期刊
APPLIED MATHEMATICS LETTERS
卷 120, 期 -, 页码 -出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.aml.2021.107187
关键词
Boltzmann equation; Fourier-Galerkin spectral method; Steady-state preserving; Micro-macro decomposition; Local Maxwellian; Stability
资金
- Labex CEMPI [ANR-11-LABX-0007-01]
- ANR Project MoHyCon [ANR-17-CE40-0027-01]
- MIUR-PRIN Project 2017 [2017KKJP4X]
The article introduces the effectiveness of using spectral methods to approximate the Boltzmann collision operator, and proposes an equilibrium-preserving spectral method to overcome the wrong long time behavior. Through perturbation arguments, the stability, convergence, and spectrally accurate long time behavior of the method are proven.
Spectral methods, thanks to the high accuracy and the possibility to use fast algorithms, represent an effective way to approximate the Boltzmann collision operator. On the other hand, the loss of some local invariants leads to the wrong long time behavior. A way to overcome this drawback, without sacrificing spectral accuracy, has been proposed recently with the construction of equilibrium preserving spectral methods. Despite the ability to capture the steady state with arbitrary accuracy, the theoretical properties of the method have never been studied in detail. In this paper, using the perturbation argument developed by Filbet and Mouhot for the homogeneous Boltzmann equation, we prove stability, convergence and spectrally accurate long time behavior of the equilibrium preserving approach. (C) 2021 Elsevier Ltd. All rights reserved.
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