A non-hydrostatic micro-scale model (MITRAS) is used to simulate the flow field over a beam. The model is run with a constant grid size of 1/5 times the beam height representing a relatively coarse resolution. Different types of k-epsilon closures are used, the standard k-epsilon closure and modified ones. A comparison of model results (mean values, turbulent kinetic energy and momentum fluxes) with wind tunnel data confirms the finding of earlier studies performed with models of higher resolution, that the standard k-epsilon closure overestimates the turbulent kinetic energy in stagnation points. The comparison with wind tunnel data reveals that the momentum fluxes are overestimated at stagnation points as well. A modification of the standard k-epsilon closure is introduced that reduces both, the modelled momentum fluxes and the turbulent kinetic energy at stagnation points.