Spectral method for a kinetic swarming model
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.
 Authors:

^{[1]};
^{[2]};
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 Univ. of Texas at Austin, Austin, TX (United States)
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Arizona State Univ., Tempe, AZ (United States)
 Publication Date:
 Report Number(s):
 LAUR1520570
Journal ID: ISSN 00219991; PII: S0021999115002892
 Grant/Contract Number:
 AC5206NA25396; 1107444; 1107465
 Type:
 Accepted Manuscript
 Journal Name:
 Journal of Computational Physics
 Additional Journal Information:
 Journal Volume: 297; Journal Issue: C; Journal ID: ISSN 00219991
 Publisher:
 Elsevier
 Research Org:
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Sponsoring Org:
 USDOE
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; Spectral method; Finite Volume method; Kinetic equation; Vicsek model; Hyperbolic systems
 OSTI Identifier:
 1254839
Gamba, Irene M., Haack, Jeffrey R., and Motsch, Sebastien. Spectral method for a kinetic swarming model. United States: N. p.,
Web. doi:10.1016/j.jcp.2015.04.033.
Gamba, Irene M., Haack, Jeffrey R., & Motsch, Sebastien. Spectral method for a kinetic swarming model. United States. doi:10.1016/j.jcp.2015.04.033.
Gamba, Irene M., Haack, Jeffrey R., and Motsch, Sebastien. 2015.
"Spectral method for a kinetic swarming model". United States.
doi:10.1016/j.jcp.2015.04.033. https://www.osti.gov/servlets/purl/1254839.
@article{osti_1254839,
title = {Spectral method for a kinetic swarming model},
author = {Gamba, Irene M. and Haack, Jeffrey R. and Motsch, Sebastien},
abstractNote = {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.},
doi = {10.1016/j.jcp.2015.04.033},
journal = {Journal of Computational Physics},
number = C,
volume = 297,
place = {United States},
year = {2015},
month = {4}
}