Discrete filters for large-eddy simulation of forced compressible magnetohydrodynamic turbulence

We discuss results of the applicability of discrete filters for the large-eddy simulation (LES) method of forced compressible magnetohydrodynamic (MHD) turbulent flows with the scale-similarity model. New results are obtained for cross-helicity and residual energy. Cross-helicity and residual energy are important quantities in magnetohydrodynamic turbulence and have no hydrodynamic counterpart. The influences and effects of discrete filter shapes on the scale-similarity model are examined in physical space using finite-difference numerical schemes. We restrict ourselves to the Gaussian filter and the top-hat filter. Representations of this subgrid-scale model, which correspond to various 3- and 5-point approximations of both Gaussian and top-hat filters for different values of parameter $ϵ$ (the ratio of the cut-off length-scale of the filter to the mesh size), are investigated. Discrete filters produce more discrepancies for the magnetic field. It is shown that the Gaussian filter is more sensitive to the parameter ϵ than the top-hat filter in compressible forced MHD turbulence. The 3-point filters at $ϵ=2$ and $ϵ=3$ give the least accurate results whereas the 5-point Gaussian filter shows the best results at $ϵ=2$ and $ϵ=3$. There are only very small differences deep into the dissipation region in favor of $ϵ=2$. For cross-helicity, the 5-point discrete filters are in good agreement with the results of direct numerical simulation (DNS), while the 3-point filter produces the largest discrepancies with DNS results. There is no strong dependence on the choice of the parameter $ϵ$ and order approximation is a much more important factor for the cross-helicity. The difference between the filters is less for the residual energy compared with total energy. Thus, the total energy is more sensitive to the choice of discrete filter in the modeling of compressible MHD turbulence using the LES method. (paper)