2004/05/10 by L. Fainsilber, Laura Fainsilber, Fainsilber, L. +6
Computer Science · Mathematics · #11E25 (Secondary) #11N64 #82C40 (Primary) 11L07 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Number Theory (math.NT) #Numerical methods in inverse problems #math.AP #math.NT #msc:11E25 #msc:11L07 #msc:11N64 #msc:82C40
paper · pdf · doi:10.48550/arxiv.math/0405171
23 pages, 2 figures. Full resolution images are available at http://www.math.chalmers.se/~wennberg/Uppsatser/FKW/index.html
arxiv created 2004/05/10 · openalex publication_date 2004/05/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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. However, by showing that lattice points on most circles are equidistributed we find that the collision operator can indeed be approximated as a sum over lattice points in the two-dimensional case. For higher dimensions, this result has already been obtained by A. Bobylev et. al. (SIAM J. Numerical Analysis 34 no 5 p. 1865-1883 (1997))