The velocity in the SC model

Hi, everyone,
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.

Dear Nash,

let me be a bit more precise: There are more than two velocities in Shan-Chen.

  1. There is the “common” equilibrium velocity which is computed by the 1/tau-averaged momentum.
  2. There is also the average fluid velocity which does not depend on tau.
  3. 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!