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

2017/05/23 by Francis Filbet, Chi‐Wang Shu, Filbet, Francis +1
Engineering · Mathematics · Physics and Astronomy · #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Lattice Boltzmann Simulation Studies #Micro and Nano Robotics #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1705.08129

openalex publication_date 2017/05/23 · openalex created_date 2017/06/05 · openalex updated_date 2026/08/01

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.

Citations

• Total variation diminishing Runge-Kutta schemes
• THE EFFECTS OF SHAPE ON THE INTERACTION OF COLLOIDAL PARTICLES
• Strong Stability-Preserving High-Order Time Discretization Methods

Related

• Macroscopic models of collective motion with repulsion
• Reduced fluid models for self-propelled particles interacting through alignment
• Well posedness for systems of self-propelled particles
• Kinetic equations and self-organized band formations
• A two-species hydrodynamic model of particles interacting through self-alignment