حل معادلات ناویر استوکس با cfd

21
. » « !" #$ SIMPLE -/ 12 &!. , 34 &!(5 6" !"# $ % & !’( )*+ ,-. !/ http://CFD.iut.ac.ir " 1 7-89 ,4"

Upload: szxd

Post on 17-Dec-2015

91 views

Category:

Documents


19 download

DESCRIPTION

SIMPLE Method

TRANSCRIPT

  • .

    !" #$

    SIMPLE

    -/ 12

    &!. , 34 &!(5 6"

    !"# $ % & !'( )*+ ,-. !/

    http://CFD.iut.ac.ir

    " 1 7-89 ,4"

  • SIMPLE

    1 4" :( ," ;--

    ( )

    0 (1)ii

    ij i ij i

    i i i

    uxu u u bx x x

    =

    + = +

    ; .1=>/t

    % 3

    ib? @ >A9 B&!ix&ij

    @C(1>/ &)FC! B/ (,

    (3)ij ij ijP = +

    F !% @- , C! B/

    (4)jiijj i

    uux x

    = +

    B! H@ :9 6-2 !? -)- IC $ J!

    @ -?& @C :( B! B.K&@-ProjectioK&@ LM? )& !@"!< @2 B/

    ! @J >/ !OA % ," ,->/ & -" % !. ,"

    V@-- /-W X.1!B/ Y B! 4R1! ,4

    G& @$ .

  • )2(;-- :(,5N"! !? @ -< B!O .( :( 1! ,4Y B!

    ! !! XV@-(1&@ % ( 1! ;-- ,5 .;I 15& 1!)

    ( )

    ( )

    ij i i

    i j i j

    ij i i

    i i j i i i j j

    u Pu u bx t x x x

    u u u bt x x x x x x x x

    + = +

    + =

    @ !% :( , @C $.

    ( )2

    j i ij ii i i j i j i

    P u u bx x x x x x x

    = +

    (F Z! , ,?- C! B/

    ji

    i j j i j j i i i j

    uux x x x x x x x x x

    + = +

    & - /-W !,5 B)5(:( ,

    ,J->A B)1(&)2(8 ) ,J->A F , % @" 1 N@ @C .G9 1

    6: \! @- , &- > @C @J< & ;-- - .-< ,5 :()-

    < @ % 1C!. XV@- $ & " ;-- ;A !% @- , ,"-:

    2

    (5)

    ( ) (6)

    iji

    j

    iji

    i i i j j

    bx

    P bx x x x x

    +

    + +

    N@ -< 0ii

    ux

    =

    &1! --< ,5

    ( ) (7)ij ii j i

    bx x x

    +

    -QW B! & >A9 _( ),cte cte = =.

    2 2ji

    j j i i i j

    uux x x x x x

    +

    ,5 , ,?- -< B0ii

    ux

    =! !!

    !" #

    G !? :9 @,4-BJ! % @ .B!

    6-2 H@ I6R%- ]"! /

    @ B! / 1 ]"!5 % 1C!. XV@-- ,

    G9 ,5 % ,( , ,?-

    9 B/&! @-^9 ;J 59 @! !W$ @J & /-W

    @ > @ @J & !/ ,"

    @ !% $.

  • ( )2

    j ii i i j

    P u ux x x x

    =

    ] BJ K&@ !".

    @-!< ," XV@- & !.@-!< < BJ 1>R @ 1 !% :

    1 1 1, ,

    i ii

    u un n nui pP L i LA u A u S+ + ++ =

    B2i=? J! y,c8 @! & >A9 B&! >? &

    L/ ,2>/ d8 BP-

    1 Semi implicit method for pressure linke equation

    (8)

    e&! @C --< $ :9 B! & % -

    M5 1 @- @ ( :

    :>J @C ! ," 1 ?

    ," b->A @ @ ,>+ ,4>? @ & %

    e equation

    )7(&)8( ,-<

    ( , ,?- FR 1 B @

    A @

    @&$ @.

