Model Reduction of a Two-Dimensional Kinetic Swarming Model by Operator Projections

Abstract

Hyperbolic, rotation invariant moment systems are derived for a non-linear kinetic description of two-dimensional Vicsek swarming model. The systems also preserve mass conservation, and numerical experiments show that this approach captures the key features of the model such as shock waves, contact discontinuities, rarefaction waves, vortex formations. If the system order increases, the solutions of the moment systems converge to the solution of the corresponding kinetic equation.