A nonlinear structural subgrid-scale closure for compressible MHD Part II: a priori comparison on turbulence simulation data

Even though compressible plasma turbulence is encountered in many astrophysical phenomena, its effect is often not well understood. Furthermore, direct numerical simulations are typically not able to reach the extreme parameters of these processes. For this reason, large-eddy simulations (LES), which only simulate large and intermediate scales directly, are employed. The smallest, unresolved scales and the interactions between small and large scales are introduced by means of a subgrid-scale (SGS) model. We propose and verify a new set of nonlinear SGS closures for future application as an SGS model in LES of compressible magnetohydrodynamics (MHD). We use 15 simulations (without explicit SGS model) of forced, isotropic, homogeneous turbulence with varying sonic Mach number $\mathrm{M_s} = 0.2$ to $20$ as reference data for the most extensive \textit{a priori} tests performed so far in literature. In these tests we explicitly filter the reference data and compare the performance of the new closures against the most widely tested closures. These include eddy-viscosity and scale-similarity type closures with different normalizations. Performance indicators are correlations with the turbulent energy and cross-helicty flux, the average SGS dissipation, the topological structure and the ability to reproduce the correct magnitude and direction of the SGS vectors. We find that only the new nonlinear closures exhibit consistently high correlations (median value \textgreater$0.8$) with the data over the entire parameter space and outperform the other closures in all tests. Moreover, we show that these results are independent of resolution and chosen filter scale. Additionally, the new closures are effectively coefficient-free with a deviation of less than $20\%$.