# Physical force scaling factor

Hello everyone,

I am trying to couple a LBM-DEM programme together with my supervisor. For now we have just hit the wall and we do not know exactly how to find/use correctly the scaling factor from force in LB units to physical ones. We are following an equation found in the literature [Lattice-Boltzmann Method on quadtree type grids for Fluid-Structure-Interaction, Sebastian Geller, et.al.]

Force (physical) = Force(LB) ((lenght-LB * density-phy * viscosity^2-phy) / (lenght-phy * density-LB * viscosity^2-LB))

We consider physical properties of water, viscosity-LB = 1/6 and density-LB = 1, lattice unit = 1 representing 0.001m.

We obtain a value of order 10e-5 which seems to be very small and we do not know if our assumptions are correct. I have not found any other source describing a force scaling factor so I decided to come to the forums and ask for some help or guidance which will be very valuable.

Kind regards.

Hello Rodrigo,

I am currently doing the same thing - realizing an LB-DEM coupling. The conversion I came up with reads

F_phys = dx_lb^4/dt_lb^2 * rho_phys * l_phys^4 / t_phys^2

which has already been validated by comparisons to analytic and numeric results. I don’t quite get why you divide by the physical length and the viscosity, in my understanding there should be a “*” where you have a “/”.

best
Philippe

Hi Philippe,

thank you for your reply. I am using two non-dimensional factors, I equaled the drag coefficients in both systems, then, similarly I introduced the Reynolds number and with some algebra get to the equation I typed. I can provide details if necessary.

Can I kindly ask you for reference(s) where to find more details about the factor you are using?

Thank you.

Hello Rodrigo,

my conversions are based on this document:

http://wiki.palabos.org/_media/howtos:lbunits.pdf

I came up with the force conversion myself, but - as mentioned - validated it by comparison to analytic results and simulations with finite volume solvers. This is not (yet) published though.

best
Philippe