  We propose a new generalized compressible diphasic Navier-Stokes
Cahn-Hilliard model that we name G-NSCH. This new G-NSCH model takes into
account important properties of diphasic compressible fluids such as possible
non-matching densities and contrast in mechanical properties (viscosity,
friction) between the two phases of the fluid. the model also comprises a term
to account for possible exchange of mass between the two phases. Our G-NSCH
system is derived rigorously and satisfies basic mechanics of fluids and
thermodynamics of particles. Under some simplifying assumptions, we prove the
existence of global weak solutions. We also propose a structure preserving
numerical scheme based on the scalar auxiliary variable method to simulate our
system and present some numerical simulations validating the properties of the
numerical scheme and illustrating the solutions of the G-NSCH model.
