Hi all;

We know in any iteration discretized form of any equation is: Ap*Phi_p=An*Phi_n+As*Phi_s+Aw*Phi_w+Ae*Phi_e+Sp (a)

On the other hand, Residual is defined as follows:

R=Ap*Phi_p-(An*Phi_n+As*Phi_s+Aw*Phi_w+Ae*Phi_e+Sp) (b)

therefor,with due attention to discretized form (a), Why is there residual in any iteration?

Thanks in advance for everybody help me in finding of an answer to this question.

You sove equation (a) for every node (i,j,k). For the first (i,j,k) the residual R=0. But in every equation each node depends on the neighborhood nodes and also the coefficients depend on the velocities etc. Also every equation (3 momentums, continuity, energy and so on) depend on the other variables. So at the end of the first iteration no equation will have converged. Too bad that the problem is coupled...otherwise one iteration (or two) would be enough