Numerical Dispersion and Attenuation in the M3 Modeling System
, by Chuck Sword

Lattice gases represent a new and interesting approach to the modeling of wave-propagation
and fluid-dynamic processes. As pointed out by Muir (1987b), discrete lattice gases can
be generalized as ensembles, and calculations can be carried out on probability values rather
than on the individual particles. Furthermore, the probability values can be linearized, resulting
in the M3 modeling system. A method has been developed that allows the calculation of the
dispersion (phase velocity versus spatial frequency), attenuation (decrease in amplitude with respect to time),
and anisotropy of acoustic waves in the M3 system. These numerical results can, in turn, be
applied to the original lattice-gas method. They confirm theoretical results (d'Humieres et al., 1986)
regarding the isotropy of certain lattices.