Research output: Contribution to journal › Article › peer-review
A Deterministic Algorithm for Calculating the Boltzmann Collision Integral for a Small Impurity with Characteristic Velocities Widely Different from the Background Distribution. / Fedorenkov, E. A.; Beklemishev, A. D.
In: Computational Mathematics and Mathematical Physics, Vol. 66, No. 3, 01.05.2026, p. 592-607.Research output: Contribution to journal › Article › peer-review
}
TY - JOUR
T1 - A Deterministic Algorithm for Calculating the Boltzmann Collision Integral for a Small Impurity with Characteristic Velocities Widely Different from the Background Distribution
AU - Fedorenkov, E. A.
AU - Beklemishev, A. D.
N1 - Fedorenkov, E. A. A Deterministic Algorithm for Calculating the Boltzmann Collision Integral for a Small Impurity with Characteristic Velocities Widely Different from the Background Distribution / E. A. Fedorenkov, A. D. Beklemishev // Computational Mathematics and Mathematical Physics. – 2026. – Vol. 66, No. 3. – P. 592-607. – DOI 10.1134/S0965542525702033. – EDN QYGBPI.
PY - 2026/5/1
Y1 - 2026/5/1
N2 - An algorithm for calculating the Boltzmann collision integral for a small impurity in a background gas has been developed. The method is able to calculate the evolution of the impurity distribution function on a compact local velocity grid that can be significantly smaller than the domain of the background distribution. The algorithm is based on preliminary computation of the transition frequency matrix from one grid cell to another. Calculation of the frequency matrix is reduced to integration over a plane in velocity space determined by the energy and momentum conservation laws. A modification of the method that strictly preserves the number of particles in the computational domain is presented. The method is extended to the case of arbitrary cross sections and inelastic collisions. Tests for relaxation to a Maxwellian distribution, scattering by flow, and beam deceleration confirm the accuracy and applicability of the method to problems of energy and momentum transfer in mixtures with widely varying temperatures.
AB - An algorithm for calculating the Boltzmann collision integral for a small impurity in a background gas has been developed. The method is able to calculate the evolution of the impurity distribution function on a compact local velocity grid that can be significantly smaller than the domain of the background distribution. The algorithm is based on preliminary computation of the transition frequency matrix from one grid cell to another. Calculation of the frequency matrix is reduced to integration over a plane in velocity space determined by the energy and momentum conservation laws. A modification of the method that strictly preserves the number of particles in the computational domain is presented. The method is extended to the case of arbitrary cross sections and inelastic collisions. Tests for relaxation to a Maxwellian distribution, scattering by flow, and beam deceleration confirm the accuracy and applicability of the method to problems of energy and momentum transfer in mixtures with widely varying temperatures.
KW - Boltzmann kinetic equation
KW - collision integral
KW - deterministic method
KW - discrete velocity grid
KW - impurities
KW - Кинетическое уравнение Больцмана
KW - интеграл столкновений
KW - примеси
KW - детерминированный метод
KW - дискретная сетка по скоростям
UR - https://www.mendeley.com/catalogue/66cab4ad-0007-3c08-8107-44dc10bbb6ba/
UR - https://www.scopus.com/pages/publications/105038012099
UR - https://elibrary.ru/item.asp?id=90808800
U2 - 10.1134/S0965542525702033
DO - 10.1134/S0965542525702033
M3 - Article
VL - 66
SP - 592
EP - 607
JO - Computational Mathematics and Mathematical Physics
JF - Computational Mathematics and Mathematical Physics
SN - 0965-5425
IS - 3
ER -
ID: 85119863