COMSOL Multiphysics code for Hueschen, Dunn, Phillips, "Wildebeest herds on rolling hills: flocking on arbitrary curved surfaces"
See HowToGuide.pdf for an orientation to the files in this repo and a quick-start tutorial on working with them.
Manuscript text is available at https://arxiv.org/abs/2206.01271. In the manuscript, we present a formulation of the Toner-Tu flocking theory that uses the finite element method to solve the governing equations on arbitrary curved surfaces. First, we test the developed formalism and its numerical implementation in channel flow with scattering obstacles and on cylindrical and spherical surfaces, comparing our results to analytical solutions. We then progress to surfaces with arbitrary curvature, moving beyond previously accessible problems to explore herding behavior on a variety of landscapes. This approach allows the investigation of transients and dynamic solutions not revealed by analytic methods. It also enables versatile incorporation of new geometries and boundary conditions and efficient sweeps of parameter space.
We hope that others will find our approach user-friendly and adaptable for solving the Toner-Tu equations on other complex curved surfaces, for solving other continuum equations on curved surfaces, or for additional study of the cases presented here. For more details and context, the section titled "Formulating the Surface Toner-Tu Equations for Numerical Implementation" in the main text and the section titled "Implementation in COMSOL Multiphysics" in the appendix may be particularly useful. While we chose COMSOL Multiphysics for its accessibility and learner-friendly interface, we note with regret that the use of these files requires access to a paid COMSOL Multiphysics license. If you do not already have a license and are affiliated with an institution, we recommend looking into access options through a shared software library.