Abstract
We present the numerical solution of a hydrodynamics model of flocking using a suitable modified semi-implicit discontinuous Galerkin method. The investigated model describing the dynamics of flocks of birds or other individual entities forming herds or swarms was introduced by Fornasier et al. (Physica D 240(1):21-31, 2011).
The main idea of this model comes from the well known Cucker-Smale model. The resulting equations consist of the Euler equations for compressible flow with an additional non-local non-linear source term.
The model is discretized by the semi-implicit discontinuous Galerkin method for the compressible Euler equations of Feistauer and Kučera (J Comput Phys 224(1):208-221, 2007). We show that with a suitable treatment of the source term we can use this method for models like the model of flocking and find a numerical solution very efficiently.