Direct numerical simulation of the Brownian motion of particles by using fluctuating hydrodynamic equations

In this paper, we present a direct numerical simulation scheme for the Brownian motion of particles. In this approach, the thermal fluctuations are included in the fluid equations via random stress terms. Solving the fluctuating hydrodynamic equations coupled with the particle equations of motion result in the Brownian motion of the particles. There is no need to add a random force term in the particle equations. The particles acquire random motion through the hydrodynamic force acting on its surface from the surrounding fluctuating fluid. The random stress in the fluid equations are easy to calculate unlike the random terms in the conventional Brownian dynamics type approaches. We present a three-dimensional implementation along with validation.