A mass-energy-conserving discontinuous Galerkin scheme for the isotropic multispecies Rosenbluth–Fokker–Planck equation

• Published in: Journal of computational physics Vol. 449; p. 110813
• Main Authors: Shiroto, Takashi, Matsuyama, Akinobu, Aiba, Nobuyuki, Yagi, Masatoshi
• Format: Journal Article
• Language: English
• Published: Cambridge Elsevier Inc 15-01-2022; Elsevier Science Ltd
• Subjects: Computational physics; Conservation; Discontinuous Galerkin method; Fokker-Planck equation; Galerkin method; Particle collisions; Roundoff error; Skew-symmetric form; Symmetry; Thermal relaxation; Truncation errors; Unlike-particle collision; Discontinuous Galerkin method; Skew-symmetric form; Fokker–Planck equation; Unlike-particle collision
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2021.110813

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 in 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.