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.

有源粒子系统的连续描述是一种有效的工具，可以分析在大量粒子限制下的有限尺寸粒子动力学。但是，通常这样的方程式表现为非线性积分微分方程式，并且纯粹的分析处理变得十分有限。我们提出了一个有限体积方法（FVM）的通用框架，以数值方法求解局限于二维的非局部相互作用手性活性粒子系统的连续极限的偏微分方程（PDE）。我们证明了该方法在空间均质问题（可与分析结果进行比较）以及一般空间非均质方程（其中通过动力学理论预测模式形成）上的性能。