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

Francis Filbet; Chi-Wang Shu

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arXiv · 1705.08129

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

Francis Filbet·Chi-Wang Shu

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Abstract

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 [18, 17] 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.

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Francis Filbet, Chi-Wang Shu. 2017-05-23. Discontinuous-galerkin methods for a kinetic model of self-organized dynamics. https://arxiv.org/abs/1705.08129

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