Boundary condition of cell-centered FVM
 

Is it possible to make the velocity be zero exactly at solid boundary(viscous no slip BC) by the cell-centerd finite volume method:confused:, i knew finite difference method and vertex based finite volume method can do that ,but not clear of whether cell centered FVM could or not

hi jackson，my answer is a big YES coz I've tried that way and it work just fine.
Good luck!

Jackson:

I agree with Jiannan, it does work. I've also used it. For a viscous flow, you can simply set the velocity in the next-to-boundary cells to zero.

For an inviscid flow, where the velocity in those cells is finite and always parallel to the surface, you have to be more formal. I've found that you can derive governing equations that apply specifically to the boundary cells. In an inviscid flow, the "V dot dS" term in the integral form of the governing equations is always zero for the cell wall that forms the boundary. Rederive your equations with that term set to zero for that wall and apply them to the boundary cells, and those cells operate just as they should.


Rich

Set the velocity in the next-to-boundary cells to zero is not strictly right way? Is there a more accurate method? For my code, i give some special treatments for no slip B.C:
1.gradient computation in the cell next to wall boundary(Gauss Green Method,the face velocity on wall is set zero )
2.i think the flux on wall is the same as inviscid flux,so no more special treatment
3.viscous flux calculation contains face velocity and it is set zero exactly

Then the code ran, but i found the velocity on boundary face is not zero by Tecplot.....................

IS THERE SOME PROBLEMS OF MY TREATMENT?
THANK YOU FOR YOUR HELP

You are doing it correctly.

For cell-centered scheme, boundary conditions are imposed through appropriate definition of boundary fluxes.

Dont worry if tecplot shows velocity on boundary not satisfying the boundary condition. Tecplot does not know your boundary condition, so it is doing some interpolation to get the boundary values.

No, I think your treatment is correct. I was just pointing out what would be necessary IF you were working with an INviscid system. Sorry I confused you.


Rich

that probably is interpolation issue.

i output the cell-centered value for tecplot cell centered mode,tecplot auto interpolate them to vertexes, i changed it to cell centered display mode and found it is not closed to zero. so i think it is not interpolation's problem. can someone offer me some paper about
the implement of BC?