analytical solutions

does anybody know of good flow problems with analytical solutions? I am trying to debug my LBM code.


I guess you are looking for something slightly more complicated than the Pouiseuille flow.
Look at the jlatt’s thesis:

i.e. pag 35-------------> Womersley flow. (a time dependent flow with the same geometry of the Pouiseuille flow)


In fact there are not that much analytical solutions to test your code accuracy. Here are some references where you might find some answers… There are of course the poiseuille, and couette flows, the womersley (which is time dependent), there also is a 3d analytical solution for rectangular “poiseuille” flow.

author = {O. Walsh},
title = {Eddy solutions of the {N}avier-{S}tokes equations},
editor = {J. G. Heywood and K. Masuda and R. Rautmann and S. A. Solonnikov},
pages = {305–309},
booktitle = {The {N}avier-{S}tokes Equations II – Theory and Numerical Methods},
year = {1991},
publisher = {Springer-Verlag},
series = {Lecture Notes in Mathematics},
volume = {1530},

For benchmarcks you oculd look at the benchmark section where some are done to test BC conditions.


Good answer!

Dear all,
I am new to LBM. I made a run using Palabos (twoSphere) and I got my results for fluid flow average velocity. How can I can compare my numerical results with analytical results. what are the equations to do that?
thank you very much