A local meshless method for solving multi-dimensional Vlasov-Poisson and Vlasov-Poisson-Fokker-Planck systems arising in plasma physics

摘要

In this paper, we use a linear combination of the shape functions of reproducing kernel particle method (RKPM) and RBFs for achieving the unknown weights into each stencil. We obtain an error bound for the new shape function. Also, in this paper, we investigate a numerical procedure based on the presented technique for solving the Vlasov-Poisson and Vlasov-Poisson-Fokker-Planck systems. The Vlasov equation is a differential equation describing time evolution of the distribution function of plasma. The Vlasov-Poisson equations are used to describe various phenomena in plasma, in particular Landau damping and the distributions in a double layer plasma. We use the RKPM/RBF-FD technique for discretization of space direction and employ the method of lines to achieve a high-order accuracy in temporal direction. Numerical examples are reported which demonstrate the theoretical results and the efficiency of proposed scheme.