A note on the correspondence of an immersed boundary method incorporating thermal fluctuations with Stokesian–Brownian dynamics

In this paper a direct correspondence is made between the effective stochastic dynamics of elastic structures of an Immersed Boundary Method incorporating thermal fluctuations and Stokesian–Brownian Dynamics. The correspondence is made in the limit of small Reynolds number, in which the fluid relaxes rapidly on the time scale of the motion of the immersed structures, by performing an averaging procedure directly on the stochastic equations of the Immersed Boundary Method. It is found that there is agreement with Stokesian–Brownian Dynamics for the far-field hydrodynamic interactions and that a fluctuation–dissipation relation is satisfied for the stochastic fluctuations of the effective equations.