  The Chapman-Enskog expansion was used in the lattice Boltzmann method (LBM)
to derive a Navier-Stokes-like equation and a formula was obtained to correlate
the LBM model parameters to the kinematic viscosity implicitly implemented in
LBM simulations. The obtained correlation formula usually works as long as the
model parameters are carefully selected to make the Mach number and Knudsen
number small although the validity of Chapman-Enskog expansion that has a
formal definition of time derivative without tangible mathematical sense is not
recognized by many mathematicians.
