A computational tool is introduced and applied to the emergence of supersonic liquid jets in quiescent compressible gas. A diffuse interface wave propagation method along with an interface sharpening technique is employed to solve the governing equations of compressible multiphase flows. Adaptive mesh refinement (AMR) strategy is utilized to improve the ability of the solver in better resolving the flow features. The accuracy of our method is benchmarked with four experimental and numerical test problems. Then, the evolution of supersonic liquid jets in compressible gaseous media is simulated; demonstrating a good agreement with experimental observations. Moreover, the impact of physical parameters, such as increment in ambient pressure and inlet velocity on the flow characteristics, is examined. The results indicate that the penetration length of the liquid jet decreases with an increase in the ambient pressure. The values of this parameter compare reasonably well with the experiment-based correlations. Further, with lower ambient pressure the Mach cone generated ahead of the liquid jet has a narrower half angle, situated closer to the jet tip. A similar behavior is demonstrated by the induced shock-front when the inlet Mach number of the liquid jet is increased. The simulations indicate the applicability of our numerical methodology to supersonic liquid jet flows for the analysis of shock waves dynamics and shock–interface interaction.