Abstract

Estimations of the grid size and computational cost for direct numerical simulation (DNS) and large-eddy simulation (LES) of Rayleigh-Bénard convection (RBC) are presented in the {Ra, P r} phase space. Computational requirements to reach the so-called asymptotic Kraichnan or ultimate regime of turbulence using DNS are far too expensive. Therefore, we turn to LES to predict the large-scale behavior at very high Ra-numbers. However, a priori alignment studies clearly show why the modelization of the SGS heat flux is the main difficulty that (still) precludes reliable LES of buoyancy-driven flows at (very) high Ra-numbers. This inherent difficulty can be by-passed by carrying out simulations at low-P r numbers where no SGS heat flux activity is expected. This opens the possibility to reach the ultimate regime carrying out LES of RBC at low-P r using meshes of 10101011grid points. Nevertheless, to do so, we firstly need to combine proper numerical techniques for LES (also DNS) with an efficient use of modern hybrid supercomputers.