Discontinuous Galerkin method for a 2D nonlocal flocking model

Abstract

We present our work on the numerical solution of a continuum model of flocking dynamics in two spatial dimensions. The model consists of the compressible Euler equations with a nonlinear nonlocal term which requires special treatment.

We use a semi-implicit discontinuous Galerkin scheme, which proves to be efficient enough to produce results in 2D in reasonable time. This work is a direct extension of the authors' previous work in 1D.

Keywords

• discontinuous Galerkin method
• semi-implicit time discretization
• nonlocal problems
• flocking dynamics