A conservative, implicit solver for 0D-2V multi-species nonlinear Fokker-Planck collision equations
<|reference_start|>A conservative, implicit solver for 0D-2V multi-species nonlinear Fokker-Planck collision equations: In this study, we present an optimal implicit algorithm specifically designed to accurately solve the multi-species nonlinear 0D-2V axisymmetric Fokker-Planck-Rosenbluth (FPR) collision equation while preserving mass, momentum, and energy. Our approach relies on the utilization of nonlinear Shkarofsky's formula of FPR (FPRS) collision operator in terms of Legendre polynomial expansions. The key innovation lies in the introduction of a new function named King (Eq.(54)) with the adoption of the Legendre polynomial expansion for the angular direction and King function expansion for the velocity axis direction. The Legendre polynomial expansion will converge exponentially and the King method, a moment convergence algorithm, could ensure the conservation with high precision in discrete form. Additionally, a post-step projection to manifolds is employed to exactly enforce symmetries of the collision operators. Through solving several typical problems across various nonequilibrium configurations, we demonstrate the superior performance and high accuracy of our algorithm.<|reference_end|>
@article{wang2024a,
    title={A conservative, implicit solver for 0D-2V multi-species nonlinear
  Fokker-Planck collision equations},
    author={Yanpeng Wang, Jianyuan Xiao, Yifeng Zheng, Zhihui Zou, Pengfei Zhang,
  Ge Zhuang},
    journal={arXiv preprint arXiv:2408.01616},
    year={2024},
    archivePrefix={arXiv},
    eprint={2408.01616},
    primaryClass={math.NA cs.NA physics.plasm-ph}
}