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