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              <p>De nombreux systèmes de lois de conservation sont intégrés à l'aide du formalisme lagrangien où les sommets des mailles voient leurs position varier au cours du temps. La forme des mailles ne permet pas toujours d'assurer une bonne précision du calcul et les techniques ALE sont nécessaires. Nous nous intéressons ici à des phénomènes de conduction dépendant du gradient de vitesse couplés à la dynamique des gaz. Pour cela, nous proposons l'étude d'un simulacre de modèle de mélange turbulent du second ordre construit pour combiner terme elliptique et noyau hyperbolique. La partie hyperbolique est résolue par des schéma centrés volumes-finis et le remaillage de la phase ALE est celui décrit dans [7]. Une partie importante de ce papier est la discrétisation de l'équation parabolique anisotrope sur maillage polygonal non régulier. Celle-ci s'inspire du schéma dans [9] qui assure la positivité de la solution numérique. Nous proposons une variante basée sur le découpage en triangles des mailles polygonales. Nous montrons quelques résultats préliminaires sur un couplage faible hydrodynamique et équation parabolique dont le tenseur de diffusion dépend des tensions de Reynolds.</p>
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