Can anyone recommend or provide references for compressible flow turbulence models? I am modelling a supersonic impinging jet. Cheers Shuo

Farge and Sadourny, 1989, Journal of Fluid Mechanics, n.206, page 433. That's a 2D simulation of compressible turbulence, you might want to have a look at it, but that's not about a jet.

For supersonic jets there are some astrophysical simulation of supersonic jets launched by magnetic field. See e.g.

http://arxiv.org/abs/astro-ph/9810352

You can also check that site http://arxiv.org/ and look for simulations of jets (usually in the astrophysical part).

Good luck.

Also for Navier-stokes equation what is the benefit of using viscous Jacobian as opposed to just modifying the inviscid fluxes?

What do you mean by viscous Jacobian or modifying the inviscid fluxes? Navier-Stokes equations are including the viscosity. But there are different approximation to including the viscosity and different numerical approaches to include these approximation. If you have shocks with your supersonic jet then you want to have in addition a way to capture the shock and keep the fine structure of the flow while getting rid of oscillations due to the discontinuity (shock).