Numerical Accuracy Necessary for Large-Eddy Simulation of Planetary Boundary Layer Turbulence Using the Discontinuous Galerkin Method

Abstract

Abstract In large-eddy simulations (LES), it is crucial to ensure that discretization errors do not contaminate the subgrid effect of the turbulence model in a wavelength range larger than the effective resolution. Recently, we showed that a seventh- or eighth-order accuracy is required for advection terms in planetary boundary layer simulations when using conventional gridpoint methods. However, a significant amount of communication between parallel computers is necessary to achieve high-order accuracy in gridpoint methods, and this can degrade computational efficiency. The discontinuous Galerkin method (DGM) is a promising approach for overcoming these limitations. Therefore, this study focuses on the numerical criteria of the DGM at LES from the viewpoint of numerical diffusion and dispersion. We extend our earlier study to the DGM framework and clarify the necessary order of the polynomial (p). We find that p = 4 is required based on the numerical criteria at the grid spacing of O(10) m with sufficiently scale-selective modal filters. The examination of temporal accuracy suggests that the fourth-order is sufficient when a fully explicit temporal scheme is used. In addition, we investigate the effect of hyperupwinding that is usually met when the Rusanov flux is employed in the low Mach number flows. It suggests that the choice of numerical flux has little effect on simulation results when the high-order DGM is used. Furthermore, we perform a series of LES in the planetary boundary layer and confirm that the indication obtained from the criteria holds for an actual LES.