Eigenvalues of the boltzmann collision operator for binary gases: Relaxation of anisotropic distributions

1983 ◽  
Vol 77 (3) ◽  
pp. 417-427 ◽  
Author(s):  
B. Shizgal ◽  
R. Blackmore
Keyword(s):  
Collision Operator ◽  
Boltzmann Collision Operator

Moments of the Boltzmann collision operator for Coulomb interactions

2021 ◽  
Vol 28 (7) ◽  
pp. 072113
Author(s):  
Jeong-Young Ji ◽  
Min Uk Lee ◽  
Eric D. Held ◽  
Gunsu S. Yun
Keyword(s):  
Collision Operator ◽  
Coulomb Interactions ◽  
Boltzmann Collision Operator

On the Inversion of the Linearized Collision Operator

1981 ◽  
Vol 36 (2) ◽  
pp. 113-120 ◽  
Author(s):  
Ulrich Weinert
Keyword(s):  
Kernel Function ◽  
Inverse Operator ◽  
Integral Kernel ◽  
Collision Operator ◽  
Boltzmann Collision Operator ◽  
Linearized Collision Operator

Abstract Some features are discussed in connection with the representation of the linearized Boltzmann collision operator and its inversion. It is shown that under certain assumptions the inverse operator can be given explicitly as an integral kernel function.

Matrix Elements of the Linearized Collision Operator for Multi-temperature Gas-mixtures

1978 ◽  
Vol 33 (4) ◽  
pp. 480-492
Author(s):  
Ulrich Weinert
Keyword(s):  
Collision Operator ◽  
Basis Functions ◽  
Inelastic Collisions ◽  
Matrix Elements ◽  
Flux Vector ◽  
Balance Equations ◽  
Heat Flux Vector ◽  
The Matrix ◽  
Boltzmann Collision Operator ◽  
Linearized Collision Operator

For a multi-component and multi-temperature gas-mixture the matrix elements of the linearized Boltzmann collision operator are investigated for isotropic interaction potentials. The representation by means of Burnett basis functions simplifies the algebraic structure and enables closed expressions for the general results, which can also be used for an investigation of inelastic collisions. For the elastic case those collision terms are given explicitely which appear in the balance equations for mass, momentum, energy and heat flux-vector.

The role of pseudo-eigenvalues of the Boltzmann collision operator in thermalization problems

1983 ◽  
Vol 61 (7) ◽  
pp. 1038-1041 ◽  
Author(s):  
R. Blackmore ◽  
B. Shizgal
Keyword(s):  
Hard Sphere ◽  
Large Fraction ◽  
Collision Operator ◽  
Matrix Methods ◽  
Continuum Spectrum ◽  
Rigorous Treatment ◽  
Boltzmann Collision Operator ◽  
The Continuum

The calculation of the eigenvalues of the hard sphere Boltzmann collision operator using discrete matrix methods yields discrete eigenvalues, a large fraction of which are unconverged and lie in the continuum spectrum of the operator. The role of these pseudo-eigenvalues is examined. The results strongly suggest that for practical calculations the rigorous treatment of the continuum is not necessary provided that a moderately large number of pseudo-eigenvalues are included.

scholarly journals Some Estimates on the Boltzmann Collision Operator

1997 ◽  
Vol 07 (07) ◽  
pp. 1023-1033 ◽  
Author(s):  
Jens Struckmeier
Keyword(s):  
Density Function ◽  
Interaction Potential ◽  
Hard Sphere ◽  
Collision Operator ◽  
Gain Term ◽  
Boltzmann Collision Operator ◽  
Maxwellian Molecules ◽  
Collision Kernels ◽  
Loss Term

The paper presents some new estimates on the gain term of the Boltzmann collision operator. For Maxwellian molecules, it is shown that the L∞-norm of the gain term can be bounded in terms of the L1- and L∞-norm of the density function f. In the case of more general collision kernels, like the hard-sphere interaction potential, the gain term is estimated pointwise by the L∞-norm of the density function and the loss term of the Boltzmann collision operator.

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