BC for Pressure Correction on Colocated Grid
 

For a FORTRAN code I am working with, I am using Pressure-Weighted Interpolation Method (PWIM) for solution of incompressible Navier-Stokes on colocated grid. I am using SIMPLEC for pressure correction. As is typical for many colocated grids, the boundaries of the control volumes extend to the domain boundary and no nodes are located exactly on the domain boundary (They are 1/2 grid spacing away). I would like to set a boundary condition on domain boundary of constant pressure. Since I am not solving an equation for pressure, but rather pressure correction, what is a reasonable way to implement this boundary condition when the known pressure does not coincide with an actual grid node. I realize if it did that the boundary condition is simply to set the pressure correction to zero; however, that is not the current situation.

Suggestions (especially from those of you who have written your own code and dealt with this situation) would be appreciated.

Thanks, Matt

Re: BC for Pressure Correction on Colocated Grid
 

Before writing a note I assume you used cell-centered colocated scheme. You should solve momentum equaion in each direction and pressure correction equation. Boundary cells which mean the cells adjacent to boundary require the solutions on the boundary faces to integrate all the fluxes. Pressure gradient term included in the momentum equations also requires boundary pressure. If you use mass conservation condition for exit-boundary, you don't need to apply pressure on the outlet. you can solve the incompressible problems without pressure information. On the wall pressure can be extrapolated from the interior of the domain with 1st or high order scheme. For pressure correction equation, p' on the boundary is just same as boundary cell except the pressure exit. It works well because p' should be zero if the solution is converged. On the bounday with pressure specified p' is zero and mass correction on that boundary should be implemented into the p' equation similar to interior cell faces.