Publications
The collisional particle-in-cell method for the Vlasov-Maxwell-Landau equations
Rafael Bailo
José Antonio Carrillo
Jingwei Hu
Rafael Bailo · José Antonio Carrillo · Jingwei Hu
arXiv: 2401.01689, 2024.
arXiv: 2401.01689, 2024.
@Article{BCH2024
title={The collisional particle-in-cell method for the {V}lasov-{M}axwell-{L}andau equations},
author={Bailo, Rafael and Carrillo, José Antonio and Hu, Jingwei},
journal={Preprint arXiv: 2401.01689},
year={2024},
doi={10.48550/arXiv.2401.01689},
archivePrefix={arXiv},
arXivId={2401.01689},
eprint={2401.01689},
}We introduce an extension of the particle-in-cell (PIC) method that captures the Landau collisional effects in the Vlasov-Maxwell-Landau equations. The method arises from a regularisation of the variational formulation of the Landau equation, leading to a discretisation of the collision operator that conserves mass, charge, momentum, and energy, while increasing the (regularised) entropy. The collisional effects appear as a fully deterministic effective force, thus the method does not require any transport-collision splitting. The scheme can be used in arbitrary dimension, and for a general interaction, including the Coulomb case. We validate the scheme on scenarios such as the Landau damping, the two-stream instability, and the Weibel instability, demonstrating its effectiveness in the numerical simulation of plasma.
We introduce an extension of the particle-in-cell (PIC) method that captures the Landau collisional effects in the Vlasov-Maxwell-Landau equations. The method arises from a regularisation of the variational formulation of the Landau equation, leading to a discretisation of the collision operator that conserves mass, charge, momentum, and energy, while increasing the (regularised) entropy. The collisional effects appear as a fully deterministic effective force, thus the method does not require any transport-collision splitting. The scheme can be used in arbitrary dimension, and for a general interaction, including the Coulomb case. We validate the scheme on scenarios such as the Landau damping, the two-stream instability, and the Weibel instability, demonstrating its effectiveness in the numerical simulation of plasma.