Upwind Stabilized Finite Element Modelling of Non-hydrostatic Wave Breaking and Run-upReport as inadecuate




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1 BACCHUS - Parallel tools for Numerical Algorithms and Resolution of essentially Hyperbolic problems Inria Bordeaux - Sud-Ouest, UB - Université de Bordeaux, CNRS - Centre National de la Recherche Scientifique : UMR5800 2 IMB - Institut de Mathématiques de Bordeaux 3 EPOC - Environnements et Paléoenvironnements OCéaniques

Abstract : In the following report a new methodology is presented to model the propagation, wave breaking and run-up of waves in coastal zones. We represent the different coastal phenomena through the coupling of non-linear shallow water equations with the extended Boussinesq equations of Madsen and Sørensen. Each of the involved equations has a major role in describing a particular physical behaviour of the wave: the latter equations permit to model the propagation, while the non-linear shallow water ones lead waves to locally converge into discontinuities. We start from the third-order stabilized finite element scheme for the Boussinesq equations, developed in a previous scientific work Ricchiuto and Filippini, J.Comput.Phys. 2014 and develop a non-linear variant, and detach the dispersive from the shallow water terms. A shock-capturing technique based on local non-linear mass lumping that permits in the shallow water regions to degrade locally the scheme to a first-order one across bores shocks and dry fronts is proposed. As for the detection of the breaking fronts, the shallow water areas, this involves physics based breaking criteria. We present different definitions of the breaking criterion, including a local implementation of the convective criterion of Bjørkavåg and H. Kalisch, Phys.Letters A 2011, and the hybrid models of Kazolea et. al, J.Comput.Phys. 2014, and Tonelli and Petti, J.Hydr.Res. 2011. The behavior of different breaking criteria is investigated on several cases for which experimental data are available.

Résumé : On décrit une approche pour la simulation de la propagation et déferlement des vagues en proche cote basée sur la couplage entre les équations de Boussinesq améliorées de Madsen and Sorensen, pour la propagation, et les équations Shallow Water, pour le déferlement et le runup. La contruction de ce modele hybride passe d-abord la proposition une variante non-linéaire du schéma élément finis stabilisé de Ricchiuto and Filippini, J.Comput.Phys. 2014 capable de résoudre les chocs de maniere monotone. Cela est obtenu par un operateur locale de condensation de la matrice de masse qui réduit le schéma de Ricchiuto and Filippini, J.Comput.Phys. 2014 au schéma de Roe classique. Le couplage entre le modèle Boussinesq et Shallow Water est en suite étudié. On considere différents critères physiques de détection de fronts déferlants. En particulier, on présente une implémentation numérique locale du critère convectif de Bjorkavag and H. Kalisch, Phys.Letters A, 2011, qui est comparée au critères proposés dans Kazolea et. al, J.Comput.Phys., 2014 et Tonelli and Petti, J.Hydr.Res. 2011. Le modèle obtenu est validé sur des nombreux benchmarks avec données expérimentales.





Author: Paola Bacigaluppi - Mario Ricchiuto - Philippe Bonneton -

Source: https://hal.archives-ouvertes.fr/



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