SIMPLE algorithm and coefficient
 

According to the book `An introduction to computational fluid dynamic the finite volume method, H K Versteeg, first edition`

page 139, the momentum equations are defined as follows:

a(i,J)u(i,J) = SUM(a(nb)u(nb)) + (P(I-1,J) - P(I,J))A(i,J) + b(i,J)

As SIMPLE algorithm needs P(guess) to change the above equation to scaler equation and then for each velocity u and v we have an equation.

My question is about the coefficient of above equation which contains the F and D, both F and D equation contains u and v values.

in page 142, the description of SIMPLE algorithm :

1) P(guess)
2) scaler equation --> iteration --> result = v(star) and u(star)
3) find P' with the continuity equation
4) correct all P,u and v
5) check the convergence
6) yes or no and loop

my question is the coefficients ??!!!! :confused::confused::confused:
their elements should be multiplied by the u(star) and v(star) ??? i am totally :confused:

Someone helps me :)

Now, what exactly is your question? Do you want to know how the coefficients are calculated, since they need the unknown velocities?

yes exactly, yes, yes, ... the mentioned book says:

1) guess P
2) v (star) and u(star) will be calculated ?? HOW they are calculated when the coefficient are unknown ??

You always need to initialize all the variables. Also the velocities. Thus, you can use the initializations to calculate the coefficients. Later on you can use the "last known" velocities for that.

thank you man for all the responses ;)

but I am still thinking ;)