论文标题
堆积刚体的流体动力模型的双曲线和非保守性
Hyperbolicity and non-conservativity of a hydrodynamic model of swarming rigid bodies
论文作者
论文摘要
在本文中，我们研究了一个一阶偏微分方程的非线性系统，描述了相互作用的自行刚性刚体的宏观行为。这种系统可能与鸟类羊群，鱼类学校或无人机舰队的建模有关。我们表明该系统是双曲线的，可以通过放松通过保守的系统近似。我们还从动力学模型的流体力学极限中得出了粘性校正。该分析准备了该系统数值近似的未来开发。
In this paper, we study a nonlinear system of first order partial differential equations describing the macroscopic behavior of an ensemble of interacting self-propelled rigid bodies. Such system may be relevant for the modelling of bird flocks, fish schools or fleets of drones. We show that the system is hyperbolic and can be approximated by a conservative system through relaxation. We also derive viscous corrections to the model from the hydrodynamic limit of a kinetic model. This analysis prepares the future development of numerical approximations of this system.
