A finite volume algorithm for the dynamics of filaments, rods, and beams

Paul M. Ryan, Charles W. Wolgemuth

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


Filaments, rods, and beams are ubiquitous in biology and in many man-made products and structures. While a substantial amount of research has been done to understand the statics and dynamics of these long, thin objects, there remain many unanswered and unstudied problems related to the dynamics of bending and twisting filamentary objects. Simulating the general dynamics of these structures in 3D remains challenging. For example, the net force and torque on a free filament immersed in fluid at low Reynolds number must be zero. However, standard finite difference approaches will often fail to preserve the zero force and torque conditions. These numerical artifacts cause spurious rotations and translations that prohibit, or at least limit, their accuracy in simulating the dynamics of filaments, rods, and beams in these contexts (such as the free-swimming motion of a filamentary microorganism). Here we develop a finite volume discretization based on the Kirchoff equations that naturally guarantees the correct total integral of the forces and torques on filaments, rods, or beams. We then couple this discretization to resistive force theory to develop a stable, accurate dynamic algorithm of filament motion at low Reynolds number. We use a range of sample problems to highlight the utility, stability, and accuracy of this method. While our sample problems focus on low Reynolds number dynamics in the context of resistive force theory (RFT), our discretized finite volume algorithm is general and can be applied to inertial dynamics, immersed boundary methods, and boundary integral methods, as well.

Original languageEnglish (US)
Article number111375
JournalJournal of Computational Physics
StatePublished - Oct 1 2022


  • Cellular motility
  • Filament dynamics
  • Finite volume
  • Fluid-structure interactions

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • General Physics and Astronomy
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics


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