The governing equations for Direct Numerical Simulation are assumed to be the Navier–Stokes equations, and correspondingly the governing equations for Large Eddy Simulation are derived therefrom. We consider both incompressible and compressible flow, with the limitation in theNagnibeda, E. latter to calorically and thermally perfect gases for simplicity. Non-equilibrium effects (e.g., dissociation, ionization, thermochemical reaction, and radiation) may be important in highKogan, M.-speed flowsBoyd, I. and the reader is referred to the literatureBrun, R. including (Brun 2009; Nagnibeda and Kustova 2009), and rarefied gas dynamics in Kogan (1969), Boyd and Schwartzentruber (2017).