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Title: Spectral method for a kinetic swarming model

Journal Article · · Journal of Computational Physics
 [1];  [2]; ORCiD logo [3]
  1. Univ. of Texas at Austin, Austin, TX (United States)
  2. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
  3. Arizona State Univ., Tempe, AZ (United States)
+ Show Author Affiliations

Here we present the first numerical method for a kinetic description of the Vicsek swarming model. The kinetic model poses a unique challenge, as there is a distribution dependent collision invariant to satisfy when computing the interaction term. We use a spectral representation linked with a discrete constrained optimization to compute these interactions. To test the numerical scheme we investigate the kinetic model at different scales and compare the solution with the microscopic and macroscopic descriptions of the Vicsek model. Lastly, we observe that the kinetic model captures key features such as vortex formation and traveling waves.

Research Organization:
Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
Sponsoring Organization:
USDOE
Grant/Contract Number:
AC52-06NA25396; 11-07444; 11-07465
OSTI ID:
1254839
Report Number(s):
LA-UR-15-20570; PII: S0021999115002892
Journal Information:
Journal of Computational Physics, Vol. 297, Issue C; ISSN 0021-9991
Publisher:
ElsevierCopyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 11 works
Citation information provided by
Web of Science

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Cited By (3)

Global Weak Solutions for Kolmogorov–Vicsek Type Equations with Orientational Interactions journal April 2016
Kinetic Models for Topological Nearest-Neighbor Interactions journal October 2017
Vehicular traffic, crowds, and swarms: From kinetic theory and multiscale methods to applications and research perspectives journal September 2019

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Related Subjects

97 MATHEMATICS AND COMPUTING
Spectral method
Finite Volume method
Kinetic equation
Vicsek model
Hyperbolic systems