# Spurious Velocity in MCSH

Hello
for checking the spurious velocity in MCSH ( accourding to the book have been written by sokup ) I simulated a fixed droplet with periodic boundary condition but I realized that when I state G about 1.5 and both densities equal to 1, the spurious magnitude is so large about 0.3, This result is so different compared with the articles in this field because I have seen that the magnitude of spurious in the articles is about 0.001
would u plz help me?
regards

Dear king_3000,

in multicomponent-shan-chen simulations, there are various different velocities that can easily be mixed up. So the question is, how do you calculate your velocity? Sometimes, people falsely take the composite velocity

u’ = ( \sum_k ( (\sum_i f_i^k e_i) / tau_k ) ) / ( \sum_k ( sum_i f_i^k ) / tau_k )

where k is the index for the component. It could also be that you use the raw first-order moment of one component. However, the velocity you are actually interested in is the physical velocity of the mixture which has to be force-corrected and (for the standard shan-chen-multicomponent model) can be calculated with

u_mixture = ( \sum_k ( \sum_i f_i^k e_i + 0.5*F_k ) ) / ( \sum_k ( sum_i f_i^k ) )

If you want to look at spurious velocities in your simulation, this is the velocity you should use (cf. Shan, X.; Doolen, G.: Multicomponent lattice-Boltzmann model with interparticle interaction. Journal of Statistical Physics 81, 379-393 (1994)).

Another difference between your results and the ones from your references might be due to the way the interaction force is incorporated into the Lattice Boltzmann Equation. There are numerous ways to do this and they each have an effect on the magnitude of the spurious velocities.

Regards,

kk

thank you it worked very well