A variational principle for two-fluid models

Sergey L. Gavrilyuk , Henri Gouin (1, 2) , Yurii Perepechko

1 LMMT - Laboratoire de Modélisation Mécanique et Thermodynamique, EA 2596
2 IUSTI - Institut universitaire des systèmes thermiques industriels

A variational principle for two-fluid mixtures is proposed. The Lagrangian is constructed as the difference between the kinetic energy of the mixture and a thermodynamic potential conjugated to the internal energy with respect to the relative velocity of phases. The equations of motion and a set of Rankine-Hugoniot conditions are obtained. It is proved also that the convexity of the internal energy guarantees the hyperbolicity of the one-dimensional equations of motion linearized at rest.

Mots clés: Two-fluid mixtures; variational principle

Domaines: Mécanique des fluides [physics.class-ph]; Physique mathématique [math-ph]

Sergey L. Gavrilyuk, Henri Gouin, Yurii Perepechko. A variational principle for two-fluid models. Comptes rendus de l’Académie des sciences. Série IIb, Mécanique, physique, astronomie, 1997, 324 (8), pp.483-490. ⟨10.1016/S1251-8069(97)80186-8⟩. ⟨hal-00239305⟩