# Mach number limits (little strange)

Hello
In many papers it is said that for incompressible flows the best choice is when Ma << 1.
But when we take simple example:
dt_lb = dx_lb = 1 (as it is established in many papers)
u_lb = dx_lb / dt_lb = 1
c_s = u_lb/sqrt(3) = 1/sqrt(3)
so
Ma = u_lb / c_s > 1

So this is correct, where do I make a mistake in my thinking?

Hi, as I know the u_lb is found by another formula: u_lb= u_ph dt_ph / dx_ph.
It is necessary to provide that Ma=|u_lb |/c_s should be small where c_s=1/sqrt(3).
Details will be explained by more skilled experts…

Hi
Yes, I think that your equation are also right.
But I think also that:
u_lb = dx_lb / dt_lb

so my question is still unresolved:)

Hello,

But, Is Mach Number u_flow/c_s ?

u_flow: flow velocity
c_s: speed of sound

Hi

There are three categories velocity in LBM: the first one is molecular velocity (v_molecular) which is as the same order with Sound speed, in the LBM v_molecular=u_lb ; the second is the fluid velocity (v_fluid); the third is the peculiar velocity: v_perculiar=v_molecular-v_fluid.

Ma=v_fluid/Sound_speed——as daralcan posted.

So if want to calculate Ma in blood flow
I need sound_speed in blood ???

Hello,

Speed of sound;

c_s= u_lb/3^0.5.

So speed of sound depends on your mesh conditions and time step size.

Daralcan