Symmetric forms for hyperbolic-parabolic systems of multi-gradient fluids - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik Année : 2019

Symmetric forms for hyperbolic-parabolic systems of multi-gradient fluids

Résumé

We consider multi-gradient fluids endowed with a volumetric internal energy which is a function of mass density, volumetric entropy and their successive gradients. We obtained the thermodynamic forms of equation of motions and equation of energy, and the motions are compatible with the two laws of thermodynamics. The equations of multi-gradient fluids belong to the class of dispersive systems. In the conservative case, we can replace the set of equations by a quasi-linear system written in a divergence form. Near an equilibrium position, we obtain a symmetric-Hermitian system of equations in the form of Godunov's systems. The equilibrium positions are proved to be stable when the total volume energy of the fluids is a convex function with respect to convenient conjugated variables-called main field-of mass density, volumetric entropy, their successive gradients, and velocity.
Fichier principal
Vignette du fichier
2018-07-08- Parabolic_hyperbolic_systems.pdf (148.95 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01956138 , version 1 (14-12-2018)

Identifiants

Citer

Henri Gouin. Symmetric forms for hyperbolic-parabolic systems of multi-gradient fluids. Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 2019, ⟨10.1002/zamm.201800188⟩. ⟨hal-01956138⟩
43 Consultations
77 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More