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We present a polar coordinate lattice Boltzmann kinetic model forcompressible flows. A method to recover the continuum distribution functionfrom the discrete distribution function is indicated. Within the model, ahybrid scheme being similar to, but different from, the operator splitting isproposed. The temporal evolution is calculated analytically, and the convectionterm is solved via a modifiedWarming-Beam (MWB) scheme.Within theMWB scheme asuitable switch function is introduced. The current model works not only forsubsonic flows but also for supersonic flows. It is validated and verified viathe following well-known benchmark tests: (i) the rotational flow, (ii) thestable shock tube problem, (iii) the Richtmyer-Meshkov (RM) instability, and(iv) the Kelvin-Helmholtz instability. As an original application, we studiedthe nonequilibrium characteristics of the system around three kinds ofinterfaces, the shock wave, the rarefaction wave, and the material interface,for two specific cases. In one of the two cases, the material interface isinitially perturbed, and consequently the RMinstability occurs. It is foundthat themacroscopic effects due to deviating from thermodynamic equilibriumaround thematerial interface differ significantly from those around themechanical interfaces. The initial perturbation at the material interfaceenhances the coupling of molecular motions in different degrees of freedom. Theamplitude of deviation from thermodynamic equilibrium around the shock wave ismuch higher than those around the rarefaction wave and material interface. Bycomparing each component of the high-order moments and its value inequilibrium, we can draw qualitatively the main behavior of the actualdistribution function.

Polar coordinate lattice Boltzmann modeling of compressible flows