A curvilinear, fully implicit, conservative electromagnetic PIC algorithm in multiple dimensions
Abstract
Here, we extend a recently proposed fully implicit PIC algorithm for the Vlasov–Darwin model in multiple dimensions (Chen and Chacón (2015) [1]) to curvilinear geometry. As in the Cartesian case, the approach is based on a potential formulation (Φ, A), and overcomes many difficulties of traditional semiimplicit Darwin PIC algorithms. Conservation theorems for local charge and global energy are derived in curvilinear representation, and then enforced discretely by a careful choice of the discretization of field and particle equations. Additionally, the algorithm conserves canonicalmomentum in any ignorable direction, and preserves the Coulomb gauge ∇ • A = 0 exactly. An asymptotically wellposed fluid preconditioner allows efficient use of large cell sizes, which are determined by accuracy considerations, not stability, and can be orders of magnitude larger than required in a standard explicit electromagnetic PIC simulation. We demonstrate the accuracy and efficiency properties of the algorithm with numerical experiments in mapped meshes in 1D3V and 2D3V.
 Authors:

 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Publication Date:
 Research Org.:
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Sponsoring Org.:
 USDOE
 OSTI Identifier:
 1255248
 Alternate Identifier(s):
 OSTI ID: 1348010
 Report Number(s):
 LAUR1527639
Journal ID: ISSN 00219991
 Grant/Contract Number:
 AC5206NA25396
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Journal of Computational Physics
 Additional Journal Information:
 Journal Volume: 316; Journal Issue: C; Journal ID: ISSN 00219991
 Publisher:
 Elsevier
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; Mathematics; Magnetic Fusion Energy
Citation Formats
Chacon, L., and Chen, G. A curvilinear, fully implicit, conservative electromagnetic PIC algorithm in multiple dimensions. United States: N. p., 2016.
Web. doi:10.1016/j.jcp.2016.03.070.
Chacon, L., & Chen, G. A curvilinear, fully implicit, conservative electromagnetic PIC algorithm in multiple dimensions. United States. doi:10.1016/j.jcp.2016.03.070.
Chacon, L., and Chen, G. Tue .
"A curvilinear, fully implicit, conservative electromagnetic PIC algorithm in multiple dimensions". United States. doi:10.1016/j.jcp.2016.03.070. https://www.osti.gov/servlets/purl/1255248.
@article{osti_1255248,
title = {A curvilinear, fully implicit, conservative electromagnetic PIC algorithm in multiple dimensions},
author = {Chacon, L. and Chen, G.},
abstractNote = {Here, we extend a recently proposed fully implicit PIC algorithm for the Vlasov–Darwin model in multiple dimensions (Chen and Chacón (2015) [1]) to curvilinear geometry. As in the Cartesian case, the approach is based on a potential formulation (Φ, A), and overcomes many difficulties of traditional semiimplicit Darwin PIC algorithms. Conservation theorems for local charge and global energy are derived in curvilinear representation, and then enforced discretely by a careful choice of the discretization of field and particle equations. Additionally, the algorithm conserves canonicalmomentum in any ignorable direction, and preserves the Coulomb gauge ∇ • A = 0 exactly. An asymptotically wellposed fluid preconditioner allows efficient use of large cell sizes, which are determined by accuracy considerations, not stability, and can be orders of magnitude larger than required in a standard explicit electromagnetic PIC simulation. We demonstrate the accuracy and efficiency properties of the algorithm with numerical experiments in mapped meshes in 1D3V and 2D3V.},
doi = {10.1016/j.jcp.2016.03.070},
journal = {Journal of Computational Physics},
number = C,
volume = 316,
place = {United States},
year = {2016},
month = {4}
}
Web of Science
Works referencing / citing this record:
Verification of long wavelength electromagnetic modes with a gyrokineticfluid hybrid model in the XGC code
journal, May 2017
 Hager, Robert; Lang, Jianying; Chang, C. S.
 Physics of Plasmas, Vol. 24, Issue 5
Verification of long wavelength electromagnetic modes with a gyrokineticfluid hybrid model in the XGC code
journal, May 2017
 Hager, Robert; Lang, Jianying; Chang, C. S.
 Physics of Plasmas, Vol. 24, Issue 5