Development and application of numerical methods for large-scale cilia simulation
File(s)
Author(s)
Su, Hang
Type
Thesis
Abstract
Cilia are slender, active filaments whose coordinated beating plays a vital role in organism locomotion and fluid transport. Their collective dynamics often form metachronal waves, whose origin of formation and influence on ciliary function are still not fully understood. Capturing these behaviours requires resolving hydrodynamic interactions among thousands of filaments, which is computationally challenging: traditional methods quickly become prohibitively expensive and often numerically intractable. Minimal models, such as the squirmer model or rotor framework, are computationally efficient but neglect important mechanical details such as waveform adaptation and hydrodynamic dissipation. This leaves a gap between coarse conceptual models and fully filament-resolved simulations. This thesis addresses this gap through the development and implementation of the Fast Force-Coupling Method (FFCM), a versatile, GPU-accelerated solver for efficiently computing low-Reynolds number hydrodynamics. On top of this, a filament oscillator framework based on the Lagrangian Mechanics of Active Systems was developed, in which each cilium is represented by a reduced set of phase and shape variables that evolve according to prescribed beat sequences and hydrodynamic coupling. This framework enables the simulation of coordination dynamics among thousands of cilia. Large-scale simulations reveal bistability between symplectic and diaplectic metachronal waves, with stability strongly influenced by filament stiffness. It is shown that the symplectic wave, which is naturally observed in Volvox carteri, persists at larger swimmer sizes as we successfully solve for the coordination of 4291 cilia, a scale comparable to that of a real Volvox carteri, on a single consumer-grade GPU. Further investigations inspired by Volvox demonstrate that beat-plane tilt induces a rotational velocity proportional to the tilt angle. Comparative studies show that propulsion is strongly influenced by beat geometry through hydrodynamic asymmetries in the stroke cycle, consistent with classical wall- and orientation-mediated mechanisms, with a lowered recovery stroke enhancing forward transport.
Version
Open Access
Date Issued
2025-09-29
Date Awarded
2026-02-01
Copyright Statement
Attribution-NonCommercial 4.0 International Licence (CC BY-NC)
License URL
Advisor
Keaveny, Eric
Publisher Department
Department of Mathematics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)