A Finite Volume Method for Continuum Limit Equations of Nonlocally Interacting Active Chiral Particles

The continuum description of active particle systems is an efficient instrument to analyze a finite size particle dynamics in the limit of a large number of particles. However, it is often the case that such equations appear as nonlinear integro-differential equations and purely analytical treatment becomes quite limited. We propose a general framework of finite volume methods (FVMs) to numerically solve partial differential equations (PDEs) of the continuum limit of nonlocally interacting chiral active particle systems confined to two dimensions. We demonstrate the performance of the method on spatially homogeneous problems, where the comparison to analytical results is available, and on general spatially nonhomogeneous equations, where pattern formation is predicted by the kinetic theory. We numerically investigate phase transitions of particular problems in both spatially homogeneous and nonhomogeneous regimes and report the existence of different first and second order transitions. These are the videos related to our recent preprint in arXiv:2008.08493.