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Yogesh Talekar August 25, 1999 00:37

Euler & N-S EQUATIONS from Boltzmann EQUATION

Can anybody tell me some literature where derivation of NAvier-Stokes and Euler equations FROM BOLTZMANN EQUATION of statstical kinematics is given.

I checked in few books but the methos they talk of are very difficult to understand.

Thank You


Jim Park August 25, 1999 07:43

Re: Euler & N-S EQUATIONS from Boltzmann EQUATION
For a very readable development, try

Present, R. D., "Kinetic Theory of Gases," McGraw-Hill, 1958.


Mayer & Mayer, "Statistical Mechanics," Wiley, 1940.

Some of you newer fellows might recommend some newer books.

An August 29, 1999 12:38

Re: Euler & N-S EQUATIONS from Boltzmann EQUATION
Hello Mr Talekar:

Exa Corporation in the US has developed a new class of CFD solver based on kinetic theory and statistical physics (lattice Boltzmann). The macroscopic Navier-Stokes equations are recovered from Exa's digital physics algorithm. There is more technology information at the Exa web site:


Andrzej Matuszkiewicz August 29, 1999 23:35

Re: Euler & N-S EQUATIONS from Boltzmann EQUATION
Do they have derivation of NS eqs or references to it at their web page?


Yogesh Talekar August 30, 1999 00:22

Re: Euler & N-S EQUATIONS from Boltzmann EQUATION
No there is no such reference to the derivations on the web-page. But still I am quite a lot in dark about the derivation.

Somebody should help me!

Praveen Chandrashekar August 30, 1999 09:31

Re: Euler & N-S EQUATIONS from Boltzmann EQUATION

Here are some published papers on kinetic schemes for Euler Equations, which also show the connection between the Boltzman equation and the Euler equations.

1. SM DESHPANDE, "Kinetic theory based new upwind methods for inviscid compressible flows", AIAA Paper, 86-0275, 1986

2. JC MANDAL & SM DESPHANDE, "Kinetic Flux Vector Splitting for the Euler Equations", Computers and Fluids, vol.23, pp. 447-478, 1994 (You should be able to get this easily)

I found the following book to be very good. It contains a section on kinetic schemes. You will find more references in this book.

GODLEWSKI and RAVIART: Numerical Approximations to Hyperbolic Systems of Conservation Laws, Springer.

Hope this helps.

Mayank Tyagi August 30, 1999 15:50

Re: Euler & N-S EQUATIONS from Boltzmann EQUATION
Hi Yogesh..

There is ICASE report 99-21 ( by Qian et al titled "On higher order dynamics in lattice-based models using Chapman-Ensog method".... You can download that...

Y.H. Qian's Phd dissertation is " Lattice gas and lattice kinetic theory applied to the Navier-Stokes equation"

Hopefully this will give you a start...


Mayank Tyagi

Yogesh Talekar August 31, 1999 05:31

Thankx a lot
Respected "gurus"

Thank u very much for you help and guidance.

But still something more is needed


Yogesh Talekar August 31, 1999 05:35

Re: Euler & N-S EQUATIONS from Boltzmann EQUATION
Dear Praveen

Thank you very much for the suggestions. I will certainly try to go through the litureature

Thank you once again


Dave Higbie September 1, 1999 12:11

Re: Euler & N-S EQUATIONS from Boltzmann EQUATION

Here are some more references you can try:

"The Mathematical Theory of Non-Uniform Gases", S. Chapman, T.G. Cowling, Cambridge University Press

"Statistical Mechanics", K. Huang, John Wiley & Sons., Inc. Chapters 3-6

On Exa's website there is a paper called: "Digital Physics Approach to Computational Fluid Dynamics: Some Basic Theoretical Features", Chen, Teixeira and Molvig. Journal of Modern Physics C., Vol. 8 (1997) pg. 675

a postscript file link to the above paper can be found at

Hope this helps.


alfred almer September 13, 1999 09:00

fluent bfc 2 triangular mesh
I would like to convert a bfc-mesh A created by fluent into a mesh B . The format of the mesh B should be similar to the one ,i would use in povray to render the object depicted by A . That is, find triangles,that make up the surface of the object,that has been rendered into mesh A . UNfortunately,i donīt have access to a copy of the fluent software. Is there a way to to do this conversion by hand ?

Mesh A looks like #!fluent.1

2 Created by : ICEM CFD/CAE FLUENT Interface Vers. 3.3.2 #

1 Title FLUENT Grid File /* CONFIGURATION = tbif */ #

6 Grid Type

2 1 3 14 98 51 #

9 BFC Grid -1.214401E-08 -9.703458E-06 -1.838437E-05 -2.586320E-05 -3.196537E-05 -3.652791E-05 -3.939371E-05 -4.040466E-05 -3.939997E-05 -3.626388E-05 .........

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