Numerical Solution of a New Hydrodynamic Model of Flocking

• ID: 2702, RIV: 10314914
• ISSN: not specified, ISBN: 978-80-85823-64-6
• source: PROGRAMS AND ALGORITHMS OF NUMERICAL MATHEMATICS 17
• keywords: Discontinuous Galerkin; flocking dynamics
• authors: Václav Kučera, Andrea Živčáková
• authors from KNM: Kučera Václav, Živčáková Andrea

Abstract

This work is concerned with the numerical solution of a hydrodynamic model of the macroscopic behavior of flocks of birds due to Fornasier et al., 2011. The model consists of the compressible Euler equations with an added nonlocal, nonlinear right-hand side. As noticed by the authors of the model, explicit time schemes are practically useless even on very coarse grids in 1D due to the nonlocal nature of the equations. To this end, we apply a semi-implicit discontinuous Galerkin method to solve the equations. We present a simple numerical test of the resulting scheme.