Dust devils are organized convective vortices with pressure drops of hundreds of pascals that spirally lift surface material into the air. This material modifies the radiation budget by contributing to the atmospheric aerosol concentration. Quantification of this contribution requires good knowledge of the dust devil statistics and dynamics. The latter can also help to understand vortex genesis, evolution and decay, in general. Dust devil-like vortices are numerically investigated mainly by large-eddy simulation (LES). A critical parameter in these simulations is the grid spacing, which has a great influence on the dust devil statistics. So far, it is unknown which grid size is sufficient to capture dust devils accurately. We investigate the convergence of simulated convective vertical vortices that resemble dust devils by using the LES model PALM. We use the nesting capabilities of PALM to explore grid spacings from 10 to 0.625 m. Grid spacings of 1 m or less have never been used for the analysis of dust devil-like vortices that develop in a horizontal domain of more than 10 km2. Our results demonstrate that a minimum resolution of 1.25 m is necessary to achieve a convergence for sample-averaged quantities like the core pressure drop. This grid spacing or smaller should be used for future quantifications of dust devil sediment fluxes. However, sample maxima of the investigated dust devil population and peak velocity values of the general flow show no convergence. If a qualitative description of the dust devil flow pattern is sufficient, we recommend a grid spacing of 2.5 m or smaller.