Spectral method for a kinetic swarming model

Irene M. Gamba, Jeffrey R. Haack, Sebastien Motsch

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


In this paper 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. We observe that the kinetic model captures key features such as vortex formation and traveling waves.

Original languageEnglish (US)
Pages (from-to)32-46
Number of pages15
JournalJournal of Computational Physics
StatePublished - Sep 5 2015


  • Finite Volume method
  • Hyperbolic systems
  • Kinetic equation
  • Spectral method
  • Vicsek model

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics


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