30 research outputs found
A mass-energy-conserving discontinuous Galerkin scheme for the isotropic multispecies Rosenbluth--Fokker--Planck equation
Structure-preserving discretization of the Rosenbluth-Fokker-Planck equation
is still an open question especially for unlike-particle collision. In this
paper, a mass-energy-conserving isotropic Rosenbluth-Fokker-Planck scheme is
introduced. The structure related to the energy conservation is skew-symmetry
in mathematical sense, and the action-reaction law in physical sense. A thermal
relaxation term is obtained by using integration-by-parts on a volume integral
of the energy moment equation, so the discontinuous Galerkin method is selected
to preserve the skew-symmetry. The discontinuous Galerkin method enables ones
to introduce the nonlinear upwind flux without violating the conservation laws.
Some experiments show that the conservative scheme maintains the
mass-energy-conservation only with round-off errors, and analytic equilibria
are reproduced only with truncation errors of its formal accuracy
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