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, Un modèle numérique prenant en compte le couplage bidirectionnel entre les modèles de uide parfait potentiel loin de la structure et de uide visqueux au voisinage de celle-ci est présenté pour résoudre le problème de l

, Au voisinage de la structure, cet écoulement complémentaire est résolu en utilisant un modèle uide réel basé sur la méthode SWENSE (Spectral Wave Explicit Navier-Stokes Equation) qui consiste à écrire les équations RANS (Reynolds Averaged Navier-Stokes) pour les variables complémentaires, les termes incidents apparaissant alors comme des termes de forçage, L'écoulement total est décomposé en un écoulement incident et un écoulement complémentaire (diracté)

, La présente étude se résume comme suit

L. ,

, Les modèles de houle incidente non-linéaire pour des houles régulières et irrégulières sont résumés

. Pour-la-houle-régulière, Rienecker and Fenton, 1981) s'appuie sur la fonction de courant développée en série de Fourier. La librairie open-source pour les ondes régulières nonlinéaires appelé CN-Stream développé par Ducrozet et al. (2019) est utilisé pour la génération d'ondes incidentes régulières

. Ducrozet, La méthode HOS pour les houles irrégulières en mer ouverte (HOS-ocean) ou en bassin limité (HOS-NWT) est ensuite rappelée, 2007.

. Choi, La librairie open-source pour la reconstruction des houles HOS sur un maillage quelconque est publiée sous licence GPL, 2018.

, La procédure de reconstruction proposée est validée avec un modèle d'écoulement de uide visqueux basé sur la modélisation des équations RANS par des schémas discrets de type volumes nis ainsi qu'une résolution découplée en vitesses-pression et la mise à jour de l'interface par une procédure VOF. Les ondes HOS sont générées dans le modèle à écoulement visqueux et validées par simulation HOS pour diérents modèles HOS. Ceux-ci montrent un bon accord les uns avec les autres. De plus

. Ans-dans-le-golfe-du-mexique, Gulf of Mexico) est pris en compte pour validation. Un événement de déferlement est prédit à l'aide d'un modèle simple inclus dans le modèle HOS

, L'événement extrême simulé dans le modèle à écoulement visqueux est validé avec la simulation et les expériences HOS. L'accord entre ces diérents résultats est satisfaisant

L. ,

, Une nouvelle représentation de la vitesse de Poincaré pour un écoulement à surface libre en profondeur innie est proposée dans le cadre de la théorie de uide parfait potentiel linéarisé, La contribution des dipôles dans l'équation

, est remplacée par une contribution source équivalente avec une vitesse tangentielle à la surface de la frontière. La vitesse du uide complémentaire au point du calcul peut être calculée par la distribution de la vitesse du uide sur la surface correspondante et de l'élévation de la houle sur la ligne de ottaison de la surface correspondante

, Deux types de fonction de Green dans le domaine temporel doivent être évaluées pour la représentation de la vitesse de Poincaré pour un écoulement de surface libre instable. Il est prouvé que les deux types de la fonction de Green dans le domaine temporel et leurs dérivées spatiales sont les solutions de l

, Ces éléments, 1998.

, sont calculés en utilisant une méthode de Frobenius à avance temporelle proposée par Chuang et al, 2007.

, La représentation de vitesse proposée est validée avec la solution analytique de l'écoulement