The present paper is devoted to the computation of single phase or
two phase flows using the single-fluid approach. Governing equations
rely on Euler equations which may be supplemented by conservation
laws for mass species. Emphasis is given on numerical modelling
with help of Godunov scheme or an approximate form of Godunov scheme
called VFRoe-ncv based on velocity and pressure variables. Three
distinct classes of closure laws to express the internal energy in
terms of pressure, density and additional variables are exhibited.
It is shown first that a standard conservative formulation of above
mentioned schemes enables to predict “perfectly” unsteady contact
discontinuities on coarse meshes, when the equation of state (EOS)
belongs to the first class. On the basis of previous work issuing
from literature, an almost conservative though modified version of
the scheme is proposed to deal with EOS in the second or third
class. Numerical evidence shows that the accuracy of approximations
of discontinuous solutions of standard Riemann problems is
strengthened on coarse meshes, but that convergence towards the
right shock solution may be lost in some cases involving complex EOS
in the third class. Hence, a blend scheme is eventually proposed to
benefit from both properties (“perfect” representation of contact
discontinuities on coarse meshes, and correct convergence on finer
meshes). Computational results based on an approximate Godunov
scheme are provided and discussed.