An Energy- and Charge-conserving, Implicit, Electrostatic Particle-in-Cell Algorithm in curvilinear geometry

Details An Energy- and Charge-conserving, Implicit, Electrostatic Particle-in-Cell Algorithm in curvilinear geometry An Energy- and Charge-conserving, Implicit, Electrostatic Particle-in-Cell Algorithm in curvilinear geometry

Mar 2012

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2012aps..apr.k1058c&link_type=abstract

American Physical Society, APS April Meeting 2012, March 31-Apr 3, 2012, abstract #K1.058

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A recent proof-of-principle study proposes an energy- and charge-conserving, fully implicit particle-in-cell algorithm in one dimension [1], which is able to use timesteps comparable to the dynamical timescale of interest. Here, we generalize the method to employ non-uniform meshes via a curvilinear map. The key enabling technology is a hybrid particle pusher [2], with particle positions updated in logical space and particle velocities updated in physical space. The self-adaptive, charge-conserving particle mover of Ref. [1] is extended to the non-uniform mesh case. The fully implicit implementation, using a Jacobian-free Newton-Krylov iterative solver, remains exactly charge- and energy-conserving. The extension of the formulation to multiple dimensions will be discussed. We present numerical experiments of 1D electrostatic, long-timescale ion-acoustic wave and ion-acoustic shock wave simulations, demonstrating that charge and energy are conserved to round-off for arbitrary mesh non-uniformity, and that the total momentum remains well conserved.[4pt] [1] Chen, Chac'on, Barnes, J. Comput. Phys. 230 (2011). [0pt] [2] Camporeale and Delzanno, Bull. Am. Phys. Soc. 56(6) (2011); Wang, et al., J. Plasma Physics, 61 (1999).

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