I have a simple question. Is a distribution function (i.e. the distribution of the number of molecules at a given location into the different directions ) still a distribution after streaming and bounce back ?

In other words, given the distribution f(i,j, , after streaming and bounce back is the new f such that sum(f(i,j,:),3)=1 ?

thank you in advance

I do not entirely understand your question. In compressible LBM, the sum of the populations at a given point is the density. This density is not necessarily 1 due to compressibility effects.

If your Mach number is sufficiently small, after collision and propagation or after bounce-back and propagation, the sum of the populations in the fluid is very close to 1 (if 1 is the mean density in the fluid). But be aware that the populations temporarily sitting on the obstacles cannot be treated like this. On the obstacles, the density is not defined if you use a standard bounce-back boundary condition.

Timm

Thank you Timm for your satisfacing answer. I applied â€śZou He Open Boundary Conditionsâ€ť. I found that the recalculated distribution can take negative values.

Is this possible or maybe there are some mistakes in my code? maybe due to the fact I do not change the corner conditions?

What do you think about this?

Thanks again in advanceâ€¦

Michele

In some lattice Boltzmann models, negative populations are valid. In the standard LBM, however, I believe that this is a problem. You should take into account the corners and debug your code.