Phase change in multiphase flows occurs in many natural and industrial applications, e.g., rain formation, internal combustion engines, heat exchangers, multiphase reactors, etc. In dense two-phase flows, quantitative experimental results are scarce due to the complexity of the configuration and experimental techniques limitations. Hence, the interest in the direct numerical simulation of such flows has grown recently to better understand and access quantitative data in this kind of flows. When simulating phase change in multiphase flows, advanced numerical method are needed to consider the jump conditions at the interface, and to ensure mass, energy, momentum and species conservation. In the literature, this problem is mainly investigated with an incompressible formalism. However, this assumption is not longer suitable for simulation of multiphase flows with phase change in enclosed environment or in atomized/aerated flows. The purpose of this work is to present a numerical formalism dedicated to turbulent two phase flows, including acoustics and compressible effects with a proper treatment of the jump conditions at the interface due to phase change. To achieve this task, first, the incompressible level-set method for vaporizing two-phase flows proposed by Tanguy et al. (2007) is revisited and adapted to a mass conservative interface representation: The Coupled Level-set/Volume of Fluid method. In this context, evaporating static cylinder with a constant vaporization rate and a droplet vaporization (D2 law) have been performed as validation cases. Both cases illustrate the method accuracy and robustness in presence of velocity discontinuities at the interface due to the presence of the Stefan flow. The D2 law configuration is used as validation of the implementation of the heat and mass transfer transport equations with their jump conditions and the coupling of the evaporation rate with the flow dynamic. Then, the numerical method is extended to compressible flows using the framework dedicated to the pressure based method proposed by Duret et al. (2018). The main advantage of this framework is the ability to consider acoustics effects, variable density and multiple gas inclusions with its own thermodynamic pressure. A modified Volume of Fluid transport equation is presented, including phase change and compressibility effects. Navier–Stokes and heat and mass transfer transport equation are solved using compressible assumptions. A validation case of a static evaporating cylinder in an enclosed environment is studied to illustrate and quantify the mass conservation properties of the method and the mass transfer between the two phases. Finally, a 3D two-phase Homogeneous Isotropic Turbulence (HIT) configuration is presented to demonstrate the potential of this method in presence of breakup, gas encapsulation, coalescence and evaporation processes.