Large eddy simulations of Rayleigh–Bénard convection using subgrid scale estimation model

Abstract

The subgrid scale estimation model, which has been previously studied for large eddy simulations of turbulent channel flow, was extended to convective flows. The estimation procedure involves expanding the temperature and velocities to scales smaller than the grid size using the properties of the top-hat filter, Fourier expansions, and nonlinear interactions among the resolved scales. An expanded field, which contains subgrid scales two times smaller than the grid size, is used to calculate the subgrid scale stresses directly from the definition. In an a priori analysis, the exact quantities computed from the direct numerical simulation data are compared with results from the estimation model and the Smagorinsky model applied without wall functions. The subgrid scale stresses from the estimation model agree well with the exact quantities, but the Smagorinsky model results do not. The same conclusions are reached after both models are implemented in actual large eddy simulations. For both the velocities and temperature, the estimation model produces a more realistic distribution of subgrid scale stresses across the convective layer, does not require wall functions for correct behavior near the boundary, and does not contain any arbitrary constants, in contrast to the Smagorinsky model. Additionally, numerically stable backscatter is inherent in the estimation model.