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Article Dans Une Revue Mathematical Models and Methods in Applied Sciences Année : 2018

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

Résumé

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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Dates et versions

hal-01526278 , version 1 (22-05-2017)

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Domaine public

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Francis Filbet, Chi-Wang Shu. Discontinuous-galerkin methods for a kinetic model of self-organized dynamics. Mathematical Models and Methods in Applied Sciences, In press, 28 (6), pp.1171-1197. ⟨10.1142/S0218202518500318⟩. ⟨hal-01526278⟩
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