  A new approach of implementing initial and boundary conditions for the
lattice Boltzmann method is presented. The new approach is based on an extended
collision operator that uses the gradients of the fluid velocity. The numerical
performance of the lattice Boltzmann method is tested on several problems with
exact solutions and is also compared to an explicit finite difference
projection method. The discretization error of the lattice Boltzmann method
decreases quadratically with finer resolution both in space and in time. The
roundoff error of the lattice Boltzmann method creates problems unless double
precision arithmetic is used.
