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To study simultaneously the hydrodynamic and thermodynamic behaviors incompressible flow systems with spherical or cylindrical symmetry, we present atheoretical framework for constructing Discrete Boltzmann Model(DBM) withspherical or cylindrical symmetry in spherical or cylindrical coordinates. Tothis aim, a key technique is to use \emph{local} Cartesian coordinates todescribe the particle velocity in the kinetic model. Thus, the geometriceffects, like the divergence and convergence, are described as a\textquotedblleft force term\textquotedblright . Even though the hydrodynamicmodels are one- or two-dimensional, the DBM needs a Discrete VelocityModel(DVM) with 3 dimensions. We use a DVM with 26 velocities to formulate theDBM which recovers the Navier-Stokes equations with spherical or cylindricalsymmetry in the hydrodynamic limit. For the system with \emph{global}cylindrical symmetry, we formulated also a DBM based on a DVM with 2 dimensionsand 16 velocities. In terms of the nonconserved moments, we define two sets ofmeasures for the deviations of the system from its thermodynamic equilibriumstate. The extension of current model to the multiple-relaxation-time versionis straightforward.

Discrete Boltzmann model of compressible flows with spherical or cylindrical symmetry