Large Eddy Simulations (LES) are of raising interest for numerous engineering applications in which an accurate flow prediction is necessary. This paper searches for the optimum mesh resolution in numerical simulations reliably predicting dispersion of pollutants in the lower part of the Atmospheric Boundary Layer (ABL). For the dispersion of pollutants, turbulent quantities have been assessed at several distances from the release point and compared to each other. Areas close to release points located at low altitudes are given a particular importance, because air pollutant concentrations can be too high for people present at such places. To achieve a realistic prediction of the flow and pollutant concentrations close to populated areas, LES are preferred over the Reynolds-Averaged Navier Stokes (RANS) models (Vita et al, 2020). A mesh resolution of 0.5 m is recommended at distances from the release point shorter than 40 m. Near the release point, physical effects like building downwash and horizontal plume enlargement due to the downstream wake region of buildings have a direct impact on pollutant concentrations and particle trajectories. In built-up areas at intermediary distances where the dispersion of the plume is directly influenced by buildings in their given constellation and where the energy production is high, a mesh resolution of 1.5 m is suggested. In areas where the plume is already dispersed and geometrical obstacles are rare, a mesh resolution of 3 m and more is sufficient. In these areas, the dissipation of energy and the transport of particles (mean quantities) that determine the flow are less affected by the mesh size.