Name
Title | ||
|---|---|---|
Spectral methods for the non cut-off Boltzmann equation and numerical grazing collision limit |
Abstract | ||
|---|---|---|
Summary. In this paper we study the numerical passage from the spatially homogeneous Boltzmann equation without cut-off to the Fokker-Planck-Landau
equation in the so-called grazing collision limit. To this aim we derive a Fourier spectral method for the non cut-off Boltzmann
equation in the spirit of [21,23]. We show that the kernel modes that define the spectral method have the correct grazing
collision limit providing a consistent spectral method for the limiting Fokker-Planck-Landau equation. In particular, for
small values of the scattering angle, we derive an approximate formula for the kernel modes of the non cut-off Boltzmann equation
which, similarly to the Fokker-Planck-Landau case, can be computed with a fast algorithm. The uniform spectral accuracy of
the method with respect to the grazing collision parameter is also proved.
|
Year | DOI | Venue |
|---|---|---|
2003 | 10.1007/s002110100384 | Numerische Mathematik |
Keywords | Field | DocType |
boltzmann equation,cut-off assumption,spectral methods,grazing collision limit.,fokker-planck- landau equation,fokker planck,numerical analysis,plasma physics,statistical mechanics,spectral method | Kernel (linear algebra),Boltzmann equation,Mathematical analysis,Lattice Boltzmann methods,Fourier transform,Collision,Scattering,Cut-off,Spectral method,Mathematics | Journal |
Volume | Issue | ISSN |
93 | 3 | Numerische Mathematik, 93, pp.527-548, (2003) |
Citations | PageRank | References |
7 | 1.90 | 1 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Lorenzo Pareschi | 1 | 421 | 64.78 |
| Giuseppe Toscani | 2 | 138 | 24.06 |
| Cédric Villani | 3 | 8 | 2.33 |