A gallery of maximum-entropy distributions: 14 and 21 moments

TL;DR

This paper investigates the shapes of velocity distribution functions derived from fourth-order maximum-entropy methods, revealing complex non-equilibrium structures and their relation to transport phenomena in gases.

Contribution

It provides a detailed analysis of 14- and 21-moment maximum-entropy distributions, highlighting their deviations from equilibrium and their implications for non-equilibrium gas dynamics.

Findings

Maximum-entropy distributions exhibit multiple lobes and branches.

Equilibrium distributions are recovered as special cases.

Eigenvalues illustrate non-uniform propagation of perturbations.

Abstract

This work explores the different shapes that can be realized by the one-particle velocity distribution functions (VDFs) associated with the fourth-order maximum-entropy moment method. These distributions take the form of an exponential of a polynomial of the particle velocity, with terms up to the fourth-order. The 14- and 21-moment approximations are investigated. Various non-equilibrium gas states are probed throughout moment space. The resulting maximum-entropy distributions deviate strongly from the equilibrium VDF, and show a number of lobes and branches. The Maxwellian and the anisotropic Gaussian distributions are recovered as special cases. The eigenvalues associated with the maximum-entropy system of transport equations are also illustrated for some selected gas states. Anisotropic and/or asymmetric non-equilibrium states are seen to be associated with a non-uniform spacial propagation of perturbations.