NUMERICAL SOLUTION OF A NEW HYDRODYNAMIC MODEL OF FLOCKING DYNAMICS

• ID: 2679, RIV: 10286279
• ISSN: not specified, ISBN: 978-80-7494-108-5
• source: International Conference PRESENTATION of MATHEMATICS ’14
• keywords: Flocking dynamics; discontinuous Galerkin method; nonlocal source terms; semi-implicit time discretization
• authors: Václav Kučera, Andrea Živčáková
• authors from KNM: Kučera Václav, Živčáková Andrea

Abstract

This work is concerned with the numerical solution of a new hydrodynamic model describing the macroscopic dynamics of flocks of birds, due to Fornasier et al., 2011. The model consists of the compressible Euler equations with an additional non-local nonlinear source terms. Due to its nonlocality, the model is very challenging and time consuming from the computational point of view. We discretize the equations in 1D using the discontinuous Galerkin method along with a semi-implicit time discretization. Special care must be taken to treat the nonlocality in such a way as to obtain a sparse system matrix on each time level. The resulting scheme is tested and numerical results are presented.