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.

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.

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.

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?