Different Approaches to Numerical Solution of the Boltzmann Equation with Model Collision Integral Using Tensor Decompositions

2021 ◽  
pp. 105-116
Author(s):  
Aleksandr V. Chikitkin ◽  
Egor K. Kornev
Keyword(s):  
Boltzmann Equation ◽  
Numerical Solution ◽  
Collision Integral ◽  
Tensor Decompositions ◽  
The Boltzmann Equation ◽  
Model Collision

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.

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