Geoscience Reference
In-Depth Information
Figure 4.25
Staggered grid in SIMPLE algorithm: (a) sketch of global grid, (b) control volume for
u
x
,
(c) control volume for
u
y
, and (d) control volume for
p
.
a
n
u
y
,
n
=
a
l
u
y
,
l
+
p
P
−
p
∗
N
)
S
v
+
A
n
(
(4.174)
l
The approximate velocities
u
x
and
u
y
do not satisfy the continuity equation. Hence,
the pressure correction
p
and velocity corrections
u
x
and
u
y
are defined as
p
=
p
n
+
1
p
∗
−
(4.175)
u
x
=
u
n
+
1
x
u
x
,
u
y
=
u
n
+
1
y
u
y
−
−
(4.176)
Subtracting Eq. (4.173) from Eq. (4.171) and neglecting the term
l
a
l
u
x
,
l
yields
the
u
x
-equation:
u
x
,
e
=
p
P
−
p
E
)
d
e
(
(4.177)
a
e
.
where
d
e
=
A
e
/
