ASYMPTOTIC-PRESERVING SCHEME FOR THE RESOLUTION OF EVOLUTION EQUATIONS WITH STIFF TRANSPORT TERMS

Baptiste Fedele (1) , Claudia Negulescu (1) , Stefan Possanner (2)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 Institute of Theoretical and Computational Physics

We develop an asymptotic-preserving scheme to solve evolution problems containing stiff transport terms. This scheme is based to a micro-macro decomposition of the unknown, coupled with a stabilization procedure. The numerical method is applied to the Vlasov equation in the gyrokinetic regime and to the Vlasov-Poisson 1D1V equation, which occur in plasma physics. The asymptotic-preserving properties of our procedure permit to study the long-time behavior of these models. In particular, we limit drastically by this method the numerical pollution, appearing in such time asymptotics when using classical numerical schemes.

Mots clés: Vlasov-Poisson system; asymptotic analysis; asymptotic-preserving schemes; BGK equilibria; kinetic equations; Plasma physics

Domaines: Equations aux dérivées partielles [math.AP]

Baptiste Fedele, Claudia Negulescu, Stefan Possanner. ASYMPTOTIC-PRESERVING SCHEME FOR THE RESOLUTION OF EVOLUTION EQUATIONS WITH STIFF TRANSPORT TERMS. Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, In press. ⟨hal-01711545v2⟩