  A highly efficient three-dimensional (3D) Lattice Boltzmann (LB) model for
high speed compressible flows is proposed. This model is developed from the
original one by Kataoka and Tsutahara[Phys. Rev. E 69, 056702 (2004)]. The
convection term is discretized by the Non-oscillatory, containing No free
parameters and Dissipative (NND) scheme, which effectively damps oscillations
at discontinuities. To be more consistent with the kinetic theory of viscosity
and to further improve the numerical stability, an additional dissipation term
is introduced. Model parameters are chosen in such a way that the von Neumann
stability criterion is satisfied. The new model is validated by well-known
benchmarks, (i) Riemann problems, including the problem with Lax shock tube and
a newly designed shock tube problem with high Mach number; (ii) reaction of
shock wave on droplet or bubble. Good agreements are obtained between LB
results and exact ones or previously reported solutions. The model is capable
of simulating flows from subsonic to supersonic and capturing jumps resulted
from shock waves.
