Recently I found various combined slip boundary conditions (such as : bounce back with specular reflection, Mawellian slip boundary, etc) are used in LBM to study the gas flow in micro-channel or micro-tubes. Can we apply those BCs directly to porous media without modification?
Hmm - I'd say it's difficult. As far as I know, quite some models are tuned for channel flows w.r.t. parametrisation; so, going for a complex geometry such as porous media is probably not so simple. But quite much work already exists, you may e.g. check out for a start:
- Kalarakis et al; Mesoscopic Simulation of Rarefied Flow in Narrow Channels and Porous Media, Transp Porous Med, 2012
- Tang et al; Three-dimensional lattice Boltzmann model for gaseous flow in rectangular microducts and microscale porous media, J Appl Phys, 2005
- Tang et al; Gas slippage effect on microscale porous flow using the lattice Boltzmann method, Phys Rev E, 2005
Hi, Philipp,
Thanks for your answer. However, in those papers you recommend, Tang et al. didn't specify how to apply CBBSR on "solid obstacles" distributed inside of solid walls, and Kalarakis only provide the final results of LBM, the details of the flow based on LB simulation were not shown in their paper.
In my own understanding, for the solid wall or obstacles, only the distribution functions facing to the fluid domain need to be recalculated based on CBBSR/CBBDR, or other slip boundary models, meanwhile, the corner nodes need special treatments which is also pointed out in your paper "LB simulation in the slip and transition flow regime with the peano framework". For a simple geometry such as channels and tubes, it is not hard to achieve this, but I think it is unrealistic to specify every corner node or boundary for porous media, so could you please provide more suggestions on this aspect? Thanks a lot.
Regards,
Junjian
I don't get your point on "Kalarakis only provide the final results of LBM"; they describe their boundary treatment in Sec. 5 and to me, this looks like all parameters are fixed (for their first-order case); however, what's missing IMHO is the description how to determine the velocity gradient du/dn (probably finite differences or so?)...
It can also be that the discussion that we had (in the paper mentioned by you above) was just irrelevant in the porous media case, but this would still be kind of surprising to me...
Hi Philipp, I mean they only show the permeability estimated by LBM, but the details of the fluid flow aren't shown in their paper(In Tang et al's paper, you can see the distribution of velocity vectors in the porous structure).
Now I still feel confused to apply those kind of slip boundary conditions in porous media...But thank you for your answer.
I've just noticed this article (did not read it yet) in PhysRevE: http://journals.aps.org/pre/abstract/10.1103/PhysRevE.91.043305
Maybe this can help you.
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