This study presents a method to perform direct numerical simulation (DNS), in the sense of turbulence, of two-phase flows with interfaces. It is based on the compressible diffuse interface model introduced by the second gradient theory. This model assumes a continuous variation of the thermodynamic variables in the interface and add to their description a dependency on the density gradient. The interface widths as predicted by the model fall way below the typical relevant turbulent scales. We propose here a thermo…