scholarly journals A novel discrete velocity method for solving the Boltzmann equation including internal energy and non-uniform grids in velocity space

2012 ◽  
Author(s):  
P. Clarke ◽  
P. Varghese ◽  
D. Goldstein ◽  
A. Morris ◽  
P. Bauman ◽  
...  
Keyword(s):  
Boltzmann Equation ◽  
Internal Energy ◽  
Velocity Space ◽  
Discrete Velocity ◽  
The Boltzmann Equation ◽  
Discrete Velocity Method ◽  
Uniform Grids

Discretization of the Boltzmann equation in velocity space using a Galerkin approach

2000 ◽  
Vol 129 (1-3) ◽  
pp. 91-99 ◽  
Author(s):  
Jonas Tölke ◽  
Manfred Krafczyk ◽  
Manuel Schulz ◽  
Ernst Rank
Keyword(s):  
Boltzmann Equation ◽  
Velocity Space ◽  
Galerkin Approach ◽  
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.

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