Comparison of computational advantages of high-order discontinuous Galerkin and conventional finite-volume dynamical cores in atmospheric turbulent simulations

This study discusses the computational advantages of high-order dynamical cores over a conventional low-order dynamical core in atmospheric turbulent simulations. Implicit and explicit large-eddy simulations (LES) of dry Rayleigh convection were performed using two dynamical cores: one based on a high-order discontinuous Galerkin method (DGM) and the other on a totally second-order conventional finite-volume method (FVM) with advection schemes of various orders. The effective resolution and numerical energy accumulation, derived from kinetic energy spectra, were used to evaluate the physical performance of both dynamical cores. In the implicit LES experiment, we confirmed that the high-order DGM with a polynomial order of p=11 achieved a finer effective resolution than the FVM with third-order and seventh-order upwind schemes (UD3 and UD7). In contrast, in the explicit LES experiment, the effective resolution was largely determined by the subgrid-scale turbulence model, thereby reducing the relative advantage of high-order schemes. Our cost metrics, which combine the physical performance and computational resource usage, demonstrate that the DGM with p=7, 11 and the FVM with UD7 can achieve lower overall computational costs than the FVM with UD3 in both implicit and explicit LES experiments. Although the high-order DGM requires larger computational resources due to a stricter CFL condition, its overall computational costs are reduced in the implicit LES experiment because of its finer effective resolution, as well as high computational efficiency associated with superior data locality and smaller inter-node communication overhead. On the other hand, to fully exploit the advantages of high-order schemes in explicit LES, it is necessary to redesign the turbulence model so that the filter length becomes consistent with the inherent effective resolution of the dynamical cores, and to relax the stricter CFL condition for the DGM.