B.C. for pressure-correction equation
I have difficulty in specifying boundary conditions for a Poisson-type of pressure-correction equation. For example, what is the proper B.C. for p' at wall? should we set it to 0? also what to do within a boundary layer? Is it ok to say d p'/dy =0? Your advice will be highly appreciated.
Re: B.C. for pressure-correction equation
The boundary conditions for the pressure correction equation can be determined based on the projection technique you use.
If you are using the SIMPLE algorithm then the boundary condition for a wall is simply dp'/dx_i=0 for cartesian grids and dp'/dx_i + (non-orthogonal terms) = 0 for grids where the cell neighbor to the wall is not perpendicular to the wall face centroid. These relationships for the pressure correction come from the fact that at the wall you have zero flow.
For fixed pressure boundary conditions the p' is set to zero since the pressure is specified and therefore will not be corrected.
In general, all boundary conditions for the pressure correction equation can be found by simply looking at how the projection algorithm is formulated and the standard boundary conditions for flow ie. specified velocity, specified pressure, symetry, periodic......
Hope this helps,
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