In the SC model, there are two velocities: the equilibrium velocity and the whole fluid velocity. In the particle distribution function, is the equilibrium velocity used only?
Looking forward for your help.
let me be a bit more precise: There are more than two velocities in Shan-Chen.
- There is the “common” equilibrium velocity which is computed by the 1/tau-averaged momentum.
- There is also the average fluid velocity which does not depend on tau.
- Additionally, each species has its own equilibrium velocity which is velocity 1) plus a force shift due to the force this species experiences.
In order to compute the equilibrium populations for a species (there is one set of eq. populations for each single species you want to simulate) within the Shan-Chen forcing model, you have to take velocity 3).
Note that the correct average physical velocity 2) also requires a force correction: It is simply the total force acting on the fluid (sum of all species forces at a point) divided by (2 total density).
I hope this helped!