First principle basis of the direct numerical simulation for turbulence of inert and reactive gases

An open question of whether phenomenological fluid equations to be used for direct numerical simulation of turbulence are warranted on `first principles' is addressed, and the problem is posed using Klimontovich microscopic density to replace the Boltzmann function of the classical statistical mechanics. For inert monatomic gases, it is shown that all the gasdynamic equations, namely, the three conservation equations plus the Navier-Stokes stress law and the Fourier heat conduction law are retrieved as governing instantaneous quantities, without having recourse to any concepts of averaging or statistical equilibrium. For reactive gases, however, the Arrhenius reaction rate law written in terms of the fluctuating temperature is not justified, reflecting the fact that this rate law hinges crucially on these concepts.