Asymptotic Preserving schemes for highly oscillatory VlasovPoisson equations
This work is devoted to the numerical simulation of a VlasovPoisson model describing a charged particle beam under the action of a rapidly oscillating external field. We construct an Asymptotic Preserving numerical scheme for this kinetic equation in the highly oscillatory limit. This scheme enables to simulate the problem without using any time step refinement technique. Moreover, since our numerical method is not based on the derivation of the simulation of asymptotic models, it works in the regime where the solution does not oscillate rapidly, and in the highly oscillatory regime as well. Our method is based on a two scale reformulation of the initial equation, with the introduction of an additional periodic variable.
asymptotic preserving numerical schemes kinetic equations highly oscillatory problems