Polynomial expansion for the axially symmetric Boltzmann equation and relation between matrix elements of collision integral

2001 ◽  
Author(s):  
A. Ya. Ender
Keyword(s):  
Boltzmann Equation ◽  
Collision Integral ◽  
Polynomial Expansion ◽  
Matrix Elements ◽  
Axially Symmetric

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

Isotropic matrix elements of the collision integral for the Boltzmann equation

2017 ◽  
Vol 62 (9) ◽  
pp. 1307-1312 ◽  
Author(s):  
I. A. Ender ◽  
L. A. Bakaleinikov ◽  
E. Yu. Flegontova ◽  
A. B. Gerasimenko
Keyword(s):  
Boltzmann Equation ◽  
Collision Integral ◽  
Matrix Elements ◽  
Isotropic Matrix ◽  
The 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

Matrix elements and kernels of the collision integral in the Boltzmann equation

2011 ◽  
Vol 56 (4) ◽  
pp. 452-463 ◽  
Author(s):  
A. Ya. Ender ◽  
I. A. Ender ◽  
L. A. Bakaleinikov ◽  
E. Yu. Flegontova
Keyword(s):  
Boltzmann Equation ◽  
Collision Integral ◽  
Matrix Elements ◽  
The Boltzmann Equation

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.

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