The present work is concerned with the Steady RANS (Reynolds-Averaged Navier-Stokes) computations of inherently unsteady separating flow configurations. The focus is on the flow past the well-known Ahmed body (Ahmed et al., 1984), the rear slant angle of which corresponds to 25°. Unlike all (near-wall) RANS models, independent of modelling level, predicting a massive flow detachment occupying the entire slanted region, the present RANS model reproduces correctly the mean flow topology characterized by a thin separation bubble reattaching already at the slanted surface. It is achieved by intensifying appropriately the turbulence activity at the region of boundary layer separation by introducing an correspondingly formulated sink term (PΔU) into the relevant scale-supplying equation. The latter negative production term is modelled in terms of the second derivative of the mean velocity field (ΔU), as proposed originally by Rotta (1972). The underlying turbulence model, the present work is primarily focussed on, represents a differential near-wall Reynoldsstress model (RSM), but the effects of the additional source term is also checked in conjunction with the widely used k −ω-SST eddy-viscosity model. The numerical robustness of the RSM model formulation is enhanced by appropriately weighting the explicit treatment of the divergence of the Reynolds stress tensor in the momentum equation with its implicit treatment by utilizing the Boussinesq correlation; only a small portion of the implicit part – up to 20% - is needed to substantially stabilize the computation. The predictive capabilities of the extended RSM version, along with the performance of its baseline version, are in addition illustrated by computing some generic test cases subjected to separation from continuous and sharp-edged surfaces.