  To kinetically model implosion and explosion related phenomena, we present a
theoretical framework for constructing Discrete Boltzmann Model(DBM) with
spherical symmetry in spherical coordinates. To this aim, a key technique is to
use \emph{local} Cartesian coordinates to describe the particle velocity in the
kinetic model. Thus, the geometric effects, like the divergence and
convergence, are described as a \textquotedblleft force term\textquotedblright.
To better access the nonequilibrium behavior, even though the corresponding
hydrodynamic model is one-dimensional, the DBM uses a Discrete Velocity
Model(DVM) with 3 dimensions. A new scheme is introduced so that the DBM can
use the same DVM no matter considering the extra degree of freedom or not. As
an example, a DVM with 26 velocities is formulated to construct the DBM in the
Navier-Stokes level. Via the DBM, one can study simultaneously the hydrodynamic
and thermodynamic nonequilibrium behaviors in the implosion and explosion
process which are not very close to the spherical center. The extension of
current model to the multiple-relaxation-time version is straightforward.
