How to include the fluid density

Dear All


I have a question. In the LBM equations, the density (rho) is calculated by summing the distribution function f.

So How to include the fluid density, like water?
I mean where is the rho=1000 kg/m3?



In LBM you are working in a different set of units (usually number of lattice units (lu) for space and number of time steps (ts) for time). Density is also normalised to a reference density rho_0, that you can choose at any given location in your flow domain. Thus, the actual density is given by rho_0 * sum_i f_i. At the reference location, you should then have sum_i f_i = 1.


Thanks a lot!

Would you explain more with some examples?


It’s really no more than a simple scaling. The density in the computational domain, which you calculate as sum_i f_i, should thus be multiplied everywhere by rho_0 in order to get the physical density. Here rho_0 is the density at some reference location that you should have determined beforehand and depends on the problem at hand.

Dear mohammad.sarfaraz , can you tell me what the answer of your question is? Thanks