A meshfree Lagrangian method for the fluctuating hydrodynamic equations
(FHEs) with fluid-structure interactions is presented. Brownian motion of the
particle is investigated by direct numerical simulation of the fluctuating
hydrodynamic equations. In this framework a bidirectional coupling has been
introduced between the fluctuating fluid and the solid object. The force
governing the motion of the solid object is solely due to the surrounding fluid
particles. Since a meshfree formulation is used, the method can be extended to
many real applications involving complex fluid flows. A three-dimensional
implementation is presented. In particular, we observe the short and long-time
behaviour of the velocity autocorrelation function (VACF) of Brownian particles
and compare it with the analytical expression. Moreover, the Stokes-Einstein
relation is reproduced to ensure the correct long-time behaviour of Brownian
dynamics.Comment: 24 pages, 2 figure