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

作者：Filbet Francis^*; Shu Chi Wang

来源：Mathematical Models and Methods in Applied Sciences, 2018, 28(6): 1171-1197.

DOI：10.1142/S0218202518500318

• Self-propelled particles
• alignment dynamics
• kinetic model
• discontinuous Galerkin method

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 [P. Degond and S. Motsch, Continuum limit of self-driven particles with orientation interaction, Math. Models Methods Appl. Sci. 18 (2008) 1193-1215; P. Degond, J.-G. Liu, S. Motsch and V. Panferov, Hydrodynamic models of self-organized dynamics: Derivation and existence theory, Methods &pl. Anal. 20 (2013) 89-114] where alignment is taken into account in addition to 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 analyze consistency and stability of the semi-discrete scheme. We propose several numerical experiments which provide a solid validation of the method and illustrate its underlying concepts.

• 出版日期2018-6-15