  We present a numerical scheme for simulating the dynamics of Brownian
particles suspended in a fluid. The motion of the particles is tracked by the
Langevin equation, whereas the host fluid flow is analyzed by using the lattice
Boltzmann method. The friction force between a particle and the fluid is
evaluated correctly based on the velocity difference at the position of the
particle. The coupling method accurately reproduces the long-time tail observed
in the velocity auto-correlation function. We also show that the
fluctuation-dissipation relation holds between the relaxation of a single
particle and the velocity autocorrelation function of fluctuating particles.
