The problem with the noise in the lattice gas model has been overcome by the development of the first Lattice Boltzmann model [39] which replaces the Boolean lattice variables with there ensemble averaged quantities where . The averaged quantities are now real functions in the range and the average mass and momentum are given (see equations (3.9)-(3.12)) by
and
The evolution of f, the distribution function, is found by ensemble averaging the lattice gas collision function,