Biomedical Engineering Reference
In-Depth Information
Combined discrete equations of Navier-Stokes equations in
x
direction are shown as follows:
S
s% s
0.5
y
{(
u
u
)(
u
u
)-
u
u
)(
u
u
)}
ij
.
i
1.
j
i
1.
j
ij
.
i
-1.
j
ij
.
ij
.
i
-1.
j
s% s
S
0.5
x
{(
v
v
)(
v
v
)-(
v
v
)(
v
v
)}
ij
.
1
i
1.
j
1
ij
.
1
ij
.
ij
.
i
1.
j
ij
.
ij
. 1
yy
-
yy
-
j
j
-1
j
j
-1
N
(
v
-
v
) -
N
(
v
-
v
)
i
1.
j
ij
.
ij
.
i
-1.
j
x
-
x
x
-
x
i
1
i
-1
i
i
-2
xx
-
xx
-
i
i
-1
i
i
-1
N
(
v
-
v
)-
N
(
v
-
v
)
ij
.
1
ij
.
ij
.
ij
. 1
y
-
y
y
-
y
j
1
j
-1
j
j
-2
y
j
(5.72)
s
(
P
-
P
)
i
-1.
j
i j
.
y
j
-1
y
j+1
N
nw
n
n
e
e
y
j
W
w
E
sw
s
se
y
j-1
S
x
i-1
x
i
x
i+1
Figure 5.15
Diagram of discrete Navier-Stokes equation in
y
direction.
Discretization of Navier-Stokes equations in
y
direction is shown
as the same way in x direction. Thus, Navier-Stokes equations are
transformed into a machine-readable equation, we can solve the
equations by programmed calculation.
N
¥ µ
u
¥µ
u
u u
u
u
v
v
p
S
S
N
(
uv
)
(
vv
)
-
(5.73)
¦¶
¦ ¶
§·
u
x
u
y
u u u u
x
y
§ ·
y
y
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