# The physical units and LB units

hi,

I am glad to find this forum as a new to LBM. I have been confused by the conversion between LB units and physical units for a long time. Luckily, I found the article written by Jonas Latt(show my appreciate to him). However, I have a question about 2.4(simulation setup). As he wrote, the discrete grid spacing delta_x=1/100, and the time resolution delta_t=210-4. In that case, the lattice speed c=delat_x/delta_t=0.510-2. I think that if I use dimensionless in lattice system, for the BGK model, the lattice speed is usually set as unity, as a result the sound of speed c_s=c/sqrt(3)=1/sqrt(3). Does this two contradict? If the expression of sound of speed is wrong, does it mean that there is no relationship between c_s and c? Is there anyone who can clarify this for me? Many thanks.

Regards,

Beryl

Hello Beryl,

Jonas is talking about two different unit systems here. When he says that delta_x = 1 / 100 and delta_t = 2 e-4 then he means that the lattice has 100 nodes and the simulation requires 500 time steps. However, in lattice units you usually set delta_x = delta_t = 1 and thus c = 1 and c_s^2 = 1 / 3. Of course you can choose other values for delta_x and delta_t, but c_s^2 = c^2 / 3 always holds.

Timm

Hi Timm,

Thank you for your reply. According to your answer, can I draw the conclusion that the lattice speed c is 0.5*10-2? But in the fourth part, he wrote the speed of sound is a lattice constant: c_s^2=1/3, that mean he set c is equal to 1? This puzzled me. Would you explain it for me? Thanks.

Beryl

As I said, you are dealing with two different dimensionless unit systems. The one system is where you set delta_x = 1 and delta_t = 1. This is as well allowed as setting delta_x = 1 / 100 and delta_t = 2 e-4. But in both systems the speed c is different, since c = delta_x / delta_t. So you have to choose one system, and you cannot mix them. I prefer to set delta_x = 1 and delta_t = 1. This way I know that c_s^2 = 1 / 3.
The lattice speed and the sound speed are constants, since c and c_s only depend on delta_x and delta_t and not on the density or other quantities. But its value can change depending on the unit system you use.
Is it clearer now?

Yes, I got it. Thanks for your explaination.

Regards,

Beryl