    @ :9 B!? ,5 !. G9

    ," X $ @i/ S,P / ? b->A B

    !j" % ;. >/ @ /.

  • do

    End do

    :9 - :82 ! " B! ,"

    ]!H ," 1 :5 ," !" A ,M. :9 :9 B " ," !. ;A @8$ %

    @< 59 6;. !/ @ -% @ ," ! Ft !"

    & N@ % ,849 , @O. @< 59 6-? ," @O. ,52

    @< (:I 6-?

    , ,>+ ,4>? & ]!H

    :9 B)N82 K&@ (1

    N- :8 ;. , .," @ B@!(

    $ :9 B! ," @

    m @ 4W B/@!( &minner

    n+1

    n

    @& 1> :( , @C !. ,22. :( .

    ,5 N"9 )9(> @:9 >82 -!j 1niu + .K&@ 1!! @!( B/

    52 )@! ,@ /@!( ) @O. B % ;. !/6-? @&$ e/ !. N- :8

    :9 B! @!( !" " ,5 F< A$ @ :9 &" 7 " .O. 59 N/ !.

    !>/ - .:I 59 & 1 @ ," - ,?-)> !>/ " @ % ;. !/ @ :9 & N"

    2/ K%@ IC .

    ;A /@!( $ % ;" !/ @ ," -H / _ ]k & $B@!( K&@ X :8 @!>/ % X< @ N-

    , ,>+ @W @!( )-/@!( & )? @ % ;. !. n @ ?@W B/@!( )m

    - /-W !.

    S

    Do m

    end do

    ,5 @ ," - ,?-B)9(,22. - % ( B%

    GQ - cW !Y :5 ,&: ),>+ ,4>? >9

    .@! G9 @ ,52 !. ;. , Xk & - H@ B& , % @ /!j& !>/ ">/ )B@!( :9

    ! & @ >/ 16-? & >J B/

    @!( )% ;. !/ @ 1!& - ]!H

    @!( , & -> :9 @ ,4>? & ]!H $ @

    4W @!( /!% @- , :9 $!C N/

    A !")$(

    minner=1,

    &' '

    do

  • m ?@W @!( / ," ?@W @!( ,849 .

    * * 1, ,

    i ii

    u um m mui pP L i LA u A u S

    + =

    :m-1 ,-.

    ? ;-- ,5 x,22.u1J! ! & @ ," /

    :9 & - ? mz.

    )*$ %

    +,-.

    +,-./

    +,-.0

    +

    !

    , B! miu@ @C %!" /-R 7 ., :5 1>/ ,

    ,5 % )9( @"C! & N@O. X-," - ,?-miuB! >R1niu +!/ B @

    1(10)

    m

    i p

    px

    1(!j !8 %:I ?@W @!( @ B/

    < @- , ->J ; :9 N/ ! -,5 , )10( @4 !j $ @ ," /

    :9 :I ?@W ,5 Xk)- ?9

    ,/ 0

    , 0 /

    , / 0

    )10(@ @!( !/ @ ," A$ % ," N;)- J! -< ,5 @ $

    1! X- G9# @ 2- % @ ,5N" .-

    ,5 @ > @J)10

    ," - ,?- ;-- & -

    !/o ,5W @!( % -

    &.

    &.

    &.

    ,5 , ! 3I / :I @!(,&.

    :>J !% @-N":

  • 1 *,*

    ,1ii

    i i

    um mu L i Lm

    i p u upP

    S A uu

    A A

    =

    > H@ @ -< ," 1! &

    ,5 )11( F> !% :( , @-

    1* *

    , ,1i

    mm m

    ui p i pip p

    pu u xA

    =

    $.

