Multispecies structure-preserving particle discretization of the Landau collision operator

This paper proposes a novel numerical integrator for modeling multispecies Coulomb collisions in kinetic plasmas. The proposed scheme provides an energy-, momentum-, and positivity-preserving particle discretization of the nonlinear Landau collision operator, extending the works of J.A. Carrillo et al., Journal of Computational Physics, 7, 100066 (2020) and E. Hirvijoki, Plasma Physics and Controlled Fusion, 63, 044003 (2021). The discrete-time conservation properties are analyzed both algebraically and numerically, and an efficient, GPU-parallelized implementation is validated against inhomogeneous temperature relaxation, isotropization and thermalization examples. The results agree with analytical estimates, confirming the method capable of reproducing physics.Comment: 23 pages, 14 figure

Conservative Projection Between Finite Element and Particle Bases

Particle-in-Cell (PIC) methods employ particle representations of unknown fields, but also employ continuum fields for other parts of the problem. Thus projection between particle and continuum bases is required. Moreover, we often need to enforce conservation constraints on this projection. We derive a mechanism for enforcement based on weak equality, and implement it in the PETSc libraries. Scalability is demonstrated to more than 1B particles