For thermal and magnetic convection at very high Rayleigh and Hartman numbers, which are inaccessible to the conventional large eddy simulation (LES), we propose a time-dependent Reynolds-average-Navier-Stokes (T-RANS) approach in which the large-scale deterministic motion is fully resolved by time and space solution, whereas the unresolved stochastic motion is modelled by a “subscale” model for which an one-point RANS closure is used. The resolved and modelled contribution to the turbulence moments are of the same order of magnitude and in near-wall regions the modelled heat transport becomes dominant, emphasizing the role of the subscale model. This VLES approach, with an algebraic stress/flux subscale model, verified earlier in comparison with direct numerical simulation (DNS) and experiments in classic Rayleigh-Be´nrad convection, is now expanded to simulate Rayleigh-Be´nard (R-B) convection at very high Ra numbers — at present up to O(1016) — and to magnetic convection in strong uniform magnetic fields. The simulations reproduce the convective cell structure and its reorganization caused by an increase in Ra number and effects of the magnetic field. The T-RANS simulations of classic R-B indicate expected thinning of both the thermal and hydraulic wall boundary layer with an increase in the Ra number and an increase in the exponent of the NuRan correlation in accord with recent experimental findings and Kraichnan asymptotic theory.

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