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Detailed view Article in peer-reviewed journal
Meccanica 33, 2 (1998) 161-175
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Hyperbolic Models of Homogeneous Two-Fluid Mixtures
Sergey L. Gavrilyuk, Henri Gouin1, 2, Yurii Perepechko

One derives the governing equations and the Rankine - Hugoniot conditions for a mixture of two miscible fluids using an extended form of Hamilton's principle of least action. The Lagrangian is constructed as the difference between the kinetic energy and a potential depending on the relative velocity of components. To obtain the governing equations and the jump conditions one uses two reference frames related with the Lagrangian coordinates of each component. Under some hypotheses on flow properties one proves the hyperbolicity of the governing system for small relative velocity of phases.
1:  MSNMGP - Modélisation et Simulation Numérique en Mécanique et Génie des Procédés
2:  LMMT - Laboratoire de Modélisation Mécanique et Thermodynamique, EA 2596
Hamilton's principle – Hyperbolicity – Multiphase Flows.