We study the velocity boundary condition for curved boundaries in the latti
ce Boltzmann equation (LBE). We propose a LBE boundary condition for moving
boundaries by combination of the "bounce-back" scheme and spatial interpol
ations of first or second order. The proposed boundary condition is a simpl
e, robust, efficient, and accurate scheme. Second-order accuracy of the bou
ndary condition is demonstrated for two cases: (1) time-dependent two-dimen
sional circular Couette flow and (2) two-dimensional steady flow past a per
iodic array of circular cylinders (flow through the porous media of cylinde
rs). For the former case, the lattice Boltzmann solution is compared with t
he analytic solution of the Navier-Stokes equation. For the latter case, th
e lattice Boltzmann solution is compared with a finite-element solution of
the Navier-Stokes equation. The lattice Boltzmann solutions for both flows
agree very well with the solutions of the Navier-Stokes equations. We also
analyze the torque due to the momentum transfer between the fluid and the b
oundary for two initial conditions: (a) impulsively started cylinder and th
e fluid at rest, and (b) uniformly rotating fluid and the cylinder at rest.
(C) 2001 American Institute of Physics.