A finite volume method for continuum limit equations of nonlocally interacting active chiral particles

• Published in: Journal of computational physics 2021-09, Vol.440, p.110275, Article 110275
• Main Authors: Kruk, Nikita, Carrillo, José A., Koeppl, Heinz
• Format: Article
• Language: English
• Subjects: Active particle flow; Computational physics; Dimensionality splitting; Finite volume method; Kinetic theory; Mathematical analysis; Numerical methods; Partial differential equations; Phase transitions; Positivity preserving
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2021.110275

•We develop a numerical scheme that is able to capture continuum dynamics of interacting multiagent systems.•The presented finite volume method is likewise applicable to networks of coupled oscillators described by the Kuramoto model.•We reveal both first and second order phase transitions in a general spatially inhomogeneous system. 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.