  A fluid flow is described by fictitious particles hopping on homogeneously
distributed nodes with a given finite set of discrete velocities. We emphasize
that the existence of a fictitious particle having a discrete velocity among
the set in a node is given by a probability. We describe a compressible thermal
flow of the level of accuracy of the Navier-Stokes equation by 25 or 33
discrete velocities for two-dimensional space and perform simulations for
investigating internal structural evolution of a shock wave.
