I carried out 3-dimensional porous media simulation with flow driven by a body force and periodic boundary conditions on all sides of the 3-D domain but I am wondering if the result is ok. I used the “forcedPoiseuille2d” as a guide in developing the simulation.
Bounceback was used used for solid obstacles in the domain.

My data is

Velocity in lattice units: u=0.01
Reynolds number: Re=13.8
Lattice resolution: N=251
Extent of the system: lx=1
Extent of the system: ly=1
Extent of the system: lz=1
Grid spacing deltaX: dx=0.00398406
Time step deltaT: dt=3.98406e-05
Body force = 2.2e-7

However, my average energy fluctuates between two values of 1.67428e-10 and 2.59442e-12, but the ave rho is constant at 1

My questions are;
1). Is the average energy not too small?
2). Is the average energy not supposed to converge to a particular value as flow assumes steady state?

Yes, the average energy in your system is extremely low. I have the impression that there is an inconsistency in the values you are showing. On one hand, the reference velocity is 10^-2, and on the other hand, the RMS velocity (the square root of the average energy) fluctuates between 10^-5 and 10^-6. You do have a certain freedom in choosing the reference velocity, but it should certainly be of the same order of magnitude as the average velocity in your system.

Yes, the value of the body force, as chosen in lattice units, does have an importance. If you chose to define the conversion between physics and simulation with respect to a reference velocity (and I have the feeling that this is what you do), then the reference velocity must have the value you pretend it has. You somehow signed a contract in which you guaranteed that the reference velocity, as measured in lattice units, would be 0.01 in your simulation. If it’s not, your procedure of unit conversion is meaningless. And, the way to actually get a velocity of 0.01 is to play with the body force; at least, that’s the feeling I get from your description.

The fluctuation in the average energy was because my omega was not defined as a constant. As soon as I corrected that, my average energy tended towards a stead value.

I am finding interesting observations in the simulation.

First, I think the reference velocity is used, in association with the Reynolds number, to define the omega, and hence, the viscosity.
Now, my body force is defined independent of my velocity (unlike in the poiseuilleflow) , so I am wondering why the end product velocity (function of average energy) should be of the same order as the reference velocity?

As a follow up to the above, my average energy varied as I varied the body force. For example,…with a body force of the order of 1e-8, my average energy is of the order of 1e-7, while a body force of 1e-5 gave an average energy of 1e-3. This showed that the lower the body force, the lower the energy of the system and should not be a function of the reference velocity since my body fore is independent of it.