Recurrence procedure for calculating kernels of the nonlinear collision integral of the Boltzmann equation
- Authors: Bakaleinikov L.A.1, Flegontova E.Y.1, Ender A.Y.1, Ender I.A.2
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Affiliations:
- Ioffe Physical Technical Institute
- St. Petersburg State University
- Issue: Vol 61, No 4 (2016)
- Pages: 486-497
- Section: Theoretical and Mathematical Physics
- URL: https://journals.rcsi.science/1063-7842/article/view/197026
- DOI: https://doi.org/10.1134/S1063784216040071
- ID: 197026
Cite item
Abstract
A recurrence procedure for a sequential construction of kernels \(G_{{l_1},{l_2}}^l\) (c, c1, c2) appearing upon the expansion of a nonlinear collision integral of the Boltzmann equation in spherical harmonics is developed. The starting kernel for this procedure is kernel G0,00 (c, c1, c2) of the collision integral for the distribution function isotropic with respect to the velocities. Using the recurrence procedure, a set of kernels \(G_{{l_1},{l_2}}^{ + l}\) (c, c1, c2) for a gas consisting of hard spheres and Maxwellian molecules is constructed. It is shown that the resultant kernels exhibit similarity and symmetry properties and satisfy the relations following from the conservation laws.
About the authors
L. A. Bakaleinikov
Ioffe Physical Technical Institute
Author for correspondence.
Email: fl.xiees@mail.ioffe.ru
Russian Federation, Politekhnicheskaya ul. 26, St. Petersburg, 194021
E. Yu. Flegontova
Ioffe Physical Technical Institute
Email: fl.xiees@mail.ioffe.ru
Russian Federation, Politekhnicheskaya ul. 26, St. Petersburg, 194021
A. Ya. Ender
Ioffe Physical Technical Institute
Email: fl.xiees@mail.ioffe.ru
Russian Federation, Politekhnicheskaya ul. 26, St. Petersburg, 194021
I. A. Ender
St. Petersburg State University
Email: fl.xiees@mail.ioffe.ru
Russian Federation, Universitetskii pr. 28, Staryi Peterhof, St. Petersburg, 198504