An energy- and charge-conserving, implicit, electrostatic particle-in-cell algorithm

Submitted for the APR12 Meeting of The American Physical Society An Energyand Charge-conserving, Implicit, Electrostatic Particle-in-Cell Algorithm in curvilinear geometry1 G. CHEN, L. CHACÓN, Oak Ridge National Laboratory, D.C. BARNES, Coronado Consulting — A recent proof-of-principle study proposes an energyand 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 chargeand 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. [1] Chen, Chacón, Barnes, J. Comput. Phys. 230 (2011). [2] Camporeale and Delzanno, Bull. Am. Phys. Soc. 56(6) (2011); Wang, et al., J. Plasma Physics, 61 (1999). 1Work supported by ORNL LDRD Program. Guangye Chen Oak Ridge National Laboratory Date submitted: 03 Jan 2012 Electronic form version 1.4