The present paper is devoted to the computation of single phase or two phase ows using the single-uid 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 rst that standard conservative formulation of above mentionned schemes enables to predict \perfectly" unsteady contact disconti-nuities on coarse meshes, when the EOS belongs to the rst class. On the basis of previous work issuing from literature, an almost conservative though modiied 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 strenghtened 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 beneet from both properties (\perfect" representation of contact discontinuities on coarse meshes, and correct convergence on ner meshes). Computational results based on an approximate Godunov scheme are provided and discussed.