Abstract In the first part of the paper, code NASTENV is presented with its main characteristics and latest developments: the version here discussed is that of an advanced finite-volume 3D time-dependent Navier–Stokes solver, suitable for thermo-fluid-dynamical analyses of atmospheric, variable density, turbulent flow fields. Rooted on a conservative, arbitrary Lagrangian–Eulerian (ALE) scheme, it was very recently converted from explicit to a largely implicit formulation, and, to further increasing numerical efficiency, a multigrid accelerator has been implemented, thus reaching substantial savings in the number of iterations required to reach convergence. A specific aim of the study is to test the predictive capacity of NASTENV's new turbulence model by comparing predictions with the wind data obtained from US EPA's wind tunnel experiment RUSHIL, on the flow structure over isolated two-dimensional hills. To this end, the new turbulence model (TSDIA, two-scale direct-interaction approximation) recently implemented into the code in a simplified first-order version, has been extended for the present application to a higher-order level: more specifically, use is made of asymptotic expansions based on a scale parameter capable to distinguish the slow variation of mean flows from the fast variation of turbulent fluctuations. These contributions greatly help in correctly capturing significant shear stress levels in flow regions where velocity gradients are very low. The level of accuracy of the results is high, confirming the reliability of the predictive capacity attained by the solver.