NDLI: Numerical Solution of the Boltzmann Equation I: Spectrally Accurate Approximation of the Collision Operator

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Russo, Giovanni Pareschi, Lorenzo
Copyright Year	2000
Abstract	In this paper we show that the use of spectral Galerkin methods for the approximation of the Boltzmann equation in the velocity space permits one to obtain spectrally accurate numerical solutions at a reduced computational cost. We prove that the spectral algorithm preserves the total mass and approximates with infinite-order accuracy momentum and energy. Consistency of the method is also proved, and a stability result for a smoothed positive scheme is given. We demonstrate that the Fourier coefficients associated with the collision kernel of the equation have a very simple structure and in some cases can be computed explicitly. Numerical examples for homogeneous test problems in two and three dimensions confirm the advantages of the method.
Starting Page	1217
Ending Page	1245
Page Count	29
File Format	PDF
ISSN	00361429
DOI	10.1137/S0036142998343300
e-ISSN	10957170
Issue Number	4
Volume Number	37
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-07-25
Access Restriction	Subscribed
Subject Keyword	spectral Galerkin methods Boltzmann equation Finite elements, Rayleigh-Ritz, Galerkin and collocation methods Rarefied gas flows, Boltzmann equation Integral equations Kinetic theory of gases splitting algorithms
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Numerical Analysis Computational Mathematics

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