I know that speed of sound (cs) in lattice units is constant: cs(L) ^2=1/3.
I can rewrite this equation in physical units: cs§^2=1/3*delta x^2/delta t^2.
So when I want to simulate a fluid flow problem by LBM, I specify the required delta x (based on volume of the domain) and also the speed of sound in that fluid (for example 1500 m/s for water in normal temperature). Then considering the above equation which provide a relationship between delta x and delta t, I can calculate the required delta t. Finally, the relaxation parameter should be obtained based on delta x, delta t and viscosity of the fluid (of course it should be in the range of 0.5 to 2.5.
Is the mentioned approach correct?