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arXiv · 2002.09386

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

Benedikt Perse·Katharina Kormann·Eric Sonnendrücker
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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.

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Benedikt Perse, Katharina Kormann, Eric Sonnendrücker. 2020-02-21. Geometric Particle-in-Cell Simulations of the Vlasov--Maxwell System in Curvilinear Coordinates. https://arxiv.org/abs/2002.09386

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