The Boltzmann Kinetic Equation and Calculation of the Transport Coefficients

2016 ◽  
pp. 123-158
Author(s):  
Shi Nguyen-Kuok
Keyword(s):  
Kinetic Equation ◽  
Transport Coefficients ◽  
Boltzmann Kinetic Equation

Examples of two point kinetic equations obeying the entropy principle

1981 ◽  
Vol 59 (9) ◽  
pp. 1241-1250 ◽  
Author(s):  
Miroslav Grmela ◽  
Jean Salmon
Keyword(s):  
Kinetic Equation ◽  
Large Time ◽  
Transport Coefficients ◽  
Kinetic Equations ◽  
Boltzmann Kinetic Equation ◽  
Qualitative Properties ◽  
Long Time Behaviour ◽  
Long Time ◽  
Entropy Principle ◽  
Qualitative Properties Of Solutions

Qualitative properties of solutions of a two point extension of the Boltzmann kinetic equation and of solutions of the Frey–Salmon two point kinetic equation are investigated. Our attention is focussed on: (i) compatibility of the long time behaviour of solutions with equilibrium thermodynamics, (ii) the thermodynamic equation of state implied by the two point kinetic equations, (iii) one point kinetic equations whose solutions approximate well the solutions to the two point kinetic equations for large time, and (iv) transport coefficients implied by the two point kinetic equations.

Application of the Boltzmann kinetic equation to the eddy problems

2011 ◽  
Vol 50 (1) ◽  
pp. 189-198 ◽  
Author(s):  
V.V. Aristov ◽  
O.I. Rovenskaya
Keyword(s):  
Kinetic Equation ◽  
Boltzmann Kinetic Equation

scholarly journals Simulation of a two-dimensional binary gas mixture outflow into vacuum through a thin slit on the basis of direct solution of the Boltzmann kinetic equation

2021 ◽  
Vol 2056 (1) ◽  
pp. 012007
Author(s):  
S S Sitnikov ◽  
F G Tcheremissine ◽  
T A Sazykina
Keyword(s):  
Kinetic Equation ◽  
Boltzmann Kinetic Equation ◽  
Gas Mixture ◽  
Two Dimensional ◽  
Direct Solution ◽  
Steady State Regime ◽  
Collision Integrals ◽  
Flow Formation ◽  
Binary Gas Mixture ◽  
State Regime

Abstract Two-dimensional binary gas mixture outflow from a vessel into vacuum through a thin slit is studied on the basis of direct solution of the Boltzmann kinetic equation. For evaluation of collision integrals in the Boltzmann equation a conservative projection method is used. Numerical simulation of a two-dimensional argon-neon gas mixture outflow from a vessel into vacuum was performed. Graphs of mixture components flow rate dependence on time during the flow formation, as well as fields of molecular density and temperature for steady-state regime, were obtained.

Collisional transport for a superthermal ion species in magnetized plasma

1986 ◽  
Vol 36 (3) ◽  
pp. 313-328 ◽  
Author(s):  
F. Cozzani ◽  
W. Horton
Keyword(s):  
Kinetic Equation ◽  
Transport Theory ◽  
A Priori ◽  
Transport Coefficients ◽  
Kinetic Equations ◽  
High Energy ◽  
Magnetized Plasma ◽  
Fractional Density ◽  
Background Ions ◽  
Ion Species

The transport theory of a high-energy ion species injected isotropically in a magnetized plasma is considered for arbitrary ratios of the high-energy ion cyclotron frequency to the collisional slowing down time. The assumptions of (i) low fractional density of the high-energy species and (ii) average ion speed faster than the thermal ions and slower than the electrons are used to decouple the kinetic equation for the high-energy species from the kinetic equations for background ions and electrons. The kinetic equation is solved by a Chapman–Enskog expansion in the strength of the gradients; an equation for the first correction to the lowest-order distribution function is obtained without scaling a priori the collision frequency with respect to the gyrofrequency. Various transport coefficients are explicitly calculated for the two cases of a weakly and a strongly magnetized plasma.

The Boltzmann Kinetic Equation and Various Models

2010 ◽  
pp. 113-144
Author(s):  
Yurii N. Grigoriev ◽  
Nail H. Ibragimov ◽  
Vladimir F. Kovalev ◽  
Sergey V. Meleshko
Keyword(s):  
Kinetic Equation ◽  
Boltzmann Kinetic Equation

THE NUMERICAL SOLUTION OF THE BOLTZMANN KINETIC EQUATION FOR GRANULAR GASES

2019 ◽  
pp. 25-30
Author(s):  
I. Gapyak
Keyword(s):  
Cauchy Problem ◽  
Kinetic Equation ◽  
Numerical Solution ◽  
Dimensional Space ◽  
Boltzmann Kinetic Equation ◽  
Granular Gases ◽  
Two Dimensional ◽  
System Of Particles ◽  
The Cauchy Problem

For a system of particles with a dissipative interaction we consider the Boltzmann type kinetic equation for granular gases. A numerical solution of the Cauchy problem for the Boltzmann type kinetic equation is constructed in two dimensional space and its stability is investigated.

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