# Chen Shiyi's Boundary condition

Hi all. Recently, I read Chen Shiyi’s boundary condition scheme, (PoF, vol.8, No.9, 2527, 1996). I suppose the main operations are,

Collision,
a. inside the flow domain, standard relaxation,
b. on the boundary, relax according to the given condition, constant pressure or velocity
c. outside layer (extra), extrapolated according to f^{-1} = 2* f^0 - f{1}, where, f^{-1} represents the extra layer value, f^0 on the boundary and f^1 the nearest layer inside the domain.

Stream,
some f_i on the boundary are streamed from the extra nodes.

My question is, for collision case b., only one of the velocity or pressure is given as BC. How to obtain the f^{eq}?

Thank you very much.

Dear phoenixchen903

I have never used that boundary condition yet I know that for boundary conditions you always need: in the case of Velocity BC to specify the complete velocity vector at boundary (i.e. the tangential and normal components of the velocity at the boundary); in the case of Pressure BC you also always need to specify the pressure and some velocity data too (the component(s) tangential to the boundary)
Said that, what it is generally done (see for instance http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=PLEEE8000077000005056703000001&idtype=cvips&gifs=yes) is to compute the missing macroscopic quantity of interest by relating known distribution functions at that point. For example, for a D2Q9 model although we have 3 unknown distribution functions we can related the zeroth order moment ,which gives us density(pressure), and the first order moment of interest, which gives us the velocity we know or intend to know depending on the BC, so that their combined values allows one to obtain the value of the macroscopic quantity not known.
I recommend you to read the above reference that I gave you or http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=PHFLE6000009000006001591000001&idtype=cvips&gifs=yes, which contains practical examples for the D2Q9 case of what I have tried to explain.
I think that by doing this you will have all the data required to compute feq and so after you can apply the extrapolation BC method to obtain the value of the missing distribution functions.

Hope it helps.

Regards

Goncalo

P.S. By the way, I do not know what kind of problem you are simulating but the BC you are using is more or less obsolete. Please give a quick read to the references I have suggested you. There you will find some BC schemes that are as easy to implement as Chen’s BC (or perhaps even easier). Furthermore, they keep the scheme local in opposition to Chen’s BC scheme and can provide your simulation with more accurate or stable results…(depending on the BC model)…

Thanks very much! I’ll read them.

Dear GoncaloSilva,

The links you mentioned in the post are no longer valid. Can you please update them?