2.3 Implementation of Numerical Solution
33
p = p
∗
+ p
(2.35)
The corresponding velocity correction formula is:
u = u
∗
+ u
(2.36)
v = v
∗
+ v
(2.37)
w = w
∗
+ w
(2.38)
where, the velocity correction equations are respectively:
u
e =
A e
a e
p
P − p
E
= d e
p
P − p
E
(2.39)
v
n =
A n
a n
p
P − p
N
= d n
p
P − p
N
(2.40)
w
t =
A t
a t
p
P − p
T
= d n
p
P − p
T
(2.41)
Therefore, the improved velocities are:
u e = u
∗
e + d e
p
P − p
E
(2.42)
v n = v
∗
n + d n
p
P − p
N
(2.43)
w t = w
∗
t + d t
p
P − p
T
(2.44)
(4) Give a new pressure value to the formula (2.35), return to step 2, and repeat each
step until the velocity field satisfying the continuity equation is obtained. When both
the continuity equation and the momentum equation are satisfied, the obtained flow
field is the correct result.
2.3.3.2 Pressure Correction Equation
The pressure correction value is determined by the pressure correction equation.
The condition that the pressure correction value shall meet is that the velocity
field improved according to the pressure correction value can satisfy the continuity
equation. The improved velocity is substituted into the continuity equation, and the
following pressure correction algebraic equation is obtained