In previous papers, we have presented hyperbolic governing equations and jump conditions for barotropic fluid mixtures. Now we extend our results to the most general case of two-fluid conservative mixtures taking into account the entropies of components. We obtain governing equations for each component of the medium. This is not a system of conservation laws. Nevertheless, using Hamilton's principle we are able to obtain a complete set of Rankine-Hugoniot conditions. In particular, for the gas dynamics they coincide with classical jump conditions of conservation of momentum and energy. For the two-fluid case, the jump relations do not involve the conservation of the total momentum and the total energy.
@article{hal-00249829,
author = {Gouin, Henri and Gavrilyuk, Sergey, },
title = {Hamilton's Principle and Rankine-Hugoniot Conditions for General Motions of Mixtures},
journal = {HAL},
volume = {1999},
number = {0},
year = {1999},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00249829}
}
Gouin, Henri; Gavrilyuk, Sergey, . Hamilton's Principle and Rankine-Hugoniot Conditions for General Motions of Mixtures. HAL, Tome 1999 (1999) no. 0, . http://gdmltest.u-ga.fr/item/hal-00249829/