Geometric electrostatic particle-in-cell algorithm on unstructured meshes

Abstract

We present a geometric particle-in-cell (PIC) algorithm on unstructured meshes for studying electrostatic perturbations with frequency lower than electron gyrofrequency in magnetized plasmas. In this method, ions are treated as fully kinetic particles and electrons are described by the adiabatic response. The PIC method is derived from a discrete variational principle on unstructured meshes. To preserve the geometric structure of the system, the discrete variational principle requires that the electric field is interpolated using Whitney 1-forms, the charge is deposited using Whitney 0-forms and the electric field is computed by discrete exterior calculus. The algorithm has been applied to study the ion Bernstein wave (IBW) in two-dimensional magnetized plasmas. The simulated dispersion relations of the IBW in a rectangular region agree well with theoretical results. In a two-dimensional circular region with fixed boundary condition, the spectrum and eigenmode structures of the IBW are obtained from simulations. We compare the energy conservation property of the geometric PIC algorithm derived from the discrete variational principle with that of previous PIC methods on unstructured meshes. The comparison shows that the new PIC algorithm significantly improves the energy conservation property.

Computational Algorithms for Multiphase Hydrodynamics Models and Filtration

“…Методи часток широко використовуються для моделювання динамiки однорiдних рiдин та плазми [17][18][19][20][21]. Методи часток були узагальненi також до методу згладжених часток для моделювання рiзноманiтних процесiв динамiки рiдин [22][23][24][25].…”

A gauge-compatible Hamiltonian splitting algorithm for particle-in-cell simulations using finite element exterior calculus

“…Structure-preserving particle-in-cell (PIC) algorithms preserve many of the geometric and topological mathematical structures of a point-particle kinetic plasma model, including its symplectic structure, symmetries, conservation laws and cohomology (Villasenor & Buneman 1992;Esirkepov 2001;Squire, Qin & Tang 2012;Evstatiev & Shadwick 2013;Xiao et al 2013;Crouseilles, Einkemmer & Faou 2015;He et al 2015;Moon, Teixeira & Omelchenko 2015;Qin et al 2015Qin et al , 2016Xiao et al 2015;He et al 2016;Burby 2017;Kraus & Hirvijoki 2017;Morrison 2017;Xiao, Qin & Liu 2018;Xiao & Qin 2019;Glasser & Qin 2020;Hirvijoki, Kormann & Zonta 2020;Holderied, Possanner & Wang 2021;O'Connor et al 2021;Perse, Kormann & Sonnendrücker 2021;Pinto, Kormann & Sonnendrücker 2022;Wang et al 2021;Xiao & Qin 2021). One such structure, gauge symmetry, was first preserved in a PIC algorithm in the Lagrangian formalism via a variational method (Squire et al 2012).…”

“…2021; Perse, Kormann & Sonnendrücker 2021; Pinto, Kormann & Sonnendrücker 2022; Wang et al. 2021; Xiao & Qin 2021). One such structure, gauge symmetry, was first preserved in a PIC algorithm in the Lagrangian formalism via a variational method (Squire et al.…”