 1111-1118. doi : 10.5802/crmath.63. http://www.numdam.org/articles/10.5802/crmath.63/

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