A hybrid kinetic–fluid model for solving the Vlasov–BGK equation

Our purpose is to derive a model for charged particles which combines a kinetic description of the fast particles with a fluid description of the slow ones. In a previous paper, a similar model was derived from a kinetic BGK equation that uses a constant relaxation time and does not include the effect of an electric field. In this paper, we consider a more general kinetic equation including an electric field and a varying relaxation time. Fast particles will be described through a collisional kinetic equation of Vlasov–BGK type while thermal particles will be modeled by a hydrodynamic model. Then, we construct a numerical scheme for this model and validate the approach by presenting various numerical tests.