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Title: 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] ;  [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)
Publication Date:
OSTI Identifier:
1254839
Report Number(s):
LA-UR--15-20570
Journal ID: ISSN 0021-9991; PII: S0021999115002892
Grant/Contract Number:
AC52-06NA25396; 11-07444; 11-07465
Type:
Accepted Manuscript
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 297; Journal Issue: C; Journal ID: ISSN 0021-9991
Publisher:
Elsevier
Research Org:
Los Alamos National Laboratory (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