LBM Derivation

I have finished my PhD work and now getting ready to defend. I used LBM to model micro flows. Before I go into my defense, I would like to know the entire derivation of the LBM as detailed as possible. I have many many papers on LBM, but many of the derivation steps are usually omitted. Can anyone point me to a really good derivation? Thanks.


Hi Mark,

I had the same question as you. I did a few things and can send you really raw part of my thesis if you want it. Hopefully that can help.



That would be great! My email is . Thanks!

It’s time for me to do a bit of advertisement :slight_smile:

Here is an almost “official” release of my thesis (the official one should be released soon) about the simulation of viscoelastic fluids with the lattice Boltzmann method. In the first chapter there is a quite detailed derivation of the numerical scheme from the Boltzmann equation :



Hi, Mark.

I think you can find some paper from Prof. Li-Shi Luo’s homepage

There are several papers about the derivation from Boltzmann equation to Lattice Boltzmann Equation.

And also, there is a book about Lattice Boltzmann Method,

“Lattice-gas cellular automata and lattice Boltzmann models: an introduction?”

written by Dieter A. Wolf-Gladrow . You can also find the details about the derivation from the book.


Thanks for all the links!