2007 / June Volume 2 No.2
The Boltzmann equation on a two-dimensional lattice theoretical and numerical results
| Published Date |
2007 / June
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|---|---|
| Title | The Boltzmann equation on a two-dimensional lattice theoretical and numerical results |
| Author | |
| Keyword | |
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| Pagination | 667-685 |
| Abstract | The construction of discrete velocity models or numerical methods for the Boltzmann equation, may lead to the necessity of computing the collision operator as a sum over lattice points. The collision operator involves an integral over a sphere, which
corresponds to the conservation of energy and momentum. In dimension two there are difficulties even in proving the convergence
of such an approximation since many circles contain very few lattice points, and some circles contain many badly distributed lattice
points. This paper contains a brief description of the proof that was recently presented elsewhere ([L. Fainsilber, P. Kurlberg, B. Wennberg, SIAM J. Math. Anal.>, 37, p 1903-1922]). It also
presents the results of numerical experiments.
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| AMS Subject Classification |
11E25, 11L07, 82C40
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| Received |
2005-05-27
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