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.
@article{702999,
title = {Discontinuous Galerkin method for a 2D nonlocal flocking model},
booktitle = {Programs and Algorithms of Numerical Mathematics},
series = {GDML\_Books},
publisher = {Institute of Mathematics CAS},
address = {Prague},
year = {2017},
pages = {63-72},
url = {http://dml.mathdoc.fr/item/702999}
}
Kučera, Václav; Zivčáková, Andrea. Discontinuous Galerkin method for a 2D nonlocal flocking model, dans Programs and Algorithms of Numerical Mathematics, GDML_Books, (2017), pp. 63-72. http://gdmltest.u-ga.fr/item/702999/