群刚体水动力模型的双曲性和非保守性

IF 0.9 4区数学 Q3 MATHEMATICS, APPLIED

Quarterly of Applied Mathematics Pub Date : 2022-10-28 DOI:10.1090/qam/1651

P. Degond, A. Frouvelle, S. Merino-Aceituno, A. Trescases

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引用次数: 1

摘要

我们研究了描述相互作用的自走刚体系综宏观行为的非线性一阶偏微分方程组。这种系统可能与鸟群、鱼群或无人机舰队的建模有关。我们证明了该系统是双曲型的，可以通过松弛近似为一个保守系统。我们还从动力学模型的水动力极限推导出模型的粘性修正。本文的分析为该系统数值近似的进一步发展做了准备。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Hyperbolicity and nonconservativity of a hydrodynamic model of swarming rigid bodies

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.

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来源期刊

Quarterly of Applied Mathematics 数学-应用数学

CiteScore

1.90

自引率

12.50%

发文量

审稿时长

>12 weeks

期刊介绍： The Quarterly of Applied Mathematics contains original papers in applied mathematics which have a close connection with applications. An author index appears in the last issue of each volume. This journal, published quarterly by Brown University with articles electronically published individually before appearing in an issue, is distributed by the American Mathematical Society (AMS). In order to take advantage of some features offered for this journal, users will occasionally be linked to pages on the AMS website.