This study focuses on the development of a pressure based method able to capture compressibility effects and phase change in turbulent two-phase flow DNS, using the Coupled Level Set/Volume of Fluid (CLSVOF) interface capturing method. A compressible VOF equation and a new pressure equation are described, including additional terms due to vaporization and compressibility. First, validation cases without phase change such as a gas-water shock tube and an oscillating water column configuration have been performed. Concerning the first case, obtained results suggests that the method is able to capture accurately the shock wave characteristics. For the second case, a reference solution is computed and compared with DNS results, showing the method accuracy and convergence. Finally, a two-phase Homogeneous Isotropic Turbulence with compressibility and phase change is investigated. Contrary to previous works, the vaporization process has an impact on the flows dynamics. The effects of the vaporization on the gas density is illustrated and compared with a reference solution for a constant vaporization rate. Great agreement is obtained between DNS results and the reference solution. The mass balance between total mass, gas and liquid mass is also shown and demonstrates the efficiency of the CLSVOF interface capturing method regarding mass conservation, even in a turbulent atomization context.