  The lattice Boltzmann equation describes the evolution of the velocity
distribution function on a lattice in a manner that macroscopic fluid dynamical
behavior is recovered. Although the equation is a derivative of lattice gas
automata, it may be interpreted as a Lagrangian finite-difference method for
the numerical simulation of the discrete-velocity Boltzmann equation that makes
use of a BGK collision operator. As a result, it is not surprising that
numerical instability of lattice Boltzmann methods have been frequently
encountered by researchers. We present an analysis of the stability of
perturbations of the particle populations linearized about equilibrium values
corresponding to a constant-density uniform mean flow. The linear stability
depends on the following parameters: the distribution of the mass at a site
between the different discrete speeds, the BGK relaxation time, the mean
velocity, and the wavenumber of the perturbations. This parameter space is too
large to compute the complete stability characteristics. We report some
stability results for a
