A simulation platform for slender, semiflexible, and inextensible fibers with Brownian hydrodynamics and steric repulsion

The last few years have witnessed an explosion of new numerical methods for filament hydrodynamics. Aside from their ubiquity in biology, physics, and engineering, filaments present unique challenges from an applied-mathematical point of view. Their slenderness, inextensibility, semiflexibility, and meso-scale nature all require numerical methods that can handle multiple lengthscales in the presence of constraints. Accounting for Brownian motion while keeping the dynamics in detailed balance and on the constraint is difficult, as is including a background solvent, which couples the dynamics of multiple filaments together in a suspension. In this paper, we present a simulation platform for deterministic and Brownian inextensible filament dynamics, which includes nonlocal fluid dynamics and steric repulsion. For nonlocal hydrodynamics, we define the mobility on a single filament using line integrals of Rotne–Prager–Yamakawa regularized singularities and numerically preserve the symmetric positive definite property by using a thicker regularization width for the nonlocal integrals than for the self-term. For steric repulsion, we introduce a soft local repulsive potential defined as a double integral over two filaments, then present a scheme to identify and evaluate the nonzero components of the integrand. Using a temporal integrator developed in previous work, we demonstrate that Langevin dynamics sample from the equilibrium distribution of free filament shapes and that the modeling error in using the thicker regularization is small. We conclude with two examples, sedimenting filaments and cross-linked fiber networks, in which nonlocal hydrodynamics does and does not generate long-range flow fields, respectively. In the latter case, we show that the effect of hydrodynamics can be accounted for through steric repulsion.