Compressible flows are challenging. Consider looking into discretisations of the compressible Euler and compressible Navier-Stokes systems as a basis for your desired formulation. These are likely more extensively covered in the literature.
Compressible flows are challenging. Consider looking into discretisations of the compressible Euler and compressible Navier-Stokes systems as a basis for your desired formulation. These are likely more extensively covered in the literature.