Capstone Final PresentationSpring 2003
Thin Film flow
Capstone Final PresentationSpring 2003
Thin Film flow
Capstone Final PresentationSpring 2003
Thin Film flow
Capstone Final PresentationSpring 2003
Thin Film flow
Capstone Final PresentationSpring 2003
Thin Film flow
Capstone Final PresentationSpring 2003
Thin Film flow
Capstone Final PresentationSpring 2003
Thin Film flow
Capstone Final PresentationSpring 2003
Thin Film flow
Capstone Final PresentationSpring 2003
Thin Film flow
Capstone Final PresentationSpring 2003
Thin Film flow
Capstone Final PresentationSpring 2003
Thin Film flow
Capstone Final PresentationSpring 2003
Thin Film flow
Capstone Final PresentationSpring 2003
Thin Film flow
Capstone Final PresentationSpring 2003
Thin Film flow
Capstone Final PresentationSpring 2003
Thin Film flow
Capstone Final PresentationSpring 2003
Thin Film flow
Capstone Final PresentationSpring 2003
Thin Film flow
Capstone Final PresentationSpring 2003
Thin Film flow
Capstone Final PresentationSpring 2003
Thin Film flow
Numerical Analysis
Miao LiTom Schreck
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
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
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
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
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
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
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
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
Capstone Final PresentationSpring 2003
Thin Film flow
Capstone Final PresentationSpring 2003
Thin Film flow
Capstone Final PresentationSpring 2003
Thin Film flow
Capstone Final PresentationSpring 2003
Thin Film flow
Capstone Final PresentationSpring 2003
Thin Film flow
Capstone Final PresentationSpring 2003
Thin Film flow
Capstone Final PresentationSpring 2003
Thin Film flow
Capstone Final PresentationSpring 2003
Thin Film flow
Capstone Final PresentationSpring 2003
Thin Film flow
Capstone Final PresentationSpring 2003
Thin Film flow
Capstone Final PresentationSpring 2003
Thin Film flow
Capstone Final PresentationSpring 2003
Thin Film flow
Capstone Final PresentationSpring 2003
Thin Film flow
Capstone Final PresentationSpring 2003
Thin Film flow
Capstone Final PresentationSpring 2003
Thin Film flow
Capstone Final PresentationSpring 2003
Thin Film flow
Capstone Final PresentationSpring 2003
Thin Film flow
Capstone Final PresentationSpring 2003
Thin Film flow
Capstone Final PresentationSpring 2003
Thin Film flow
Capstone Final PresentationSpring 2003
Thin Film flow
Capstone Final PresentationSpring 2003
Thin Film flow
Capstone Final PresentationSpring 2003
Thin Film flow
Capstone Final PresentationSpring 2003
Thin Film flow
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