A finite volume based method for large eddy simulation of compressible isotropic turbulence is suggested. A sixth order compact interpolation method is used for computing fluxes at the cell interfaces. Dynamic Smagorinsky Model (DSM) for compressible flows is used for LES. The flow solver is validated using various benchmark problems. Decaying isotropic turbulence is simulated using both DNS and LES. Turbulent statistics and energy spectra are compared. The LES method is found to effectively model the small scales of turbulent motion. © 2019, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.