  A decoupled scheme based on the Hermite expansion to construct lattice
Boltzmann models for the compressible Navier-Stokes equations with arbitrary
specific heat ratio is proposed. The local equilibrium distribution function
including the rotational velocity of particle is decoupled into two parts, i.e.
the local equilibrium distribution function of the translational velocity of
particle and that of the rotational velocity of particle. From these two local
equilibrium functions, two lattice Boltzmann models are derived via the Hermite
expansion, namely one is in relation to the translational velocity and the
other is connected with the rotational velocity. Accordingly, the distribution
function is also decoupled. After this, the evolution equation is decoupled
into the evolution equation of the translational velocity and that of the
rotational velocity. The two evolution equations evolve separately. The lattice
Boltzmann models used in the scheme proposed by this work are constructed via
the Hermite expansion, so it is easy to construct new schemes of higher-order
accuracy. To validate the proposed scheme, a shock tube simulation is
performed. The numerical results agree with the analytical solutions very well.
