  A novel polar coordinate lattice Boltzmann kinetic model for detonation
phenomena is presented and applied to investigate typical implosion and
explosion processes. In this model, the change of discrete distribution
function due to local chemical reaction is dynamically coupled into in the
modified lattice Boltzmann equation, which could recovery the Navier-Stokes
equations, including contribution of chemical reaction, via the Chapman-Enskog
expansion. For the numerical investigations, the main focuses are the
nonequilibrium behaviors in these processes. The system at the disc center is
always in its thermodynamic equilibrium. The internal kinetic energies in
different degrees freedoms around the detonation front do not coincide due to
the fluid viscosity. They show the maximum difference at the inflexion point
where the pressure has the largest spatial derivative. The dependence of the
reaction rate on the pressure, influences of the shock strength and reaction
rate on the departure amplitude of the system from its local thermodynamic
equilibrium are probed.
