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 scheme introduced. The structure related to energy conservation skew-symmetry in mathematical sense, and action–reaction law physical sense. A thermal relaxation term obtained by using integration-by-parts on volume integral moment equation, so discontinuous Galerkin method selected preserve skew-symmetry. enables ones introduce nonlinear upwind flux without violating laws. Some experiments show that conservative maintains mass-energy-conservation only with round-off errors, analytic equilibria are reproduced truncation errors its formal accuracy.