Solving Vlasov-Poisson-Fokker-Planck Equations Using $NRxx$ method (Communications in Computational Physics, 2018)
We present a numerical method to solve the Vlasov-Poisson-Fokker-Planck(VPFP) system using the $NRxx$ method proposed in [4, 7, 9]. A globally hyperbolicmoment system similar to that in [23] is derived. In this system, the Fokker-Planck(FP) operator term is reduced into the linear combination of the moment coefficients,which can be solved analytically under proper truncation. The non-splitting method,which can keep mass conservation and the balance law of the total momentum, is usedto solve the whole system. A numerical problem for the VPFP system with an analyticsolution is presented to indicate the spectral convergence with the moment numberand the linear convergence with the grid size. Two more numerical experiments aretested to demonstrate the stability and accuracy of the $NRxx$ method when applied tothe VPFP system.