# Limitations of the forcing function

Hello,

I was wondering about the validity/limitations of using a uniform body force to drive LB simulations in a periodic domain. For example because of the use of a uniform driving force would one expect error in the local flow solution at the outer walls of an LB simulation domain of a random bead pack confined to a cylinder?

-Tyler B.

It seems to me that there are two ingredients to your question. The first, how to implement a body force properly in LB, is answered in the following article:

http://www.lbmethod.org/doku.php?id=literature:guo_02b

The second, how to avoid numerical artifacts on the forcing term close to a wall, is more complicated, and depends on the type of boundary you use. If you use wet node boundaries, the momentum balance is calculated in the same way on a boundary node as everywhere else. Thus, you should not experience numerical errors by applying the same algorithm in the bulk and on boundary nodes.

Thank you for the links with the boundary conditions summary, that’s very helpful. My question arose primarily because of a comment in a recent article[sup]1[/sup] where it was stated:

“The assumption of a uniform body force is valid locally in a bulk porous medium in situations where the gradient of the ensemble-averaged velocity is much smaller then ||/a. In general, this condition will be satisfied at distances further than an O(1) number of particle diameters from bounding walls.”

I am unsure of the limitations that follow from this statement.

Thanks again,

Tyler B.

1. “The first effects of fluid inertia on flows in ordered and random arrays of spheres”, Hill, Koch, Ladd. JFM, 2001, 448

Oh, it seems that I misunderstood your first post.

I have the feeling that this argument about a uniform body force is a porous medium thingy. In that case, the limitation which is hinted at is a limitation of the physical model, not of the numerical model. My understanding is that when you apply a pressure difference between inlet and outlet of a porous medium, then the pressure essentially drops linearly within the medium. This is of course not exactly true in a microscopic view, when you look at pores individually. But it is true in a continuum approach, if you take an ensemble average over all possible pore configurations. Further, this model does not take into account boundary conditions. I would guess that this is what the authors mean: close to the walls between which the porous medium is confined the assumption of a linear pressure drop is not valid.

Maybe one of the porous media guys can confirm this, or give a more satisfactory explanation?