Kinetic/Fluid micro-macro numerical scheme for a two component plasma

Abstract

This work is devoted to the numerical simulation of the Vlasov-BGK equation for two species in the fluid limit using a particle method. Thus, we are interested in a plasma consisting of electrons and one species of ions without chemical reactions assuming that the number of particles of each species remains constant. We consider the kinetic two species model proposed by Klingenberg, Pirner and Puppo in 2017, which separates the intra and interspecies collisions. Then, we propose a new model based on a micro-macro decomposition (see Bennoune, Lemou and Mieussens, 2007 and Crestetto, Crouseilles and Lemou, 2013). The kinetic micro part is solved by a particle method, whereas the fluid macro part is discretized by a standard finite volume scheme. Main advantages of this approach are: (i) the noise inherent to the particle method is reduced compared to a standard (without micro-macro decomposition) particle method, (ii) the computational cost of the method is reduced in the fluid limit since a small number of particles is then sufficient.