# How to understand the sound speed in LB

Dear all

I’m a newer to LB, and got a lot of help from here. Now I have a question about the sound speed in LB.
From the pdf here about howto on “units”, it seems that the time and space step can be chosen arbitrarily, so there’s no constraint on the sound speed.
But in another book, when they choose the unit, they keep the sound speed in LB is about 340m/s in the physical system, so dx/dt=c=sqrt(3)*Cs=sqrt(3)*340 is needed.
And this makes me confused.
So I want to ask if the sound speed need to be 340m/s in physical system, and whether it will affect the result if I choose the dx & dt arbitrarily, for example dx=0.005m & dt=0.001s (then the sound speed will be less than 3m/s)?
If the Cs need not to be 340m/s, then how to understand the sound speed in LB? Or the sound speed just stands for that speed of movement whose number of Mach is below 1.0 should less than Cs?

Thanks for your attention, and hope someone can give me some kind answers.

Regards,

shelley

Welcome!

In fact, the sound speed can be reduced for the simulations. The reason is that the physical properties of the fluid do not depend on the Mach number as long as it is small (say < 0.1). This you can use to decrease the computing time. Unless you are really interested in the compressibility properties of the fluid, the physical speed of sound is not important. Please make sure at all times that the numerical Mach number is not too large in your simulations. A lattice velocity of 0.1 may still be ok, but 0.3 or 0.4 is too large. Also note that a smaller Mach number usually yields more accurate results. It is up to you whether you want to have a fast or an accurate simulation. It is very hard to achieve both at the same time.

Best,
Timm