nonlinear boltzmann equation
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General Properties of Collision Integral Kernels of the Nonlinear Boltzmann Equation

2019 ◽  
Vol 64 (10) ◽  
pp. 1400-1408
Author(s):  
L. A. Bakaleinikov ◽  
E. Yu. Flegontova ◽  
E. A. Tropp
Keyword(s):  
Boltzmann Equation ◽  
Collision Integral ◽  
Nonlinear Boltzmann Equation ◽  
General Properties

Two variants of Monte Carlo projection method for numerical solution of nonlinear Boltzmann equation

2019 ◽  
Vol 34 (3) ◽  
pp. 143-150
Author(s):  
Sergey V. Rogasinsky
Keyword(s):  
Boltzmann Equation ◽  
Projection Method ◽  
Orthonormal Basis ◽  
Statistical Modelling ◽  
Hermite Functions ◽  
Nonlinear Boltzmann Equation ◽  
Kinetic Boltzmann Equation ◽  
Relaxation Problem ◽  
Nonlinear Kinetic ◽  
Approximation Of A Function

Abstract The paper is focused on justification of a statistical modelling algorithm for solution of the nonlinear kinetic Boltzmann equation on the base of a projection method. Hermite functions are used as an orthonormal basis. The error of approximation of a function by a partial sum of Hermite functions series is estimated in the L2 norm. The estimates are compared for two variants of the projection method in the case of solutions to the homogeneous gas relaxation problem with a known solution.

Kernels of the Direct Collision Integral of the Nonlinear Boltzmann Equation

2018 ◽  
Vol 63 (10) ◽  
pp. 1445-1454 ◽  
Author(s):  
L. A. Bakaleinikov ◽  
E. A. Tropp ◽  
E. Yu. Flegontova ◽  
I. A. Ender
Keyword(s):  
Boltzmann Equation ◽  
Collision Integral ◽  
Nonlinear Boltzmann Equation ◽  
Direct Collision

Recurrent procedure for constructing nonisotropic matrix elements of the collision integral of the nonlinear Boltzmann equation

2017 ◽  
Vol 62 (8) ◽  
pp. 1148-1155 ◽  
Author(s):  
I. A. Ender ◽  
L. A. Bakaleinikov ◽  
E. Yu. Flegontova ◽  
A. B. Gerasimenko
Keyword(s):  
Boltzmann Equation ◽  
Collision Integral ◽  
Matrix Elements ◽  
Nonlinear Boltzmann Equation

Statistical modelling algorithm for solving the nonlinear Boltzmann equation based on the projection method

2017 ◽  
Vol 32 (3) ◽  
Author(s):  
Sergey V. Rogazinsky
Keyword(s):  
Boltzmann Equation ◽  
Projection Method ◽  
Hermite Polynomials ◽  
Statistical Modelling ◽  
Nonlinear Boltzmann Equation ◽  
One Dimensional ◽  
Kinetic Boltzmann Equation ◽  
Nonlinear Kinetic

AbstractA statistical modelling algorithm is constructed for solution of the nonlinear kinetic Boltzmann equation based on the projection method. Hermite polynomials are used as an orthonormalized basis. The algorithm was tested on calculations for the problem of one-dimensional relaxation of gas with a known solution.

The collision integral kernels of the scalar nonlinear Boltzmann equation for pseudopower potentials

2015 ◽  
Vol 60 (1) ◽  
pp. 8-13 ◽  
Author(s):  
L. A. Bakaleinikov ◽  
E. A. Tropp ◽  
E. Yu. Flegontova ◽  
A. Ya. Ender ◽  
I. A. Ender
Keyword(s):  
Boltzmann Equation ◽  
Collision Integral ◽  
Nonlinear Boltzmann Equation

Construction of the collision integral kernel for the nonlinear Boltzmann equation from its matrix elements

2014 ◽  
Vol 59 (6) ◽  
pp. 796-807
Author(s):  
L. A. Bakaleinikov ◽  
E. Yu. Flegontova ◽  
A. Ya. Ender ◽  
I. A. Ender
Keyword(s):  
Boltzmann Equation ◽  
Integral Kernel ◽  
Collision Integral ◽  
Matrix Elements ◽  
Nonlinear Boltzmann Equation
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