On the Five-Moment Maximum Entropy System of One-Dimensional Boltzmann Equation (Communications in Computational Physics, 2021)
The maximum entropy moment system extends the Euler equation to nonequilibrium gas flows by considering higher order moments such as the heat flux.This paper presents a systematic study of the maximum entropy moment system ofBoltzmann equation. We consider a hypothetical one-dimensional gas and study afive-moment model. A numerical algorithm for solving the optimization problem isdeveloped to produce the maximum entropy distribution function from known moments, and the asymptotic behaviour of the system around the singular region knownas the Junk’s line, as well as that near the boundary of the realizability domain is analyzed. Furthermore, we study the properties of the system numerically, including thebehaviour of the system around the Maxwellian and within the interior of the realizability domain, and properties of its characteristic fields. Our studies show the higherorder entropy-based moment models to differ significantly from the Euler equations.Much of this difference comes from the singularity near the Junk’s line, which wouldbe removed if a truncation of the velocity domain is employed.