Addressing the Grid size Sensitivity Issue in Large eddy Simulations of Stable Boundary Layers

Abstract

In current study, several fundamental and inherent problems in original Deardorff subgrid model are identified under stably stratified condition. It is found that the mixing length parameterization in this subgrid model is at the root of a long trouble problem of grid size sensitivity in large-eddy simulation (LES). A new formulation of mixing length is proposed under the consideration of some basic elements including the presence of surface, the dependence of grid size Δ and a smoothing interpolation. The performance of this modified scheme is remarkable regarding the improvement of the simulation quality and accuracy. In other words, not only is the convergence of the simulated results from a range of grid size achieved but also in the precise intensity of physical variables are modelled. The only discrepancies display in the variance of temperature in the middle of boundary layer and high turbulent kinetic energy near the surface.

To further experiment the performance of the new scheme under different scenarios, the cases of different stability condition, an independent LES code with same modification, the cases of different advection schemes and different prescribed parameters are explored. In very stable condition, the first order variables from the modified scheme are in reasonable range but with some spreads compared to the results from a dynamic code. The deviation of second order statistics shows that the proposed formulation of mixing length meets limitations due to the complex interaction between the surface and turbulent flow in shallower boundary layer. The modified scheme is model system independent based on the similar improvement of simulation results in an independent LES code system. The sensitivity of advection schemes is surprisingly hardly found in new proposed SGS model. The cases of tested parameters further verifies the limitation of original Deardroff subgrid model.