# Efficient simulation of filament elastohydrodynamics in three dimensions

## TL;DR

This paper introduces an efficient computational method for simulating the complex three-dimensional motion of slender, flexible filaments in viscous fluids, overcoming previous limitations to planar configurations.

## Contribution

It extends coarse-graining simulation frameworks to three dimensions, addressing coordinate singularities and enabling rapid, accurate modeling of filament dynamics in complex environments.

## Key findings

- Enables efficient 3D filament simulations
- Circumvents coordinate-system singularities
- Applicable to various biological and physical systems

## Abstract

Fluid-structure simulations of slender inextensible filaments in a viscous fluid are often plagued by numerical stiffness. Recent coarse-graining studies have reduced the computational requirements of simulating such systems, though have thus far been limited to the motion of planar filaments. In this work we extend such frameworks to filament motion in three dimensions, identifying and circumventing coordinate-system singularities introduced by filament parameterisation via repeated changes of basis. The resulting methodology enables efficient and rapid study of the motion of flexible filaments in three dimensions, and is readily extensible to a wide range of problems, including filament motion in confined geometries, large-scale active matter simulations, and the motility of mammalian spermatozoa.