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 inhomogeneous equations, where pattern formation is predicted by kinetic theory. We numerically investigate phase transitions of particular problems in both spatially homogeneous and inhomogeneous regimes and report the existence of different first and second order transitions. (C) 2021 The Author(s). Published by Elsevier Inc.

Automated summary

The continuum description of active particle systems is a useful tool for analyzing the dynamics of a large number of particles, but the equations often appear as complex nonlinear integro-differential equations. This paper proposes a general framework of finite volume methods to numerically solve partial differential equations of chiral active particle systems, demonstrating the method's performance on both spatially homogeneous and inhomogeneous problems. The study investigates phase transitions of specific problems in both spatially homogeneous and inhomogeneous regimes, reporting the existence of different first and second order transitions.