The present study focuses on a turbulence modeling strategy aiming at advancement of the Reynolds-averaged Navier-Stokes (RANS) approach. The modeling strategy relies on an anisotropy-resolving near-wall second-moment closure model, which is extended to behave as an eddy-resolving model with respect to capturing spatial and temporal variability of turbulence scales. The model should not comprise any parameter depending explicitly on the grid spacing. It means the objective is to formulate a “true” Unsteady RANS (URANS) model. An additional term in the corresponding length-scale determining equation providing a selective assessment of its production represents a key parameter in this novel URANS approach. This term modeled in terms of the von Karman length scale representing the ratio of the second to the first derivative of the velocity field in line with the scale-adaptivity concept (SAS - scale adaptive simulation) introduced by Menter and Egorov. In addition, the background RANS model has been “numerically stabilized” by reformulating some terms - primarily diffusive transport and gradient production - in conjunction with an appropriately defined wall boundary condition for the dissipation rate of kinetic energy of turbulence. Herewith, the use of high-order numerical schemes, such as 2nd order central differencing scheme, is promoted; this issue is of crucial importance with respect to preventing the possible fallback from mainly resolved turbulent structures to modeled ones. The predictive performances of this instability-sensitive, eddy-resolving model was checked by computing different flow cases including separation from a sharp-edged surface (backward-facing step configurations) and continuous flat and curved surfaces (flow past a tandem cylinder configuration, flow over a 2D Hill and in a 3D Diffuser in a range of geometrical parameters and Reynolds numbers). The results obtained are in closest agreement with available reference data, outperforming significantly the results pertinent to the conventional model of turbulence. Prior to that several globally stable flows, such as natural decay of homogeneous isotropic turbulence and flow in a plane channel have been computed in course of the model calibration. It should be emphasized that in all cases considered the fluctuating velocity field was obtained started from the steady RANS results. Finally, an appropriate modification of the background second-moment closure model in the “Steady RANS” framework is proposed leading to substantially improved turbulence level prediction - and consequently the mean flow field - in the separating flow regions; by simultaneously retaining good results in attached flow regions.