Conservative formulation for compressible multiphase flows
  Derivation of governing equations for multiphase flow on the base of thermodynamically compatible systems theory is presented. The mixture is considered as a continuum in which the multiphase character of the flow is taken into account. The resulting governing equations of the formulated model belong to the class of hyperbolic systems of conservation laws. In order to examine the reliability of the model, the one-dimensional Riemann problem for the four phase flow is studied numerically with the use of the MUSCL-Hancock method in conjunction with the GFORCE flux. 
Evgeniy Romenski, Alexander A. Belozerov and Ilya M. Peshkov
physics.flu-dyn