一种精确的尺度速度方法用于某些群体动力学模型
An Exact Rescaling Velocity Method for some Kinetic Flocking Models
AI总结：
本文提出一种精确的尺度速度方法，用于研究Cucker-Smale和Motsch-Tadmor类型的群体动力学模型，通过避免重新网格化或使用细密速度网格，实现数值观察群体行为。
摘要：
本文讨论了群体动力学模型的动能描述，即Cucker-Smale和Motsch-Tadmor类型模型，这些模型由Vlasov型方程给出，仅考虑长程双粒子相互作用势。我们引入了一种新的精确尺度速度方法，受Filbet和Rey最近工作的启发，允许在不重新网格化或使用非常细的网格的情况下数值观察这些方程解的群体行为。为了稳定精确方法，我们还引入了经典迎风有限体积方案的修改版本，该版本保持了解的物理特性，如动量守恒。
英文摘要：
In this work, we discuss kinetic descriptions of flocking models, of the so-called Cucker-Smale and Motsch-Tadmor types. These models are given by Vlasov-type equations where the interactions taken into account are only given long-range bi-particles interaction potential. We introduce a new exact rescaling velocity method, inspired by a recent work of Filbet and Rey, allowing to observe numerically the flocking behavior of the solutions to these equations, without a need of remeshing or taking a very fine grid in the velocity space. To stabilize the exact method, we also introduce a modification of the classical upwind finite volume scheme which preserves the physical properties of the solution, such as momentum conservation.
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