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

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.