Biomedical Engineering Reference
In-Depth Information
Tabl e 2. 5
Geometry, fluid and structure parameters used in Example 1
Parameters
Values
Parameters
Values
Radius R (cm)
0:5
Length L (cm)
6
In. press. p
in
(dyne/cm
2
)
Out. press. p
out
(dyne/cm
2
)
250
0
Fluid density
f
(g/cm
3
)
1
Dyn. viscosity (g/cm s)
0:35
Thin wall:
Density
m
(g/cm
3
)
1:1
Thickness h (cm)
0:02
Lamé coeff.
m
(dyne/cm
2
)
1:07
10
6
Lamé coeff.
m
(dyne/cm
2
)
4:29
10
6
Thick wall:
Density
s
(g/cm
3
)
1:1
Thickness H (cm)
0:1
Lamé coeff.
s
(dyne/cm
2
)
1:07
10
6
Lamé coeff.
s
(dyne/cm
2
)
4:29
10
6
Spring coeff. (dyne/cm
4
)
0
1
x
10
−3
15
200
10
0.5
100
5
0
0
0
−0.5
0
0.5
0
5
0
5
r axis (cm)
z axis (cm)
z axis (cm)
Fig. 2.14
Comparison between the computed solution (in
blue
) and the exact solution (in
red
). The
two are superimposed.
Left
: Axial velocity.
Middle
: Fluid pressure.
Right
: Radial displacement
relative error between the computed and exact solution was less than 0.08% (namely,
0.000778).
Figure
2.14
shows a comparison between the computed (blue) and the exact solu-
tion (red) for axial velocity (left), fluid pressure (middle), and radial displacement
(right), showing excellent agreement. The corresponding relative errors are given by
the following:
jj
u
e
D 7:78 10
4
;
jj
p
e
u
jj
L
2
.
f
/
jj
u
e
pjj
L
2
.
f
/
jjp
e
D 1:17 10
4
;
jj
L
2
.
f
/
jj
L
2
.
f
/
jj
r
r
jj
L
2
.0;L/
jj
r
jj
L
2
.0;L/
D 3:82 10
5
;
jj
d
r
d
r
jj
L
2
.
s
/
jjd
r
jj
L
2
.
s
/
D 3:82 10
5
:
We conclude that the scheme behaves well for this simplified FSI problem with
multiple structural layers.
Example 2
In this example we solve the full, nonlinear FSI problem (
2.177
)-(
2.191
) with the
structure consisting of two layers, using the data that correspond to a benchmark
problem in FSI with a single thick structure. Moreover, we solve a sequence of
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