Numerical solution of the Boltzmann equation on the uniform grid |
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Authors: | I Ibragimov S Rjasanow |
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Affiliation: | Fachrichtung 6.1 – Mathematik Universit?t des Saarlandes Postfach 151150 66041 Saarbrücken Germany e-mails: ilgis@num.uni-sb.de; rjasanow@num.uni-sb.de, DE
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Abstract: | In the present paper a new numerical method for the Boltzmann equation is developed. The gain part of the collision integral
is written in a form which allows its numerical computation on the uniform grid to be carried out efficiently. The amount
of numerical work is shown to be of the order O(n
6log(n)) for the most general model of interaction and of the order O(n
6) for the Variable Hard Spheres (VHS) interaction model, while the formal accuracy is of the order O(n
−2). Here n denotes the number of discretisation points in one direction of the velocity space. Some numerical examples for Maxwell pseudo-molecules
and for the hard spheres model illustrate the accuracy and the efficiency of the method in comparison with DSMC computations
in the spatially homogeneous case.
Received June 18, 2002; revised August 23, 2002 Published online: October 24, 2002 |
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Keywords: | AMS Subject Classification: 82C40 82C80 65R20 |
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