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19th GAMM-Seminar Leipzig on
High-dimensional problems - Numerical treatment and applications

Max-Planck-Institute for Mathematics in the Sciences
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  19th GAMM-Seminar
January, 23th-25th, 2003
 
     
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  Abstract Sergej Rjasanow, Thu, 15.00-15.25 Previous Contents Next  
  Numerical solution of the Boltzmann equation on the uniform grid
Sergej Rjasanow (Uni Saarbrücken)

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 tex2html_wrap_inline11 for the most general model of interaction and of the order tex2html_wrap_inline13 for the Variable Hard Spheres (VHS) interaction model, while the formal accuracy is of the order tex2html_wrap_inline15. 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.

[1] Rjasanow, S. and Ibragimov, I., Numerical solution of the Boltzmann equation on the uniform grid, Preprint 63, University of Saarland, 2002, to appear in "`Computing"'

This talk presents joint work with Ilgis Ibragimow.
 

 
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