Velocity autocorrelation function of fluctuating particles in   incompressible fluids. Toward direct numerical simulation of particle   dispersions
  Motions of fluctuating Brownian particles in an incompressible viscous fluid have been studied by coupled simulations of Brownian particles and host fluid. We calculated the velocity autocorrelation functions of Brownian particles and compared them with the theoretical results. Extensive discussions have been made on the time scales for which our numerical model is valid. 
Takuya Iwashita, Yasuya Nakayama, and Ryoichi Yamamoto