Geometric Particle-in-Cell Simulations of the Vlasov-Maxwell System in Curvilinear Coordinates

Benedikt Perse, Katharina Kormann, Eric Sonnendrücker

2021 · SIAM Journal on Scientific Computing · vol. 43 · no. 1 · pp. B194-B218 · Society for Industrial & Applied Mathematics (SIAM) · 10.1137/20M1311934

Abstract

Numerical schemes that preserve the structure of the kinetic equations can provide stable simulation results over a long time. An electromagnetic particle-in-cell solver for the Vlasov-Maxwell equations that preserves at the discrete level the non-canonical Hamiltonian structure of the Vlasov-Maxwell equations has been presented in [Kraus et al. 2017]. Whereas the original formulation has been obtained for Cartesian coordinates, we extend the formulation to curvilinear coordinates in this paper. For the discretisation in time, we discuss several (semi-)implicit methods either based on a Hamiltonian splitting or a discrete gradient method combined with an antisymmetric splitting of the Poisson matrix and discuss their conservation properties and computational efficiency.

BibTeX

@article{Perse_2021,
 title={Geometric Particle-in-Cell Simulations of the Vlasov-Maxwell System in Curvilinear Coordinates},
 volume={43},
 ISSN={1095-7197},
 url={http://dx.doi.org/10.1137/20M1311934},
 DOI={10.1137/20m1311934},
 number={1},
 journal={SIAM Journal on Scientific Computing},
 publisher={Society for Industrial & Applied Mathematics (SIAM)},
 author={Perse, Benedikt and Kormann, Katharina and Sonnendrücker, Eric},
 year={2021},
 month=jan,
 pages={B194–B218} }