Question about discretizing Laplace equation of potential flow

I’ve learned from fluid mechanic class that the laplace equation of stream function $Phi$ can be discretized by $Phi_{0}=frac{Phi_{A}+phi_{B}+Phi_{C}+Phi_{D}}{4}$, if the flow is irrotational and that leads to circulation $0$.

However can we do the same thing to fluid potential $phi$, by applying same approach to $phi$? I tried to follow what I learned from class however I didn’t get useful results.

Any help or hint is appreciated.