Module 5: Solution of Navier-Stokes Equations for Incompressible Flows Using SIMPLE and MAC Algorithms
  Lecture 29:
 

 

 

Now, substituing into (27.5) using (29.3) and (29.4) produces

(29.5)

where, Eq. (29.5) is basically a discrete form of Poisson equation that is equivalent to

(29.6)

It may be noted that the solution converges as Eq. (29.3) and (29.4) can be also represented as

(29.7)

The algorithm may be summarized as

  1. u* is obtained from equations (28.3) and (28.4).
  2. is obtained from equation (29.5)
  3. uc is obtained from equations (29.3) and (29.4).
  4. is obtained from where is a relaxation parameter.