Dissipative Two-Fluid Models

Henri Gouin (1, 2) , Sergey Gavrilyuk

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

From Hamilton's principle of stationary action, we derive governing equations of two-fluid mixtures and extend the model to the dissipative case without chemical reactions. For both conservative and dissipative cases, an algebraic identity connecting equations of momentum, mass, energy and entropy is obtained by extending the Gibbs identity in dynamics. The obtained system is hyperbolic for small relative velocity of the phases.

Mots clés: Hamilton's principle; multiphase flows; hyperbolicity; second law of thermodynamics; symmetric forms; fluid mechanics

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

Henri Gouin, Sergey Gavrilyuk. Dissipative Two-Fluid Models. Rendiconti del Circolo Matematico di Palermo, 2006, suppl. 78 (Serie II), pp.133-145. ⟨hal-00204894⟩