Energyconserving perfectconductor boundary conditions for an implicit, curvilinear Darwin particleincell algorithm
Abstract
We propose here a conservative prescription for perfectconductor boundary conditions for a Darwin particleincell (PIC) model on curvilinear meshes and arbitrarily shaped boundaries. The Darwin model is a subset of Maxwell's equation in which the electromagnetic mode (light wave) has been analytically removed. This renders the Darwin formulation elliptic, instead of hyperbolic. Historically, DarwinPIC practitioners have had difficulty implementing a wellposed set of boundary conditions for realistic applications. In this study, we demonstrate the wellposedness and effectiveness of a simple boundarycondition prescription for perfect conductors of specified potential and of arbitrary shape in multiple dimensions, using a recently developed conservative, implicit DarwinPIC algorithm. The boundary conditions conserve the electromagnetic energy, and preserve the Coulomb gauge of the vector potential, $\mathrm{\nabla}\xb7\mathbf{A}=0$ exactly. We demonstrate that global energy is exactly conserved in curvilinear, simplyconnected domains in the specific case of particles reflecting off perfect conductors.
 Authors:

 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Publication Date:
 Research Org.:
 Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); USDOE National Nuclear Security Administration (NNSA)
 OSTI Identifier:
 1511229
 Alternate Identifier(s):
 OSTI ID: 1547490
 Report Number(s):
 LAUR1821246
Journal ID: ISSN 00219991
 Grant/Contract Number:
 89233218CNA000001
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Journal of Computational Physics
 Additional Journal Information:
 Journal Volume: 391; Journal ID: ISSN 00219991
 Publisher:
 Elsevier
 Country of Publication:
 United States
 Language:
 English
 Subject:
 32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATION; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; particle in cell; curvilinear meshes; implicit timestepping; nonlinear solvers; energy conservation
Citation Formats
Chacón, L., and Chen, G. Energyconserving perfectconductor boundary conditions for an implicit, curvilinear Darwin particleincell algorithm. United States: N. p., 2019.
Web. doi:10.1016/j.jcp.2019.04.032.
Chacón, L., & Chen, G. Energyconserving perfectconductor boundary conditions for an implicit, curvilinear Darwin particleincell algorithm. United States. https://doi.org/10.1016/j.jcp.2019.04.032
Chacón, L., and Chen, G. Thu .
"Energyconserving perfectconductor boundary conditions for an implicit, curvilinear Darwin particleincell algorithm". United States. https://doi.org/10.1016/j.jcp.2019.04.032. https://www.osti.gov/servlets/purl/1511229.
@article{osti_1511229,
title = {Energyconserving perfectconductor boundary conditions for an implicit, curvilinear Darwin particleincell algorithm},
author = {Chacón, L. and Chen, G.},
abstractNote = {We propose here a conservative prescription for perfectconductor boundary conditions for a Darwin particleincell (PIC) model on curvilinear meshes and arbitrarily shaped boundaries. The Darwin model is a subset of Maxwell's equation in which the electromagnetic mode (light wave) has been analytically removed. This renders the Darwin formulation elliptic, instead of hyperbolic. Historically, DarwinPIC practitioners have had difficulty implementing a wellposed set of boundary conditions for realistic applications. In this study, we demonstrate the wellposedness and effectiveness of a simple boundarycondition prescription for perfect conductors of specified potential and of arbitrary shape in multiple dimensions, using a recently developed conservative, implicit DarwinPIC algorithm. The boundary conditions conserve the electromagnetic energy, and preserve the Coulomb gauge of the vector potential, ∇·A=0 exactly. We demonstrate that global energy is exactly conserved in curvilinear, simplyconnected domains in the specific case of particles reflecting off perfect conductors.},
doi = {10.1016/j.jcp.2019.04.032},
journal = {Journal of Computational Physics},
number = ,
volume = 391,
place = {United States},
year = {2019},
month = {4}
}
Web of Science