Hydrodynamic interaction in Lattice Fokker Planck for dilute polymer dynamics

Abstract

We extend the BGK-type kinetic model for polymer dumbbells and its lattice Boltzmann implementation by incorporating hydrodynamic interaction (HI) effects to accurately recover the slow-variable dynamics governed by the Smoluchowski equation. Unlike Brownian dynamics approaches, which demand the computationally expensive evaluation of the square root of the configuration-dependent diffusion tensor at every time step, this kinetic method is straightforward to implement and avoids such overhead entirely. Consequently, it achieves a significant reduction in computational cost. We validate the model in steady and transient shear flows, demonstrating its ability to capture the distinct signatures of hydrodynamic interactions on bulk rheological properties.