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 T e n n 1 T T m s ∆x c p T s P P n n 1 T T Qadvection P P V c P P p t m S c T m S c T f f p f f f p f f w s f e n , , a S a S f f f f f w s f e n , ,

m f <0 m f >0 D ownstream D ownstream U pstream U pstream f f P E E P FOU (First Order Upwind) Convection Scheme:

m e >0 UU U D w e E EE WW W P m e <0 D U UU

Ø f ax b = (3Ø U -Ø UU )/2 x b At 0 , UU UU m e x x At , U e a x / U UU UU D U x U UU x UU x x 3 3 U UU U UU e UU x x 3 / 2 x 2 2

Ø f = (3Ø D +6Ø U 2 ax bx c -Ø UU )/8 x c At 0 , UU UU m e x x At , U e x x At 2 , UU D D U x 2 3 4 2 UU U D UU U D x x UU 2 x x 2 2 3 6 D U UU e x x 3 2 / 8

f P m e >0 e w E W P m e <0 f E a m m e e e e U m m max( ,0) max( ,0) e P e E a m m f f f f U

f P E m e >0 e w E W P m e <0 E P f P E a m m e e e e 2 U D a m m f f f f 2

W P f m e >0 e w E EE P WW W m e <0 EE f E 3 1 a m m e e e e U UU 2 2 3 1 3 1 m m m 0 0 ax( , ) max( , ) e P W e E EE 2 2 2 2

W P E f m e >0 e w E EE m e <0 WW W P EE E f P 3 3 1 a m m e e e e D U UU 8 4 8 3 3 1 3 3 1 m m m ax( , ) 0 max( , ) 0 e E P W e P E EE 8 4 8 8 4 8

Ø f = Ø U Ø f = (Ø U +Ø D )/2 m e m e e e UU D UU D U U Ø f = (3Ø D +6Ø U Ø f = (3Ø U -Ø UU )/2 -Ø UU )/8 m e m e e e UU D UU D U U

Fm e e UU D U N Fm e UU e e = D b P E U W S

m n ∆x c p T n m w ∆y c p T w m e ∆y c p T e m s ∆x c p T s Qadvection 0 P m S c T m S c T f f p f f f p f f w s f e n , , a S a S f f f f f w s f e n , ,

, , , e P w W n P s S / 2, / 2, e E P w P W / 2, / 2 n N P s P S 3 / 2, 3 / 2, e P W w W WW 3 / 2, 3 / 2 n N n P S s S SS e w 3 6 / 8, WW e E P W W E P s F mx >0 3 6 / 8, w P W WW S 3 6 / 8, n N P S F my >0 3 6 / 8 s P S SS SS

m S c T m S c T f f p f f f p f n N f w s f e n , , n n T T e w f f WW W E P f e n f w s , , s F mx >0 / 2 S P W S F my >0 / 2 / 2 E P P W SS = / 2 / 2 N P P S 4 / 6 P W S WW SS 3 7 / 6 P E N W S WW SS