The present paper is devoted to a comparison of numerical methods for the convective part of a two-phase flow model. Four explicit schemes are tested using Riemann problems or smooth solutions. The main criteria for comparing the methods are: the accuracy for a fixed size of mesh, the convergence, the robustness and the CPU time cost necessary to reach a fixed error. The conclusions of this study are the following. The classical Rusanov scheme is not competitive, as expected. The relaxation scheme seems to be more efficient than the VFROE-ncv method, especially regarding robustness. The staggered scheme, recently investigated for this model, is sometimes less accurate for a fixed size of mesh than the VFROE-ncv and relaxation schemes but is the most acurate for a fixed run time.