Inelastic collision integral approximation of the Boltzmann equation

1976 ◽  
Vol 16 (1) ◽  
pp. 1-15 ◽  
Author(s):  
Pierre Ségur ◽  
Joëlle Lerouvillois-Gaillard
Keyword(s):  
Distribution Function ◽  
Boltzmann Equation ◽  
Power Series ◽  
Spherical Harmonic ◽  
Inelastic Collision ◽  
Collision Integral ◽  
Spherical Harmonic Expansion ◽  
Square Root ◽  
Integral Approximation ◽  
The Boltzmann Equation

A study is made of the inelastic collision integral of the Boltzmann equation using scattering probability formalism. The collision operators are expanded in a power series in the square root of the ratio of masses.Furthermore, a spherical harmonic expansion is made of all the operators so obtained. These developments are valid whatever the shape of the distribution function of the particles.

A multi-term spherical harmonic expansion of the Boltzmann equation for application to low-temperature collisional plasmas

2019 ◽  
Vol 26 (10) ◽  
pp. 103506 ◽  
Author(s):  
S. B. Swanekamp ◽  
P. F. Ottinger ◽  
P. E. Adamson ◽  
J. L. Giuliani ◽  
Tz. B. Petrova ◽  
...  
Keyword(s):  
Boltzmann Equation ◽  
Low Temperature ◽  
Spherical Harmonic ◽  
Spherical Harmonic Expansion ◽  
The Boltzmann Equation

INCLUSION OF FLOW TERMS IN THE CARTESIAN TENSOR EXPANSION OF THE BOLTZMANN EQUATION

1963 ◽  
Vol 41 (11) ◽  
pp. 1776-1786 ◽  
Author(s):  
I. P. Shkarofsky
Keyword(s):  
Distribution Function ◽  
Boltzmann Equation ◽  
Flow Velocity ◽  
Velocity Space ◽  
Pressure Tensor ◽  
Moment Equations ◽  
Ionized Gas ◽  
The Boltzmann Equation ◽  
Integrated Distribution Function ◽  
Boltzmann's Equation

The Cartesian tensor expansion of Boltzmann's equation as given by Johnston (1960) is extended to include terms denoting gradients in flow velocity. The expansion is performed in intrinsic velocity space. The gradient velocity terms yield a linear contribution to the tensor (f2) part of the angle-integrated distribution function from which the zero-trace pressure tensor is calculable. It is shown that the standard moment equations are obtained by further integration over the magnitude of velocity. For the case of a completely ionized gas, collisional terms are inserted appropriately.

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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