Conservative stabilized Runge-Kutta methods for the Vlasov-Fokker-Planck equation - Archive ouverte HAL
Journal Articles Journal of Computational Physics Year : 2023

Conservative stabilized Runge-Kutta methods for the Vlasov-Fokker-Planck equation

Abstract

In this work, we aim at constructing numerical schemes, that are as efficient as possible in terms of cost and conservation of invariants, for the Vlasov–Fokker–Planck system coupled with Poisson or Ampère equation. Splitting methods are used where the linear terms in space are treated by spectral or semi-Lagrangian methods and the nonlinear diffusion in velocity in the collision operator is treated using a stabilized Runge–Kutta–Chebyshev (RKC) integrator, a powerful alternative of implicit schemes. The new schemes are shown to exactly preserve mass and momentum. The conservation of total energy is obtained using a suitable approximation of the electric field. An H-theorem is proved in the semi-discrete case, while the entropy decay is illustrated numerically for the fully discretized problem. Numerical experiments that include investigation of Landau damping phenomenon and bump-on-tail instability are performed to illustrate the efficiency of the new schemes.
Fichier principal
Vignette du fichier
vfp_rkc.pdf (2.88 Mo) Télécharger le fichier
Origin Files produced by the author(s)

Dates and versions

hal-03911417 , version 1 (22-12-2022)

Licence

Identifiers

Cite

Nicolas Crouseilles, Ibrahim Almuslimani. Conservative stabilized Runge-Kutta methods for the Vlasov-Fokker-Planck equation. Journal of Computational Physics, 2023, 488, pp.1-34. ⟨10.1016/j.jcp.2023.112241⟩. ⟨hal-03911417⟩
151 View
85 Download

Altmetric

Share

More