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
