Subgrid-scale modeling of isotropic turbulence in compressible magnetohydrodynamic large eddy simulations

Despite the ever increasing availability of computational resources, fully resolved simulations of magnetohydrodynamic (MHD) turbulence are not going to be feasible for quite some time. For this reason, large eddy simulations (LES) have been introduced that only resolve large scales. In LES a low-pass filter is applied to the evolution equations, which introduces additional unknown terms. These unknown terms contain the effects below the grid scale and are accounted for by a subgridscale (SGS) model. We explore two SGS models for isotropic turbulence in LES of compressible MHD. The first model uses only turbulent cross-helicity to close the filtered MHD equations. The second, so called β − γ model, was originally introduced in the context of incompressible, Reynolds-averaged MHD and is here extended to compressible LES. It employs both SGS energy and cross-helicity in determining the closure. We conduct a priori tests of both models in the statistically stationary state of a high-resolution (5123), isothermal, driven turbulence simulation with homogeneous initial conditions. Only for the β − γ model we find collective correlations between data and model. A subsequent a posteriori verification of this model, based on a comparison between SGS and non-SGS runs of driven turbulence with varying grid resolution of 643, 1283 and 2563, suggests that it is generally stable, but does not influence the large and small scale properties of the simulation. Nevertheless, we confirm the proper application of SGS cross-helicity and energy in closure determination. Thus, we suggest the extension of the existing model to include additional physical properties such as helicity, and the application to less artificial physical problems.