Momentum transfer of a Boltzmann-lattice fluid with boundaries

We study the velocity boundary condition for curved boundaries in the lattice Boltzmann equation (LBE). We propose a LBE boundary condition for moving boundaries by combination of the "bounce-back" scheme and spatial interpolations of first or second order. The proposed boundary condition is a simple, robust, efficient, and accurate scheme. Second-order accuracy of the boundary condition is demonstrated for two cases: (1) time-dependent two-dimensional circular Couette flow and (2) two-dimensional steady flow past a periodic array of circular cylinders (flow through the porous media of cylinders). For the former case, the lattice Boltzmann solution is compared with the analytic solution of the Navier-Stokes equation. For the latter case, the 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 boundary for two initial conditions: (a) impulsively started cylinder and the fluid at rest, and (b) uniformly rotating fluid and the cylinder at rest. (C) 2001 American Institute of Physics.