Highly discretized dynamics

The efforts in the last ten years or so to find a particle dynamics, wherein, the spatial coordinates are confined to lattice positions and the velocity coordinates to a few speeds, have unfortunately failed. It was hoped to duplicate the success of the Ising model, which would have allowed, if not for an analytic treatment, at least much more efficient computational methods to deal with hydrodynamic transport phenomena, particularly turbulence. The next course of action, in view of this failure, will be discussed after the reasons for the failure are outlined.