[selig5576]

Assumptions:
1. Uniform equally spaced grid
2. 2D

When using the Chorin Projection method to solve the incompressible NS on a collocated grid we end up having to solve the following elliptic PDE



where we have the face velocities



Our boundary conditions on all four sides are


When solving the pressure Poisson equation on the 4 boundaries is the procedure the same as if we were using the staggered grid? I've read some literature on it and I still don't quite understand if the pressure boundary conditions are treated differently. In my code I have

P(1,:) = P(2,:)
P(nx,:) = P(nx-1,:)
P(:,1) = P(:,2)
P(:,ny) = P(:,ny-1)
%Corners
P(1,1) = 1.0 % degree of freedom
P(nx,ny) = P(nx-1,ny-1) top right
P(nx,1) = P(nx-1,2) bottom right
P(1,ny) = P(2,ny-1) top left

Which gives me good results for the lid driven cavity, however according to http://www3.nd.edu/~gtryggva/CFD-Cou...re-15-2017.pdf
the pressure boundaries are treated differently. I was curious if my understanding of how to implement the pressure BCs on a collocated is correct. In my code I am using standard central differencing with extra treatment for the handling the ghost points.