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.
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 :