  A D2Q9 Hybrid Lattice Boltzmann Method (HLBM) is proposed for the simulation
of both compressible subsonic and supersonic flows. This HLBM is an extension
of the model of Feng et al: [12], which has been found, via different test
cases, to be unstable for supersonic regimes. The improvements consist of: (1)
a new discretization of the lattice closure correction term making possible to
properly simulate supersonic flows, (2) a corrected viscous stress tensor that
takes into account polyatomic gases, and (3) a novel discretization of the
viscous heat production term fitting with the regularized formalism. The result
is a hybrid method that resolves the mass and momentum equations with an LBM
algorithm, and resolves the entropy-based energy equation with a finite volume
method. This approach fully recovers the physics of the Navier-Stokes-Fourier
equations with the ideal gas equation of state, and is valid from subsonic to
supersonic regimes. It is then successfully assessed with both smooth flows and
flows involving shocks. The proposed model is shown to be an efficient,
accurate, and robust alternative to classic Navier-Stokes methods for the
simulation of compressible flows
