Paralic confinement: models and simulations
نویسندگان
چکیده
This paper deals with the mathematical modelling of confinement of paralic ecosystems. It is based on the recent paper [FG07] that presents a modelling procedure in order to compute the confinement field of a lagoon. Here, we improve the existing model in order to account for tide oscillations in any kind of geometry such as non-rectangular lagoons with a non-flat bottom. The new model, that relies on PDEs rather than ODEs, is then implemented thanks to the finite element method. Numerical results confirm the feasibility of confinement studies thanks to the introduced model. Key-words: Mathematical modelling, numerical modelling, partial differential equations, numerical simulations, finite elements, confinement, ecological systems. ∗ Université Européenne de Bretagne, Lab-STICC (UMR CNRS 3192), Université de Bretagne-Sud, Centre Yves Coppens, Campus de Tohannic, F-56017, Vannes, FRANCE † INRIA CALVI, Université de Strasbourg, IRMA, 7 rue René Descartes, F-67084 Strasbourg Cedex, FRANCE ‡ INRIAMOISE, Laboratoire Jean Kuntzmann, 51 rue des mathématiques, F-38041 Grenoble Cedex 9, FRANCE ha l-0 06 44 68 6, v er si on 3 12 F eb 2 01 2 Confinement paralique modèles et simulations Résumé : Cet article traite de la modélisation mathématique du confinement dans des écosystèmes paraliques. Il se base sur un travail récent [FG07] dans lequel on trouve un modélisation qui permette de simuler le confinement dans des géométries simples. Ici, on améliore le modèle existant afin de permettre la prise en compte de la marée dans un lagon dont la géométrie est quelconque, avec un fond non nécessairement plat. Notre nouveeau modèle, qui repose sur des équations aux dérivées partielles, est alors implémenté numériquement grâce à la méthode des éléments finis,. Les résultats numériques confirment la faisabilité d’une étude du confinement grâce au modèle proposé. Mots-clés : Modélisation mathématique, modélisation numérique, équations aux dérivées partielles, équation de transport, simulations numériques, éléments finis, confinement, ecosystèmes. ha l-0 06 44 68 6, v er si on 3 12 F eb 2 01 2 Paralic Confinement Models and Simulations 3
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Paralic confinement computations in coastal environment with interlocked areas
This paper is in the continuity of a work program, initiated in Frénod & Goubert [FG07], Frénod & Rousseau [FR13] and Bernard, Frénod & Rousseau [BFRss]. Its goal is to develop an approach of the paralic confinement usable from the modeling slant, before implementing it in numerical tools. More specifically, we here deal with the multiscale aspect of the confinement. If a paralic environment is...
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