Geoscience Reference
In-Depth Information
Figure 4.22
Typical 3-D control volume.
where
V
P
is the volume of the cell centered at point
P
, defined as
V
P
=
(
J
ξηζ)
P
.
If the exponential scheme is used, the coefficients in Eq. (4.142) are
F
w
exp
(
F
w
/
D
w
)
F
e
a
W
=
1
,
a
E
=
1
,
exp
(
F
w
/
D
w
)
−
exp
(
F
e
/
D
e
)
−
F
s
exp
(
F
s
/
D
s
)
F
n
a
S
=
1
,
a
N
=
1
,
(4.143)
exp
(
F
s
/
D
s
)
−
exp
(
F
n
/
D
n
)
−
F
b
exp
(
F
b
/
D
b
)
F
t
a
B
=
1
,
a
T
=
1
,
exp
(
F
b
/
D
b
)
−
exp
(
F
t
/
D
t
)
−
a
P
=
a
W
+
a
E
+
a
S
+
a
N
+
a
B
+
a
T
+
(
F
e
−
F
w
+
F
n
−
F
s
+
F
t
−
F
b
)
, and
b
=
S
V
P
where
n
+
1
u
n
+
1
ξ
n
+
1
u
n
+
1
ξ
F
w
=
ρ
(
J
ηζ)
ˆ
,
w
,
F
e
=
ρ
(
J
ηζ)
ˆ
,
w
e
w
e
,
e
n
+
1
u
n
+
1
n
+
1
u
n
+
1
F
s
=
ρ
(
ξζ)
s
ˆ
,
F
n
=
ρ
(
ξζ)
n
ˆ
J
J
,
n
,
s
η
,
s
n
η
