Calculation of boltzmann equation collision integral and accurate solution of relaxation problem

1978 ◽  
Vol 12 (5) ◽  
pp. 749-757
Author(s):  
I. N. Kolyshkin ◽  
A. Ya. �nder ◽  
I. A. �nder
Keyword(s):  
Boltzmann Equation ◽  
Accurate Solution ◽  
Collision Integral ◽  
Relaxation Problem

scholarly journals Matrix lattice Boltzmann reloaded

2011 ◽  
Vol 369 (1944) ◽  
pp. 2202-2210 ◽  
Author(s):  
Ilya Karlin ◽  
Pietro Asinari ◽  
Sauro Succi
Keyword(s):  
Boltzmann Equation ◽  
Lattice Boltzmann ◽  
Three Dimensional ◽  
Collision Integral ◽  
Lattice Boltzmann Equation ◽  
New Paradigm ◽  
Driven Cavity ◽  
Matrix Lattice ◽  
Stability And Accuracy ◽  
Enhanced Stability

The lattice Boltzmann equation was introduced about 20 years ago as a new paradigm for computational fluid dynamics. In this paper, we revisit the main formulation of the lattice Boltzmann collision integral (matrix model) and introduce a new two-parametric family of collision operators, which permits us to combine enhanced stability and accuracy of matrix models with the outstanding simplicity of the most popular single-relaxation time schemes. The option of the revised lattice Boltzmann equation is demonstrated through numerical simulations of a three-dimensional lid-driven cavity.

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.

scholarly journals The Chapman?Enskog Solution of the Boltzmann Equation: A Reformulation in Terms of Irreducible Tensors and Matrices

1967 ◽  
Vol 20 (3) ◽  
pp. 205 ◽  
Author(s):  
Kallash Kumar
Keyword(s):  
Boltzmann Equation ◽  
Kinetic Theory ◽  
Harmonic Oscillator ◽  
Shell Model ◽  
Nuclear Physics ◽  
Collision Integral ◽  
Polar Coordinates ◽  
Irreducible Tensors ◽  
The Boltzmann Equation ◽  
Oscillator Shell

The Chapman-Enskog method of solving the Boltzmann equation is presented in a simpler and more efficient form. For this purpose all the operations involving the usual polynomials are carried out in spherical polar coordinates, and the Racah-Wigner methods of dealing with irreducible tensors are used throughout. The expressions for the collision integral and the associated bracket expressions of kinetic theory are derived in terms of Talmi coefficients, which have been extensively studied in the harmonic oscillator shell model of nuclear physics.

Recurrence procedure for calculating kernels of the nonlinear collision integral of the Boltzmann equation

2016 ◽  
Vol 61 (4) ◽  
pp. 486-497 ◽  
Author(s):  
L. A. Bakaleinikov ◽  
E. Yu. Flegontova ◽  
A. Ya. Ender ◽  
I. A. Ender
Keyword(s):  
Boltzmann Equation ◽  
Collision Integral ◽  
The Boltzmann Equation
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