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A massively parallel large-eddy simulation (LES) code for planetary boundary layers (PBLs) that utilizes pseudospectral differencing in horizontal planes and solves an elliptic pressure equation is described. As an application, this code is used to examine the numerical convergence of the three-dimensional time-dependent simulations of a weakly sheared daytime convective PBL on meshes varying from 323 to 10243 grid points. Based on the variation of the second-order statistics, energy spectra, and entrainment statistics, LES solutions converge provided there is adequate separation between the energy-containing eddies and those near the filter cutoff scale. For the convective PBL studied, the majority of the low-order moment statistics (means, variances, and fluxes) become grid independent when the ratio zi/(CsΔf) > 310, where zi is the boundary layer height, Δf is the filter cutoff scale, and Cs is the Smagorinsky constant. In this regime, the spectra show clear Kolmogorov inertial subrange scaling...

The Effect of Mesh Resolution on Convective Boundary Layer Statistics and Structures Generated by Large-Eddy Simulation