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L L ICE (0 0 C) FIRE (100 0 C) L L ICE (0 0 C) FIRE (100 0 C) (i) - - PowerPoint PPT Presentation
L L ICE (0 0 C) FIRE (100 0 C) L L ICE (0 0 C) FIRE (100 0 C) (i) - - PowerPoint PPT Presentation
L L ICE (0 0 C) FIRE (100 0 C) L L ICE (0 0 C) FIRE (100 0 C) (i) u=1 m/s, T=40 0 C (iii) u=-1m/s, T=60 0 C L L (iv) u=-100m/s, T=90 0 C (ii) u=100 m/s, T=10 0 C ICE (0 0 C) Fire (100 0 C) L 1 L 2 m n x c p T n m w y c p T w m e y c p
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ICE (00C) FIRE(1000C) L L
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ICE (00C) FIRE(1000C) L L
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(i) u=1 m/s, T=400C (ii) u=100 m/s, T=100C (iii) u=-1m/s, T=600C (iv) u=-100m/s, T=900C
ICE (00C) Fire(1000C) L L
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L2 L1
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1 n n P P
T T
1 n n P P P p
T T V c t
me ∆y cp Te mw ∆y cp Tw mn ∆x cp Tn ms ∆x cp Ts
, , , , P f f p f f f p f f w s f e n f f f f f w s f e n
Qadvection m S c T m S c T a S a S
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FOU (First Order Upwind) Convection Scheme: mf>0 P f E mf<0 Upstream Upstream Downstream Downstream P f E
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P E W me>0 e w WW me<0 EE
D U UU
UU U D
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, , / At At
UU UU U U UU U UU UU
ax b x b x x a x x x
U
me
UU D
= (3ØU -ØUU)/2 Øf
x
/ 3 2
3 3 2 2
U UU U UU e UU x x
x x e
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, , ,
2 2 2
At At At 2 2 3 4 2 2
UU UU U D UU U D UU U D UU
ax bx c x c x x x x x x x x
Øf = (3ØD +6ØU
- ØUU)/8
U
me
UU D
x
e
/ 3 2
3 6 8
D U UU e x x
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me<0
P f f E
P E W me>0
max( ,0) max( ,0)
e e e e U e P e E f f f f U
a m m m m a m m
e w
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E
P
me<0
P f E
P E W me>0 e w
f
2 2
P E e e e e U D f f f f
a m m a m m
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ax( , ) max( , ) 3 1 2 2 3 1 3 1 m 2 2 2 2
e e e e U UU e P W e E EE
a m m m m
W
EE
me<0
P f E
P E W me>0 e w
f
EE WW
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E
P
ax( , ) max( , ) 3 3 1 8 4 8 3 3 1 3 3 1 m 8 4 8 8 4 8
e e e e D U UU e E P W e P E EE
a m m m m
W
EE
P f E
P E W me>0 e w
f
EE WW me<0
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U UU D
Øf = (3ØD +6ØU
- ØUU)/8
U UU D
Øf = ØU
U UU D
Øf = (3ØU -ØUU)/2
U UU D
Øf = (ØU +ØD)/2
e e e e
me me me me
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P N S E W
U UU D U D UU
=
b
e e e
Fme Fme
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me ∆y cp Te mw ∆y cp Tw mn ∆x cp Tn ms ∆x cp Ts
, , , , P f f p f f f p f f w s f e n f f f f f w s f e n
Qadvection m S c T m S c T a S a S
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, , ,
e P w W n P s S
P W E N S SS WW
e w n s
Fmx>0 Fmy>0 3 6 / 8, 3 6 / 8, 3 6 / 8, 3 6 / 8
e E P W w P W WW n N P S s P S SS
3 / 2, 3 / 2, 3 / 2, 3 / 2
e P W w W WW n P S s S SS
/ 2, / 2, / 2, / 2
e E P w P W n N P s P S
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, , , , f f p f f f p f f w s f e n n n f f f e n f w s
m S c T m S c T T T
P W E N S SS WW
e w n s
Fmx>0 Fmy>0
/ 2
P W S
4 / 6
P W S WW SS
/ 2 / 2 / 2 / 2 =
E P P W N P P S
3 7 / 6
P E N W S WW SS