Discontinuous-galerkin methods for a kinetic model of self-organized dynamics
This work provides a numerical method for simulating collective dynamics in biological and social systems, but it is an incremental application of existing numerical techniques to a specific model.
The paper develops a discontinuous Galerkin method for solving kinetic models of self-propelled particles with alignment and attraction-repulsion interactions, demonstrating consistency and stability through numerical experiments.
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.