  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.
