Cost of low- and high-order direct numerical simulation of turbulent convection

Direct numerical simulation of turbulent flow is principally a matter of spatial and temporal resolution. If both resolutions are appropriate then any numerical method for the Navier-Stokes equations should yield acceptable predictions for averages, rms values, spectra and flow structures. The actual costs of such simulations may show large differences between methods. Low-order methods are typically inexpensive per grid cell, but many grid cells may be needed to achieve sufficient accuracy. Conversely, high-order methods present larger costs per grid cell but may achieve a good flow representation at fewer grid cells.