Hybrid Kinetic/Fluid numerical method for the Vlasov-BGK equation in the diffusive scaling

31 pages, 20 figures, 6 TablesInternational audienceThis work presents a hybrid numerical method for linear collisional kinetic equations with diffusive scaling. The aim of the method is to reduce the computational cost of kinetic equations by taking advantage of the lower dimensionality of the asymptotic fluid model while reducing the error induced by the latter approach. It relies on two criteria motivated by a perturbative approach to obtain a dynamic domain adaptation. The first criterion quantifies distance between a local equilibrium in velocity and the distribution function of particles. The second one depends only on the macroscopic quantities that are available on the whole computing domain. A key idea is the use of a micro-macro decomposition to deal with interface conditions. The method is significantly more efficient than a standard full kinetic approach. Some properties, such as the conservation of mass, are also investigated and illustrated through various examples