Analysis of the tumbling dynamics of highly resolved polymer chains in shear flow with hydrodynamic interactions through Brownian dynamics simulations on graphics processing units

Predictions of the scaling of chain end-over-end tumbling times in shear flow exist for long chains under dominant hydrodynamic interaction (HI) conditions. However, these have never been examined by simulations for highly resolved chains, to level of single Kuhn step. Brownian dynamics (BD) simulations of fairly long, highly detailed polymer chains, at the resolution of a single Kuhn step, remains computationally prohibitive even on the modern processors. This is especially true when the beads on the chain experience HI, which requires the usage of methods like Cholesky decomposition of large matrices at every time step. In this study, we perform BD simulations, with HI, of reasonably long and highly resolved polymer chains on modern graphics processing units (GPUs). First, we present the details of a highly scalable, parallel hybrid code implemented on a GPU for BD simulations of chains resolved to a single Kuhn step. In this hybrid code using compute unified device architecture (CU) and message passing interface (MPI), we have incorporated HI using the Cholesky decomposition method. Quite remarkably, our GPU implementation shows a scaling of ∼N1.2 and ∼N2.2 of the computational times for shorter and longer chains in the modern GPUs, respectively, which is significantly lower than the theoretically expected ∼N3. Furthermore, we use the BD simulations with HI using GPUs to validate predictions for chain tumbling times in shear flow. Our results clearly show the scalings of ratio of tumbling time and number of springs, N with respect to Wi are Wi−2/3 and Wi−3/4 with and without HI, respectively, for a long and highly resolved chain. However, equivalent bead-spring model fails to show any sensitivity to HI, thereby further showing the need of finely resolved models for rheological studies.