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Discontinuous-Galerkin methods for a kinetic model of self-organized dynamics

Francis Filbet Chi-Wang Shu Brown University

Numerical Analysis and Scientific Computing mathscidoc:1804.25027

Mathematical Models and Methods in Applied Sciences, 2018
This paper deals with the numerical resolution of kinetic models for systems of self-propelled particles subject to alignment interaction and attraction-repulsion. We focus on the kinetic model considered in \cite{DM, DLMP} where alignment is taken into account in addition of an attraction-repulsion interaction potential. We apply a discontinuous Galerkin method for the free transport and non-local drift velocity together with a spectral method for the velocity variable. Then, we analyse consistency and stability of the semi-discrete scheme. We propose several numerical experiments which provide a solid validation of the method and its underlying concepts.
Self-propelled particles, alignment dynamics, kinetic model, discontinuous Galerkin method
[ Download ] [ 2018-04-16 11:00:18 uploaded by chiwangshu ] [ 709 downloads ] [ 0 comments ] 
@inproceedings{francis2018discontinuous-galerkin,
  title={Discontinuous-Galerkin methods for a kinetic model of self-organized dynamics},
  author={Francis Filbet, and Chi-Wang Shu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180416110018948111062},
  booktitle={Mathematical Models and Methods in Applied Sciences},
  year={2018},
}
Francis Filbet, and Chi-Wang Shu. Discontinuous-Galerkin methods for a kinetic model of self-organized dynamics. 2018. In Mathematical Models and Methods in Applied Sciences. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180416110018948111062.
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