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.