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 -