High order numerical methods for Vlasov-Poisson models of plasma sheaths

\nThis article is a report of the CEMRACS 2022 project, called HIVLASHEA, standing for ”High order methods for Vlasov-Poisson models for sheaths”. A two-species Vlasov-Poisson model is described together with some numerical simulations, permitting to exhibit the formation of a plasma sheath. The numerical simulations are performed with two different methods: a first order classical finite difference (FD) scheme and a high order semi-Lagrangian (SL) scheme with Strang splitting; for the latter one, the implementation of (non-periodic) boundary conditions is discussed and different solvers for the electric field are compared. The codes are first evaluated on a one-species case, where an analytical solution is known. For the two-species case, cross-comparisons are performed and the numerical convergence of the SL method is investigated. The use of high order method is emphasized in this context. The (parallel) SL code turns out to be a robust tool to provide reliable numerical approximations of sheath stationary solution with realistic physical parameters.\n