FLUCTUATING HYDRODYNAMIC METHODS FOR FLUID-STRUCTURE INTERACTIONS IN CONFINED CHANNEL GEOMETRIES

Abstract. We develop computational methods for the study of fluid-structure interactions subject to thermal fluctuations when confined within a channel. Our methods take into account the hydrodynamic coupling and diffusivity of microstructures when influenced by their proximity to no-slip walls. We develop stochastic numerical methods subject to no-slip boundary conditions using a staggered finite volume discretization. We show that by imposing an exact fluctuation-dissipation condition to discretize the stochastic driving fields combined with using an exact projection method to enforce incompressibility is sufficient to ensure results consistent with statistical mechanics. We demonstrate our methods by investigating how the proximity of ellipsoidal colloids to the channel wall effects their active hydrodynamic responses and passive diffusivity. We also study the collective dynamics of a large number of particles by considering the intermediate scattering functions for the relaxation of density fluctuations. We expect our introduced stochastic computational methods to be applicable broadly to applications in which confinement effects play an important role in the dynamics of microstructures subject to hydrodynamic coupling and thermal fluctuations