Boundary Condition
 

Hello. I have a question.

I'm reading the paper. This is "Application of a Fractional-step Method to Incompressible Navier-Stokes Equations" of Kim and Moin.

They introduced two Boundary Conditions of U^hat.

One is U^hat=U^n+1. The other is U^hat=U^n+1+dt*G(phi^n).

But, I don't understand the latter case.

Since G(phi^n)*dt=U^oldhat - U^n,

U^hat=U^n+1+dt*G(phi^n)=U^n+1+U^oldhat - U^n.

Thus, U^hat=U^oldhat. Because, U^n+1- U^n=0 on the boundary.

Then, what is U^oldhat?

I can't compute U^oldhat on the boundary.

Please, help me. What's wrong?


ps : 'G' means gradient. 'hat' is about velocity.