This work intent to provide numerical tools, allowing simulations of two-phase flow incorporatingcompressible effects and a proper treatment of the jump conditions found at the interface dueto large density ratios and phase change. For achieving this task, first, the incompressiblelevel-set method for vaporizing two-phase flows proposed by Tanguy et al. [12] is revisitedand adapted to a conservative interface representation: The Coupled Level-set/Volume of Fluidmethod. In this context, results are presented for simulations of the evaporation of an isolatedstatic droplet. Then, the formalism is extended into a compressible one using as framework thepressure-based method proposed by Duret et al. [4]. For validation, a 3D simulation of a staticevaporating droplet is studied for showing the proper mass balance between the two phases.Finally, a 3D two-phase compressible Homogenous Isotropic Turbulence (HIT) configuration ispresented to demonstrate the potential of this method in presence of breakup, coalescence andevaporation processes.