Modified Bounce-Back rule for particle transport

I am trying to implement the transport of (at least) one sphere (diameter ~30 micron) in a simple straight tube, with water flowing.

I am implementing the “modified bounce-back rule” to deal with moving boundaries, initially introduced by Anthony Ladd in 1994, my reference paper was written by Feng, Han and Owen in 2007 ( available here: Feng2007) .

I have two questions:

  1. The modified bounce back rule is defined in this paper as

f_-i (x, t + 1) = f_i (x, t_+) − Alpha_ai * e_i * v_b, where Alpha_ai = 6*w_i * p / Cs^2 (Equation 33),

but other papers give a different definition of Alpha: does anybody know which value of Alpha is the good one?

  1. Using this definition, I find a particle velocity which is around 10 times smaller than the velocity of the fluid, but I am pretty sure that the transported particle should reach the same velocity of the fluid. Does anybody have some explanation for this different values of velocity, or maybe a clue to solve this problem?

Any other suggestion to easily implement millions of microspheres will be appreciated!
Thank you very much,


Dear Costanza,
Did you solve that moving wall boundary prob. If yes, then can you guide me concisely. Either by giving correct equation or the same equation in the form of code.