  We present a polar coordinate lattice Boltzmann kinetic model for
compressible flows. A method to recover the continuum distribution function
from the discrete distribution function is indicated. Within the model, a
hybrid scheme being similar to, but different from, the operator splitting is
proposed. The temporal evolution is calculated analytically, and the convection
term is solved via a modifiedWarming-Beam (MWB) scheme.Within theMWB scheme a
suitable switch function is introduced. The current model works not only for
subsonic flows but also for supersonic flows. It is validated and verified via
the following well-known benchmark tests: (i) the rotational flow, (ii) the
stable shock tube problem, (iii) the Richtmyer-Meshkov (RM) instability, and
(iv) the Kelvin-Helmholtz instability. As an original application, we studied
the nonequilibrium characteristics of the system around three kinds of
interfaces, the shock wave, the rarefaction wave, and the material interface,
for two specific cases. In one of the two cases, the material interface is
initially perturbed, and consequently the RMinstability occurs. It is found
that themacroscopic effects due to deviating from thermodynamic equilibrium
around thematerial interface differ significantly from those around the
mechanical interfaces. The initial perturbation at the material interface
enhances the coupling of molecular motions in different degrees of freedom. The
amplitude of deviation from thermodynamic equilibrium around the shock wave is
much higher than those around the rarefaction wave and material interface. By
comparing each component of the high-order moments and its value in
equilibrium, we can draw qualitatively the main behavior of the actual
distribution function.

Soft Condensed Matter