Constrained Runs Algorithm as a Lifting Operator for the One-Dimensional in Space Boltzmann Equation with BGK Collision Term

2016 ◽  
Vol 14 (4) ◽  
pp. 1488-1512
Author(s):  
Ynte Vanderhoydonc ◽  
Wim Vanroose
Keyword(s):  
Boltzmann Equation ◽  
Collision Term ◽  
One Dimensional ◽  
The One ◽  
Lifting Operator

The Boltzmann equation an d the one-fluid hydromagnetic equations in the absence of particle collisions

1956 ◽  
Vol 236 (1204) ◽  
pp. 112-118 ◽  
Keyword(s):  
Boltzmann Equation ◽  
Degrees Of Freedom ◽  
Charge Ratio ◽  
Collision Term ◽  
Particle Collisions ◽  
Special Circumstance ◽  
Dilute Gas ◽  
The Boltzmann Equation ◽  
Interparticle Collision ◽  
The One

Starting from the Boltzmann equation for a completely ionized dilute gas with no interparticle collision term but a strong Lorentz force, an attempt is made to obtain one-fluid hydromagnetic equations by expanding in the ion mass to charge ratio. It is shown that the electron degrees of freedom can be replaced by a macroscopic current, but true hydrodynamics still does not result unless some special circumstance suppresses the transport of pressure along magnetic lines of force. If the longitudinal transport of pressure is ignored, a set of self-contained one-fluid hydromagnetic equations can be found even though the pressure is not a scalar.

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