  We present an energy-conserving multiple-relaxation-time finite difference
lattice Boltzmann model for compressible flows. This model is based on a
16-discrete-velocity model. The collision step is first calculated in the
moment space and then mapped back to the velocity space. The moment space and
corresponding transformation matrix are constructed according to the group
representation theory. Equilibria of the nonconserved moments are chosen
according to the need of recovering compressible Navier-Stokes equations
through the Chapman-Enskog expansion. Numerical experiments showed that
compressible flows with strong shocks can be well simulated by the present
model. The used benchmark tests include (i) shock tubes, such as the Sod, Lax,
Sjogreen, Colella explosion wave and collision of two strong shocks, (ii)
regular and Mach shock reflections, and (iii) shock wave reaction on
cylindrical bubble problems. The new model works for both low and high speeds
compressible flows. It contains more physical information and has better
numerical stability and accuracy than its single-relaxation-time version.
