capstone final presentation spring 2003
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Capstone Final Presentation Spring 2003. Thin Film flow. Capstone Final Presentation Spring 2003. Thin Film flow. Capstone Final Presentation Spring 2003. Thin Film flow. Capstone Final Presentation Spring 2003. Thin Film flow. Capstone Final Presentation Spring 2003. Thin Film flow. - PowerPoint PPT PresentationTRANSCRIPT
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Capstone Final PresentationSpring 2003
Thin Film flow
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Capstone Final PresentationSpring 2003
Thin Film flow
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Capstone Final PresentationSpring 2003
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Capstone Final PresentationSpring 2003
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Capstone Final PresentationSpring 2003
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Capstone Final PresentationSpring 2003
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Capstone Final PresentationSpring 2003
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Capstone Final PresentationSpring 2003
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Numerical Analysis
Miao LiTom Schreck
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21( ) sin cos
ug g
t
u u u i k
3 2 3 31[ cos sin ]
3
hh h gh h gh
t
i
33 2 3[ ] ( ) [ ]
h hh h D h h
t x
Simplification of N.S. Equation
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Simplification of N.S. Equation cont.
From:
We get the 1D equation:
33 2 3[ ] ( ) [ ]
h hh h D h h
t x
3 3 3[ ] ( )[ ] ( )xxx x x x xh
h h D h h ht
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Two Methods Used
An explicit scheme using forward Euler.
An implicit scheme using Newton’s Method
( ) ( )( ) (1 ) ( )
i ii i
y t t y tf t f t t
t
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Program RunsH(X) vs. X
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 5 10 15 20 25
X
T=0
T=1
T=2
T=3
T=4
T=5
T=6
T=7
T=8
T=9
T=10
T=11
T=12
T=13
T=14
T=15
T=16
T=17
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Program Runs Cont.Compare H(x) for D=0,1,2
x
0 5 10 15 20 25
H(x
)
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
D=0 D=1 D=2
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Program Runs Cont.
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 5 10 15 20 25
Series1
Series2
Series3
Series4
Series5
Series6
Series7
Series8
Series9
Series10
Series11
Series12
Series13
Series14
Series15
Series16
Series17
Series18
Series19
Series20
Series21
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Convergence TestsMaxH vs. Time
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
0 5 10 15 20 25
Time (s)
dx = .05
dx = .1
dx = .2
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Implicit Method1 *n
i i iy y q 1n
if
=*if +
*|i jj
fq
q
*
, (1 )i
ii j j
j
ft q Rq
1,..., 1xi N
* *(1 )i
n ni i i iR y y tf tf 1,..., 1xi N
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Capstone Final PresentationSpring 2003
Thin Film flow
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Capstone Final PresentationSpring 2003
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Capstone Final PresentationSpring 2003
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Capstone Final PresentationSpring 2003
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Capstone Final PresentationSpring 2003
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Capstone Final PresentationSpring 2003
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Capstone Final PresentationSpring 2003
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Capstone Final PresentationSpring 2003
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