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

2020/02/21 by Perse, Benedikt, Kormann, Katharina, Sonnendrücker, Eric · 2 citations
#FOS: Mathematics #FOS: Physical sciences #Numerical Analysis (math.NA) #Plasma Physics (physics.plasm-ph)

paper · doi:10.48550/arxiv.2002.09386

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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• Diagnosing symplecticity in simulations of high-dimensional Hamiltonian systems
• A dual grid geometric electromagnetic particle in cell method

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