Comparative statistics of selected subgrid-scale models in large-eddy simulations of decaying, supersonic magnetohydrodynamic turbulence

摘要

Large-eddy simulations (LES) are a powerful tool in understanding processes that are inaccessible by directsimulations due to their complexity, for example, in the highly turbulent regime. However, their accuracyand success depends on a proper subgrid-scale (SGS) model that accounts for the unresolved scales in thesimulation.We evaluate the applicability of two traditional SGS models, namely the eddy-viscosity (EV) and thescale-similarity (SS) models, and one recently proposed nonlinear (NL) SGS model in the realm of compressiblemagnetohydrodynamic (MHD) turbulence. Using 209 simulations of decaying, supersonic (initial sonic Machnumber M_s ≈ 3) MHD turbulence with a shock-capturing scheme and varying resolution, SGS model, and filter,we analyze the ensemble statistics of kinetic and magnetic energy spectra and structure functions. Furthermore,we compare the temporal evolution of lower- and higher-order statistical moments of the spatial distributions ofkinetic and magnetic energy, vorticity, current density, and dilatation magnitudes.We find no statistical influenceon the evolution of the flow by any model if grid-scale quantities are used to calculate SGS contributions. Inaddition, the SS models, which employ an explicit filter, have no impact in general. On the contrary, both the EVand NL models change the statistics if an explicit filter is used. For example, they slightly increase the dissipationon the smallest scales. We demonstrate that the nonlinear model improves higher-order statistics already witha small explicit filter, i.e., a three-point stencil. The results of, e.g., the structure functions or the skewness andkurtosis of the current density distribution are closer to the ones obtained from simulations at higher resolution.In addition, no additional regularization to stabilize the model is required.We conclude that the nonlinear modelwith a small explicit filter is suitable for application in more complex scenarios when higher-order statistics areimportant.