A nonorthogonal, collocated finite-volume scheme, based on a pressure-correction strategy and originally devised for general-geometry incompressible turbulent recirculating flow, has been extended to compressible transonic conditions. The key elements of the extension are a solution for flux variables and the introduction of streamwise-directed density-retardation which is controlled by Mach-number-dependent monitor functions, and which is applied to all transported flow properties. Advective fluxes are approximated using the quadratic scheme QUICK or the second-order TVD scheme MUSCL, the latter applied to all transport equations, including those for turbulence properties. The procedure incorporates a number of turbulence models including a new low-Re k–ε eddy-viscosity variant and a Reynolds-stress-transport closure. The predictive capabilities of the algorithm are illustrated by reference to a number of inviscid and turbulent transonic applications, among them a normal shock in a Laval nozzle, combined oblique-shock reflection and shock-shock interaction over a bump in a channel and shock-induced boundary-layer separation over channel bumps. The last-named application was computed both with eddy-viscosity models and Reynolds-stress closure, leading to the conclusion that the latter yields a much greater sensitivity of the boundary layer to the shock and, arising therefrom, a more pronounced λ-shock structure, earlier separation and more extensive recirculation. On the other hand, the stress closure is found to return an insufficient rate of wake recovery following reattachment.