Recovery of transport coefficients in Navier-Stokes equations from modeled Boltzmann equation

A method for derivation of Navier-Stokes (NS) equations from the modeled Bolzmann equation (BE) by modifying the collision relaxation time in the commonly assumed Bhatnagar, Gross, and Krook (BGK) model is presented. The derived BE is valid for dense gas only when the mean free path between two successive particle collisions is very small compared with the characteristic spatial scale of the fluid system. The effect of nonreflecting boundary conditions on aeroacoustic simulations was examined, which presented good results. Further investigation of this model was conducted by considering acoustic scattering of a sinusoidal pulse by a zero circulation vortex and acoustic interaction with the line heat source. These investigations allowed assessment of the ability of the modeled BE to replicate sound scattering and the effect of the Prandtl number on sound propagation.