A Fourier spectral method for homogeneous Boltzmann equations

Lorenzo Pareschi; Benoit Perthame

doi:10.1080/00411459608220707

A Fourier spectral method for homogeneous Boltzmann equations

Lorenzo Pareschi^*, Benoit Perthame

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

117 Citations (Scopus)

Abstract

A numerical method for the solution of the spatially homogeneous Boltzmann equation is proposed. The scheme is based first in expanding the distribution function in Fourier series, then in finite difference discretizing in time and velocity space. This allows an accurate evaluation of the collision operator with a reduced computational cost. Moreover, for a class of collision kernels, this approach leads to a quadrature formula that can be computed through a fast algorithm. First results on a twodimensional problem confirm the efficiency of the method.

Original language	English
Pages (from-to)	369-382
Number of pages	14
Journal	Transport Theory and Statistical Physics
Volume	25
Issue number	3-5
DOIs	https://doi.org/10.1080/00411459608220707
Publication status	Published - 1996

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics
Transportation
General Physics and Astronomy
Applied Mathematics

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title = "A Fourier spectral method for homogeneous Boltzmann equations",

abstract = "A numerical method for the solution of the spatially homogeneous Boltzmann equation is proposed. The scheme is based first in expanding the distribution function in Fourier series, then in finite difference discretizing in time and velocity space. This allows an accurate evaluation of the collision operator with a reduced computational cost. Moreover, for a class of collision kernels, this approach leads to a quadrature formula that can be computed through a fast algorithm. First results on a twodimensional problem confirm the efficiency of the method.",

author = "Lorenzo Pareschi and Benoit Perthame",

year = "1996",

doi = "10.1080/00411459608220707",

language = "English",

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journal = "Transport Theory and Statistical Physics",

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T1 - A Fourier spectral method for homogeneous Boltzmann equations

AU - Pareschi, Lorenzo

AU - Perthame, Benoit

PY - 1996

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N2 - A numerical method for the solution of the spatially homogeneous Boltzmann equation is proposed. The scheme is based first in expanding the distribution function in Fourier series, then in finite difference discretizing in time and velocity space. This allows an accurate evaluation of the collision operator with a reduced computational cost. Moreover, for a class of collision kernels, this approach leads to a quadrature formula that can be computed through a fast algorithm. First results on a twodimensional problem confirm the efficiency of the method.

AB - A numerical method for the solution of the spatially homogeneous Boltzmann equation is proposed. The scheme is based first in expanding the distribution function in Fourier series, then in finite difference discretizing in time and velocity space. This allows an accurate evaluation of the collision operator with a reduced computational cost. Moreover, for a class of collision kernels, this approach leads to a quadrature formula that can be computed through a fast algorithm. First results on a twodimensional problem confirm the efficiency of the method.

UR - https://www.scopus.com/pages/publications/0030518624

U2 - 10.1080/00411459608220707

DO - 10.1080/00411459608220707

M3 - Article

AN - SCOPUS:0030518624

SN - 0041-1450

VL - 25

SP - 369

EP - 382

JO - Transport Theory and Statistical Physics

JF - Transport Theory and Statistical Physics

IS - 3-5

ER -

A Fourier spectral method for homogeneous Boltzmann equations

Abstract

ASJC Scopus subject areas

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