  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.
