Multi-species Rosenbluth Fokker-Planck collision operator for discontinuous Galerkin method

Abstract

We present a computationally efficient implementation of the nonlinear Rosenbluth-Fokker-Planck (RFP) collision operator for multi-species kinetic simulations within the discontinuous Galerkin (DG) framework. Interspecies collisions with significant mass disparities require high-order Gaussian quadrature integration to accurately resolve the steep gradients in the Rosenbluth potentials of slower species. To mitigate the computational overhead associated with numerous quadrature points, we employ precomputed integration matrices. Since the conventional upwind scheme for the DG method is not compatible with precomputed matrices, we implement the Harten, Lax and van Leer (HLL) flux formulation for advective flow calculations at cell boundaries. Conservation of momentum and energy is ensured through an additional advective-diffusive operator, utilizing the slow-to-fast species collision as a reference state. We address the numerical challenge of artificial non-vanishing collisional effects at equilibrium through compensatory terms, thereby achieving stable collisional equilibrium states. Comprehensive numerical benchmarks validate both the efficiency and accuracy of our proposed scheme. In particular, our model achieves robust interspecies collisional equilibrium even under conditions of extreme mass disparity and relatively low velocity resolution.