  Mathematically, the typical difference of Discrete Boltzmann Model (DBM) from
the traditional hydrodynamic one is that the Navier-Stokes (NS) equations are
replaced by a discrete Boltzmann equation. But physically, this replacement has
a significant gain: a DBM is roughly equivalent to a hydrodynamic model
supplemented by a coarse-grained model of the Thermodynamic Non-Equilibrium
(TNE) effects, where the hydrodynamic model can be and can also beyond the NS.
Via the DBM, it is convenient to perform simulations on systems with flexible
Knudsen number. The observations on TNE are being obtaining more applications
with time.
