Biomedical Engineering Reference
In-Depth Information
momentum and continuity equations. In this section, to calculate
discretization equations on the computer speciic example of
numerical solution is described. As an example of discretization
of steady incompressible viscous low, Navier-Stokes equation is
discretized by using FVM.
¥
§
¦
µ
u
u
u
u
u
u
¥
§
¦
u
u
u
x
µ
·
¶
u
u
u
u
y
·
¶
u
p
x
S
S
N
N
(
uu
)
(
vu
)
(5.66)
x
y
x
u
y
u
y
j+1
N
nw
n
y
j
ne
w
e
W
E
se
y
j-1
sw
s
S
x
i-1
x
i
x
i+1
Figure 5.14
Diagram of discrete Navier-Stokes equation in
direction.
Volume integration in
x
direction of irst convection term
u
u
u
u
±
±
±
S
%
(
u u dxdy
)
y
(
puu dx
)
x
x
% s
±
{(
S
S
y
uu
)
- (
uu
)
}
e
w
% s s s s
S
S
s
y
{0.5
(
u
u
)
u
ij
.
i
1.
j
e
ss s s
-1.
S
S
-0.5
(
u
u
)
u
}
i
j
i j
.
w
s%s
S
0.5
y
{(
u
u
)(
u
u
)
i j
.
i
1.
j
i
1.
j
i
.
j
-(
u
u
)(
u
u
)}
(5.67)
i
-1.
j
ij
.
ij
.
i
- 1.
j
second convection term
u
u
u
u
±
±
±
S
%
S
(
v u dxdy
)
x
(
vu dy
)
y
y
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