Pressure correction equation,Ferziger and Peric
 

Hi,
I am trying to follow Ferziger and Peric method on implicit pressure and velcoity coupling from page 175 of the book. I know how the method works for finite differences but I need to use finite volumes and collocated grid arrangement and I have a problem with the pressure correction equation (7.39).

My A_P matrix which is the diagonal of the A matrix obtained from discretization of the momentum equation using (1st order UPwind scheme) is equal to A_P= A_E+ A_W+ap and so it contains terms containing velocites at the nodes. So when it comes to the pressure correction equation where you need the derivative of the inverse of A_P ; I'm not sure on how to go on about differenciating that...along with the pressure gradinet term as well...
my guess is to go back to the continuity equation and substitute the u' term that has not been discretized yet and then discretize the whole equation using finite volume methods..??

Please find the attached file for my coefficient of the A matrix for the momentum equation and what I did next to derive the pressure correction equation.

Please help and thank you very much in advance.

Use OPENFVM instead , very easy to understand and modify
Detailed documentation provided