Toward turbulence description using Boltzmann: Theory and Computations

It is general consensus that most of the observed turbulence behavior in the continuum regime can be explained using the Navier-Stokes equation. It is also well known that the Boltzmann equation forms a basis of the Navier-Stokes equation. Yet, to date, little effort has been made to describe or model turbulence using the Boltzmann equation. In this talk, I will present results from direct numerical simulations (DNS) of isotropic and homogeneous turbulence performed with Boltzmann equation using the lattice Boltzmann method (LBM). Comparisons with Navier-Stokes DNS show excellent agreement. Then, I proceed to demonstrate how the Boltzmann equation can be filtered or averaged for developing closure models. It will be shown that straight-forward averaging or filtering the Boltzmann equation will not produce the desired results. A crucial transformation of the dependent and independent variables in the velocity phase-space must precede the averaging/filtering process. The similarities and difference between closure modeling in Navier-Stokes and Boltzmann contexts will also be described.