In this paper, we focus on using high-resolution implicit upwind shock-capturing scheme to avoid the formation of non-linear instabilities and numerical oscillations across shock waves or discontinuities. The governing equation is the compressible Reynolds Averaged Navier-Stokes equation based on the homogeneous mixture model. A preconditioned method is applied for enhancing efficient and accurate computations over a wide range of Mach numbers. For evaluation, the results from the present study have been compared with experiments and other numerical results. A fairly good agreement with the experimental data and other numerical results have been obtained. Finally, the simulation of ventilated supercavitating flows over a torpedo with a hot propulsive jet was conducted to verify the efficiency of numerical scheme.

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