Hi everyone,

I have still a doubt, the Mach number in LB is defined as Ma=U_lb/cs, where U_lb is the characteristic velocity (LB units) for the system and cs is speed of sound, by definition cs=1/sqrt(3). As non-dimensional number, the Mach number can be also defined as Ma=U_p/u_sound for physical units §, where U_p[m/s] and u_sound is the speed of sound through the medium (air, water, etc). Once I have calculated both dx_P and dt_P, I can calculate the characteristic velocity U_lb. Now let us consider the simplest problem, a channel flow; I define the Re=U_P*h_P/vis_P. Perhaps I want to simulate water in a microchannel with Re=100, then I know vis_P, h_P and Re; from they I calculate the velocity U_P. If I want to have this velocity in terms of lattice units I use:

U_lb= U_P*(dt_P/dx_P)

Now the question, I want to calculate the Mach number, how?

Physical Units

1.- Ma=U_P/u_sound ------> where u_sound is the speed of sound in the medium (water), must it be 1484 m/s?

or

Lattice Units

2.- Ma=U_lb/cs -----> here cs is constant, or is it possible to modify cs to consider the water

(1 and 2 might be clearly equivalent, but they are not!!!)

what about the following

3.- since I have dx_P and dt_P, a characteristic velocity could be Uc_P=dx_p/dt_P, and then

Ma= Uc_P/u_sound

could somebody help me with this small problem?

thanks a lot

Anuhar