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 be 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.
Part of the book: Kinetic Theory