A variational principle for two-fluid models

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

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