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Difference scheme for the Boltzmann equation based on the Fast Fourier Transform

A. Bobylev, +1 more
- 01 Jan 1997 - 
- Vol. 16, Iss: 2, pp 293-306
TLDR
In this paper, the authors considered the initial value problem for the spatially homogeneous Boltzmann equation with Maxwell molecules and developed a difference scheme for this problem using the Fast Fourier Transform and a study of different numerical effects.
Abstract: 
The initial value problem for the spatially homogeneous Boltzmann equation with Maxwell molecules is considered. A difference scheme for this problem is developed using the Fast Fourier Transform and a study of different numerical effects is presented.

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Chapter 2 – A Review of Mathematical Topics in Collisional Kinetic Theory

Cédric Villani
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Numerical methods for kinetic equations

Giacomo Dimarco, +1 more
- 01 May 2014 - 
TL;DR: This survey considers the development and mathematical analysis of numerical methods for kinetic partial differential equations, including the case of semi-Lagrangian methods, discrete-velocity models and spectral methods, and an overview of the current state of the art.
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A unified gas-kinetic scheme for continuum and rarefied flows IV

Chang Liu, +3 more
- 01 Jun 2016 - 
TL;DR: The UGKS as discussed by the authors is a direct modeling method in the mesh size scale, and its underlying flow physics depends on the resolution of the cell size relative to the particle mean free path.
Journal ArticleDOI

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

Lorenzo Pareschi, +1 more
- 01 Mar 2000 - 
TL;DR: It is proved that the spectral algorithm preserves the total mass and approximates with infinite-order accuracy momentum and energy, and consistency of the method is proved.
Journal ArticleDOI

Fast algorithms for computing the Boltzmann collision operator

Clément Mouhot, +1 more
- 12 Jul 2006 - 
TL;DR: For a particular class of interactions, including the so-called hard spheres model in dimension three, this work is able to derive spectral methods that can be evaluated through fast algorithms based on a suitable representation and approximation of the collision operator.