Semi-implicit DGM applied to a model of flocking

• ID: 2741, RIV: 10331095
• ISSN: not specified, ISBN: 978-3-319-39927-0
• source: Numerical Mathematics and Advanced Applications ENUMATH 2015
• keywords: Discontinuous Galerkin method; flocking dynamics; compressible Euler equations
• authors: Václav Kučera, Andrea Živčáková
• authors from KNM: Kučera Václav, Živčáková Andrea

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.