Abstract Three criteria are deduced for the prediction of grids, which allow for accurate direct numerical simulations of turbulent flows. These criteria are based on wavelength considerations, boundary layer thickness estimates, and on a simplified theoretical model to calculate the coefficient of a verified subgrid-scale heat flux model. The criteria have been successfully tested by comparing the results of several three-dimensional and time-dependent numerical simulations for the Rayleigh-Benard convection of air in an infinite channel up to Ra = 381,225. Numerical results deduced from appropriate grids are in agreement with adequate experimental data. Numerical results deduced from insufficient grids show only weak deficiencies. The most sensitive data to restricted large wavelengths are the calculated Nusselt numbers and the flow regimes in the laminar-turbulent transition range; data sensitive to insufficient vertical resolution near the walls are also the Nusselt numbers; and data sensitive to insufficient horizontal resolution are the calculated Nusselt numbers and rms values of velocity and temperature fluctuations at large Rayleigh numbers. All three criteria use data specific to the type of flow only as input parameters. Therefore, these criteria may also be used for other types of flows.