28

CFD Team

of Isfahan University of Technology

29

CFD Team

of Isfahan University of Technology

0V = ( )Vtr

r

= -

( )P f r=

30

CFD Team

of Isfahan University of Technology

31

CFD Team

of Isfahan University of Technology

( ) iji j i ii j i j

u Pu u bx t x x x

tr r

+ = - + +

( )2

( )iji j i ii i j i i i j j

u Pu u bt x x x x x x x x

tr r

+ = - + +

0

32

CFD Team

of Isfahan University of Technology

( )

( )

2

ij ii j

j ii i

i

i j

P u ux x x x

bx x x

r

t r

= -

+ +

,cte cter m= =

2 2

0

jiij

i j i j j i

ji

j j i i i j

uux x x x x x

uux x x x x x

t m

m m

= +

= + =

33

CFD Team

of Isfahan University of Technology

( )2

j ii i i j

P u ux x x x

r

= -

34

CFD Team

of Isfahan University of Technology

( ) ( )i j iji u uu prd dtr d = - + -

( )ii

j

u pHt xr d

= -

( ) ( )1n

n nii i

j

pHtu u xd

r r+ -- = D

( ) 1niur+

( ) 1 0n

i

j

ux

d rd

+

35

CFD Team

of Isfahan University of Technology

( ) ( )1n

n nii i

jj

pHtu u xxdd

r rd

+ - - = D

( ) ( )1n n ni ii

jj j j

u u pHtxx x x

d dr r ddd d d

+ -- = D

0

n ni

jj j

p Hxx xd dd

d d

=

0Since we assume that the velocity at time step n satisfy continuity

Start with

Compute and its divergence

Solve Poisson equation for

Compute new velocity field

36

CFD Team

of Isfahan University of Technology

niH

,n niu p

np

37

CFD Team

of Isfahan University of Technology

( ) ( ) ( )1 111

n nnn n i j iji i

j i j

u u Ptu ux x x

rd dtdr rd d d

+ +++ - = D - - -

38

CFD Team

of Isfahan University of Technology

( ) ( ) ( )1 1 11n n n nni ji i iji i i j i j

u uu u Ptx x x x x x

rd dr r d dtd dd d d d d d

+ + ++ - = D - - -

( ) 11 nn i jii i j

u uPxx x x

rddd ddd d d

++ = -

39

CFD Team

of Isfahan University of Technology

( ) 11 nn i jii i j

u uPxx x x

rddd ddd d d

++ = -

40

CFD Team

of Isfahan University of Technology

1n ni i iu u u+ = +D

1 1n n n n ni j i j i j

nj i i j

u u u u u u

u u u u

+ + = + D

+ D +D D

tD

~ iiuu tt

D D

41

CFD Team

of Isfahan University of Technology

( ) ( ) ( )n nn n n

i j i ji ji

j jj

nnij ij

i i j j

u u u uu uu t

x xx

P Px x x x

d dr rrdr

d dd

dt d td dd d d d

D DD = D - --

DD- - + +

42

CFD Team

of Isfahan University of Technology

Compute by using old pressure gradient

Solve Poisson equation for pressure correction

Update velocities

43

CFD Team

of Isfahan University of Technology

( )*1 iii i

P uxx t x

dd rddd d

D = D

*iu

1 *ni i

i

t Pu ux

dr d

+ D D= -