  In this work, we show that the widely used bounce-back boundary condition is
an incomplete form of the diffuse reflection boundary condition at the
continuum limit for lattice Boltzmann simulations. By utilizing this fact, we
can force the diffuse reflection scheme to work at its continuum limit so that
the no-slip boundary condition can be implemented without any non-physical slip
velocity error being induced by the standard bounce-back scheme. The revised
boundary formulation is validated numerically by solving a pressure-driven
channel flow, a lid-driven cavity flow and channel flow around a square
cylinder.
