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arXiv · 2011.13086

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

Takashi Shiroto·Akinobu Matsuyama·Nobuyuki Aiba·Masatoshi Yagi
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Abstract

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.

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Takashi Shiroto, Akinobu Matsuyama, Nobuyuki Aiba, Masatoshi Yagi. 2020-11-26. A mass-energy-conserving discontinuous Galerkin scheme for the isotropic multispecies Rosenbluth--Fokker--Planck equation. https://arxiv.org/abs/2011.13086

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