On spatial resolution capabilities with direct numerical simulations of turbulent Benard convection

In a former paper results of numerically simulated turbulent natural convection have been presented for which rather coarse finite difference grids and no subgrid-scale models have been used. These results, and the theoretically determined values for the coefficients of the subgrid-scale heat flux model are tested in this paper on the basis of recent direct numerical simulations using finer grids. As a result of increasing spatial resolution capabilities the earlier published Nusselt numbers decrease by about 6% and the rms-values of the temperature fluctuations by about 4%. Only less than 1% of the turbulence energy is neglected by the restricted spatial resolution for high wave numbers of the coarse grids used earlier. The theory to calculate the subgrid-scale model coefficients turns out to be a suitable tool to judge on the spatial resolution capabilities of the finite difference grids used actually. Due to the moderate Rayleigh number under consideration all grids used in this work are fine enough to resolve even the smallest relevant turbulence elements; therfore, subgrid-scale models have not to be used. A complete plot output of the analyzing part of the TURBIT computer program is discussed in the appendix. (orig.)