Numerical Accuracy of Advection Scheme Necessary for Large-Eddy Simulation of Planetary Boundary Layer Turbulence

Abstract

AbstractRecently, large-eddy simulation (LES) has been increasingly employed in meteorological simulations because it is a promising method for turbulent parameterization. However, it is still difficult to affirm that the numerical accuracy required for a dynamical core is fully understood. In this study, we derived two theoretical criteria for the order of accuracy of the advection term in a typical situation of the atmospheric boundary layer, and demonstrate their validity by numerical experiments. In the targeted grid-spacing of O (10 m), we determined the required order of accuracy as follows: Based on the criterion of the numerical diffusion error, the upwind scheme must have at least seventh-order accuracy. The fourth-order central scheme is barely acceptable with fourth-order explicit diffusion, provided that its coefficient is one or two orders of magnitude smaller than the implicit diffusion coefficient of the third-order upwind scheme. Based on the criterion of numerical dispersion error, at minimum, the seventh or eighth order is required. The dispersion error was indirect for the energy spectra, although we expect it may affect the local turbulence mechanism. We also investigated the effects of temporal discretization for compressible models, and found that relatively lower-order time schemes are available up to the O(10 m) grid spacing if the time step is sufficiently small due to sound wave limitations. The importance of the derived criteria is that the required order of accuracy increases as the grid spacing decreases. This suggests that considerable care should be taken regarding the numerical error problem for future high-resolution LES.