In this article, recent progress in the development of large eddy simulation (LES) for the study of compressible magnetohydrodynamic (MHD) turbulence of space plasma (Chernyshov et al.,
) is given (for LES applications in hydrodynamics of neutral gas see (Garnier et al.,
) and for incompressible MHD turbulence see (Müller and Carati,
)). The proper subgrid-scale (SGS) model relevant for space and astrophysical turbulence is selected based on this development, and the efficiency of LES for the investigation of the local interstellar gas turbulence is shown. In particular, the developed LES allows to explain observed data about the Kolmogorov-like spectrum of density fluctuations on the basis of three-dimensional modeling and, thus, to confirm a hypothesis that the weakly compressible regime of MHD turbulence in the local interstellar medium is fulfilled and density fluctuation are a passive scalar.