simple transport

Hello everyone,
I have one small question connected with transport and meaning of LBM method.
Taking into account that we have 3 dimensional environement represented by voxels.
In each voxel we have the same number of magnesium atoms for example 10.
LBM nodes are placed in the center point of voxels.

Can we treat the calculated values of lattice velocity (from velocity distribution function) in each direction (in my case 19 values because of D3Q19 model) as the portions of magnesium atoms which move from one point to the neighbouring nodes.
For example:
If the velocity east equals 0.02 in point X and lattice density equals 1 in this point during each time step 0.02 * 10 of magnesium atoms move from this point X to its nearest east neighbour node?

That’s true ?



I think that this picture is qualitatively correct. Of course you will have some problems with 10 atoms. Those are few atoms, and obviously, 0.02 * 10 = 0.2 atoms cannot move in a given direction. But I think that the picture is more or less useful as long as the atoms are purely passive and do not interfere with the advection.
What do you want to do with it?


I am interesting about using LBM as a method to calculate how the atoms in different chemical substances move. Simple example is hydrogen in water or hydrogen in H2SO4. Obviously as a simplified model. This is only idea at present:)
Or maybe atoms of some substance in fluid, but taking into account that they are mixed perfectly and this additional substance change viscosity insignificantly.

Timm, maybe, do You know how I should treat, in the above described situation, places like input, output, wall.
I try to simulate simple transport phenomena of oxygen in the H2S04, exactly saying the flow of a little modified particles of oxygen. At the beginning I prepared the f_i values of flow in the simple tube, basing on the pressure difference. Next, when the flow was stable, I modified only particles at the input (it means these input nodes posses concentration 1.0 of these modified molecules) and in others the concentration was equal 0.0. I simulate their flow (concentration) based on f_i values in appropriate directions.

For example:
Should I take ealier calculated values of f_i at walls
Should I use bounce-back rule, it means that if 0.3 molecules of oxygen go in the wall, at next step 0.3 molecules of oxygen go out from wall in the opposite direction?

Preliminary experiments, shows that first solution works better, but I validate results only visuallly (some graphical visualisation of concentration of modified molecules) but second seems more resonably

Thanks for any help

Unfortunately, I cannot help you here. I have never worked with this kind of model and do not know which boundary conditions are appropriate.
If you know the macroscopic equations, you could try to perform a Chapman_Enskog analysis.