A conformationally averaged iterative method for hydrodynamic interactions in Brownian dynamics simulations of polymer solutions

Brownian Dynamics (BD) simulations are a powerful tool for investigating polymer rheology and dynamics. They can be quantitatively compared to rheological measurements as well as direct imaging of single DNA molecules. Despite their utility, large BD polymer simulations remain a challenge; hydrodynamic interactions (HI) are necessary to capture solvent-mediated dynamics, but require computationally expensive calculations. Specifically, the decomposition of a mobility matrix is required every few time steps to account for the effects of HI on the Brownian noise. We introduce a conformationally averaged (CA) iterative method for calculating HI. We first obtain an averaged mobility matrix from a freely draining BD simulation. This averaged mobility matrix is used to perform additional simulations, which are subsequently used to obtain yet another mobility matrix in an iterative procedure until a self-consistent HI is obtained. The CA method significantly reduces computational times because the expensive decomposition is required only once per iteration. We compare the speed and accuracy of the CA method to traditional BD simulations for single chain dynamics in flow and semidilute dynamics at equilibrium. Finally, we discuss how to extend our method to semidilute solutions in flow.