Stability of a thermodynamically coherent multi-phase model
نویسندگان
چکیده
We analyze a hyperbolic system of conservation laws in dimension one, which is a drastic simplification of a multi-phase or multi-velocity fluid model. The domain of hyperbolicity is compact, which is a characteristic of multi-phase models. Our main result is the stability of the domain of hyperbolicity. Due to the degeneracy of the model on the boundary of the hyperbolicity domain, rarefaction waves are not unique. We also propose a numerical scheme for approximate resolution of the model and prove the stability of this scheme. Résumé On considère un modèle simplifié d’un système d’équations aux dérivées partielles décrivant des fluides multi-vitesses ou multi-phasiques en dimension un d’espace. Ce problème modèle est de nature elliptiquehyperbolique, avec un domaine d’hyperbolicité compact. On montre la non-unicité des courbes de détente sur le bord du domaine d’hyperbolicité. On montre ensuite la stabilité du domaine d’hyperbolicité. Puis on propose une discrétisation numérique du modèle, discrétisation dont nous montrons la stabilité. keywords Hyperbolic system of conservation laws, multi-phase flows, hyperbolicity domain stability, numerical schemes, Lax-Friedrichs (relaxation) schemes. Laboratoire Jacques-Louis Lions, 175, rue du Chevaleret, 75013, Paris, France, e-mail: [email protected] Laboratoire Jacques-Louis Lions, 175, rue du Chevaleret, 75013, Paris, France, e-mail: [email protected] Laboratoire Jacques-Louis Lions, 175, rue du Chevaleret, 75013, Paris, France, e-mail: [email protected]
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