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11.2 Finite Volume Method 211

coefficients are derived depending on the algorithms selected.
Common algorithms are the central differencing, upwinding, hybrid
differencing, power-law, and QUICK algorithms. Understanding
these algorithms and applying them appropriately can improve the
solution accuracy.
From the equations for determining the velocity com-
ponents u and v of any p cell above, the computational approach to
find the solutions should be an iteration process. The process starts
from an initial guess of the flow solution for the entire domain.
The iteration process is performed and terminated when a
converged solution is obtained. One of the efficient processes is
the SIMPLE (Semi-Implicit Method for Pressure-Linked Equation)
method. The method is briefly explained in the following section.

11.2.2 SIMPLE Method

The SIMPLE method consists of the three main steps as
follows.



Step1 Assume the velocity components u , v and the pressure

p for all cells in the flow domain. Then, determine the new
velocity components u and v from,


au  u P  P  au nb  p  x   A
u

u
nb
and av  v PP  av  p  y   A

v
v

nb nb

Step 2 Assign u , v and p as the corrections which are the
differences between the correct solutions and assumed solutions in
step 1, i.e.,




u  uu ; v  vv ; p  p  p

Then, determine the velocity components u and v from,
u
u  u  A  p

P
P
a P u x 