Mesoscopic Boltzmann model equations for thermally perfect gases

Abstract

We propose a way to derive Bhatnagar–Gross–Krook and Fokker–Planck models of the Boltzmann equation for rarefied flows of thermally perfect gases. These models can allow for various internal energies (rotation, vibration, electronic), which is required for high temperature flows, like in atmospheric reentry problems. However, our models do not contain any internal degrees of freedom; instead, they are accounted for by a mesoscopic approach. The molecular velocity is the only kinetic variable in the models that makes their computational complexity similar to that of simple monatomic gases. Moreover, we prove that these models satisfy conservation and entropy properties (H-theorem), and we derive their corresponding compressible Euler and Navier–Stokes asymptotics gases.