Asymptotic Preserving schemes for highly oscillatory Vlasov–Poisson equations

Journal Article · Sun Sep 01 04:00:00 EDT 2013 · Journal of Computational Physics

DOI:https://doi.org/10.1016/J.JCP.2013.04.022· OSTI ID:22230786

Crouseilles, Nicolas ^[1]; Lemou, Mohammed ^[2]; Méhats, Florian ^[3]

---

1. INRIA-Rennes Bretagne Atlantique, IPSO Project (France)
2. CNRS and IRMAR, Université de Rennes 1 and INRIA-Rennes Bretagne Atlantique, IPSO Project (France)
3. IRMAR, Université de Rennes 1 and INRIA-Rennes Bretagne Atlantique, IPSO Project (France)

This work is devoted to the numerical simulation of a Vlasov–Poisson 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.

• OSTI ID: 22230786
• Journal Information: Journal of Computational Physics, Journal Name: Journal of Computational Physics Vol. 248; ISSN JCTPAH; ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
ASYMPTOTIC SOLUTIONS
BEAMS
CHARGED PARTICLES
COMPUTERIZED SIMULATION
KINETIC EQUATIONS
PERIODICITY