Journal of Computational Physics
Implicit and conservative difference scheme for the Fokker-Planck equation
Journal of Computational Physics
Journal of Computational Physics
Conservative and entropy decaying numerical scheme for the isotropic Fokker-Planck-Landau equation
Journal of Computational Physics
Efficient Asymptotic-Preserving (AP) Schemes For Some Multiscale Kinetic Equations
SIAM Journal on Scientific Computing
Fast spectral methods for the Fokker-Planck-Landau collision operator
Journal of Computational Physics
Numerical Analysis of Conservative and Entropy Schemes for the Fokker--Planck--Landau Equation
SIAM Journal on Numerical Analysis
Implicit Schemes for the Fokker-Planck-Landau Equation
SIAM Journal on Scientific Computing
Journal of Computational Physics
Hi-index | 31.46 |
We present a class of asymptotic-preserving (AP) schemes for the nonhomogeneous Fokker-Planck-Landau (nFPL) equation. Filbet and Jin [16] designed a class of AP schemes for the classical Boltzmann equation, by penalization with the BGK operator, so they become efficient in the fluid dynamic regime. We generalize their idea to the nFPL equation, with a different penalization operator, the Fokker-Planck operator that can be inverted by the conjugate-gradient method. We compare the effects of different penalization operators, and conclude that the Fokker-Planck (FP) operator is a good choice. Such schemes overcome the stiffness of the collision operator in the fluid regime, and can capture the fluid dynamic limit without numerically resolving the small Knudsen number. Numerical experiments demonstrate that the schemes possess the AP property for general initial data, with numerical accuracy uniformly in the Knudsen number.