Brownian dynamics of rigid particles in an incompressible fluctuating fluid by a meshfree method

• A meshfree Lagrangian method for the fluctuating hydrodynamic equations (FHEs) with fluid-structure interactions.
• Brownian motion of the particle is investigated.
• Bidirectional coupling has been introduced between the fluctuating fluid and the solid object.
• The Stokes-Einstein relation is reproduced to ensure the correct long-time behavior of Brownian dynamics.

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 behavior 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 behavior of Brownian dynamics.