# Is body force pressure or density

Hi , I have this confusion as to what the body force is. Is the body force pressure or density in lattice units? What I really mean is that if I simulate a flow with the ForcedBGK model, is that body force a pressure or density gradient. I have used it for my simulation but I need to know exactly what it is for proper conversion to the physical units (i.e how to apply the factor of 3 arising from the equation of state between density and pressure ).

Hello,

in the 3D Navier-Stokes equations you see that pressure gradient and body force density f (force per volume) have the same units: N / m³
If you want to relate the body force density to the mass density gradient, you need an additional factor 3 (inverse sound speed square).
Example: If you have a simple pipe flow (length L) with densities den[sub]in[/sub] and den[sub]out[/sub] at inlet and outlet, the mass density gradient is (den[sub]in[/sub] - den[sub]out[/sub]) / L, right? The pressure gradient and the equivalent force density then are f = (p[sub]in[/sub] - p[sub]out[/sub]) / L = (den[sub]in[/sub] - den[sub]out[/sub]) / (3 L).

Best,
Timm

Thank you Timm. I understand your post, however, my confusion is this. If I use a body force approach for my simulation, is that equivalent to the mass density? Since only mass density can be applied directly in LBM simulation. Say for example, I use a body force of 1e-6 in my simulation. Should I take this value to be the mass density gradient or the pressure gradient?

This is exactly what I have answered in my post. Body force is pressure gradient.
In principle, if you are still unsure, you could perform a test run (Poiseuille flow) where you apply a body force and measure the average flow velocity. You know the solution for this problem in physical units, so you can directly check the numerical units as well.

Ok, now I see. Thank you. By the way, I sent in a PM. I hope you saw it.