A smooth transition approach between the Vlasov-Poisson and the Euler-Poisson system

In the present work, we extend a novel numerical algorithm which was constructed for the solution of gas dynamics problems cite{degond1, degond3} to the solution of the Vlasov-Poisson equation in combination with the Euler-Poisson system. The new method is designed for computing the solution of plasma problems which require a localized resolution of the kinetic scale. The main idea relies on the introduction of buffer zones which realize a smooth transition between the kinetic and the fluid regions. The buffer zone is drawn around the kinetic regions by introducing a cut-off function. We numerically validate the presented method and demonstrate its performances.