  A double-distribution-function based lattice Boltzmann method (DDF-LBM) is
proposed for the simulation of polyatomic gases in the supersonic regime. The
model relies on an extended equilibrium state that is constructed to reproduce
the first 13 moments of the Maxwell-Boltzmann distribution exactly. This
extends the validity of the standard 5-constraint (mass, momentum and energy)
approach and leads to the correct simulation of thermal, compressible flows
with only 39 discrete velocities in 3D. The stability of this BGK-LBM is
reinforced by relying on Knudsen-number-dependent relaxation times that are
computed analytically. Hence, high-Reynolds number, supersonic flows can be
simulated in an efficient and elegant manner. While the 1D Riemann problem
shows the ability of the proposed approach to handle discontinuities in the
zero-viscosity limit, the simulation of the flow past a NACA0012 airfoil (Mach
number $\mathrm{Ma}=1.5$, Reynolds number $\mathrm{Re=10^4}$) confirms the
excellent behavior of this model in a low-viscosity and supersonic regime. The
proposed model is substantially more efficient than the previous 5-moment
D3Q343 DDF-LBM and opens up a whole new world of compressible flow applications
that can be realistically tackled with a purely LB approach.
