Abstract.Presented are results from the application of a shock-capturing numerical scheme to the solution of the Favreaveraged Navier-Stokes fluid-flow equations, coupled with compressibility-corrected turbulence models. The relative performance of both a two-equation model and a Reynolds-stress transport model are evaluated in their application to the modelling of both moderately under-expanded, and highly under-expanded experimental releases. Both standard, and compressibility corrected models are investigated, and the superior predictive capabilities of the second-moment Reynolds-stress model are demonstrated.