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 semi-implicit 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 canonical-momentum in any ignorable direction, and preserves the Coulomb gauge ∇ • A = 0 exactly. An asymptotically well-posed 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 1D-3V and 2D-3V.
Chacon, L., and Chen, G., "A curvilinear, fully implicit, conservative electromagnetic PIC algorithm in multiple dimensions," Journal of Computational Physics 316, no. C (2016), https://doi.org/10.1016/j.jcp.2016.03.070
@article{osti_1255248,
author = {Chacon, L. and Chen, G.},
title = {A curvilinear, fully implicit, conservative electromagnetic PIC algorithm in multiple dimensions},
annote = {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 semi-implicit 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 canonical-momentum in any ignorable direction, and preserves the Coulomb gauge ∇ • A = 0 exactly. An asymptotically well-posed 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 1D-3V and 2D-3V.},
doi = {10.1016/j.jcp.2016.03.070},
url = {https://www.osti.gov/biblio/1255248},
journal = {Journal of Computational Physics},
issn = {ISSN 0021-9991},
number = {C},
volume = {316},
place = {United States},
publisher = {Elsevier},
year = {2016},
month = {04}}
Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, Vol. 544, Issue 1-2https://doi.org/10.1016/j.nima.2005.01.232