    *, ,

    1i

    mm mi p i p u

    ip p

    pu uxA

    =

    N , ( ) 0mi

    i

    ux

    =

    ( )*, im

    mii p u

    i i i P i

    u ux x x A x

    =

    p,5)14( ! , & -

    ( )*,im m

    i pxi p i iP

    p ux A x x

    =

    !% $:

    1(11)

    m

    i p

    px

    B!*miu , / ," :5 11J!,5 /m; F< & 2 6-2 -.F) *miu!" \Q @ ). @" 9@ B!

    (12)

    ,5 - @W @ )13( @ !% @- , >J

    (13)

    < ,5 @ !. 2/ " 7 -

    XN!.:

    1

    (14)m

    i p

    px

    B/ *,mi pup+ e!S " 7 -< ,5 @N@.

    (15)

    *miu,5 % /)10(:( ,

    -?& :5 ," - ,?- *!J! @ B/ @!(m

    F< B/ J! 1 G9N/.

    @!( @ @C !.m ;

    G9 ,mi puJ!B/

    ,5 % 1!)13(XV@-

    ," A$ % &J! N/-W/< ,5 !% @C --@

  • 1 *

    * ,, (16)

    i

    i

    i

    um mm u L i li p u

    p

    S A uu

    A

    =

    !( - I @C B&@ ," -< ,5 % XV@-

    :( @ J! /),5 ,5projecti e&!.

    N. @!..J! @- @ ! 1>/ /

    ;. @ @C >" & N- m-1 - ,CH .

    * (17)m mi iu u u#= + 1 (18)m mP P P #= +

    @!I ;-- ,5 &@ S N/

    ( ) (* * 1 *,i iu um m m m

    i i i i i iP LpA u u A u u S P P+ + + = #

    ( ) (* * 1, ,,i i i iu u u um m mi p i pP L i L P L LA u A u A u A u S+ + + = #

    Z! -.

    )

    !4>J B/@-!< B% ,22. @ @ :I & ;-- ,5 @ !. ,22. @-!< !

    .

    K&@ ," ! @ ," 1 % / $ \Q , XkK&@ , %!/ 889 @Q --< ,5 , !% $!C

    (19)

    (20)

  • N/-W 1! :

    ', ,

    ' 1 (22)

    i

    i

    up i p L i L

    i

    i i uiP

    PA u A ux

    Pu uxA

    #+ =#

    #= #

    ( )

    *

    *

    0

    (

    m mi i i

    i i

    mi i

    i i

    u u ux x

    u ux x

    # = + =

    # =

    ( ) ( ),i

    i i piu

    i i i iP

    uux x x xA

    ##

    =

    *i

    miu

    i i i iP

    P ux x x xA

    # =

    ,?- : ,5 1 ," N-

    ( )'i ui i P

    Au

    x x A

    =

    ,5 `- " )10(H@! -

    (21)

    .

    N@

    (23)

    (24)

    N@ N! XV@- & N" 6!H:

    (25)i

    Px

    #

    @ !% :($:

    ( )' (26)iiu

    x

    +

    - ,5 :( @ I >" @C \Q

    (27)i

    i

    uL LuP

    A u

    #

    J ,"$ !% ," @" `W /

    $ @ ," 'i

    L Li u

    P

    A uu

    A#

    =

    -< ,5 % 1=>/

    ,5 !. G9)22(@ @

    " , ," ,5 >)24(,(

    ,5)26(Q --< ,5

    @J

  • @J % !gC! :( 1 ! ,4Y @ !% $.

    *i

    miu

    i i ip

    P ux x xA

    # =

    @C \, N@-5SIMPLE e&!SIMPLE> !>/ J! , B@ & -

    N@-5 ;- 1 , -

    *

    1

    0

    0

    m mi i u i u

    m mi p u

    u u u

    P P P

    $

    $

    #= + %

    #= + %

    @!I! @C . @ &!8

    ,1ii p u

    ip p

    PuxA

    #=#

    %Y$ -.miu-.

    :N".

    ,49! ,i Lu#@ 15& )2 ;-4 %-/ /4Y B! :9 1! ,5Q B! --< B:( , @C

    (28)

    ,5 % B)28(, B!\Q B;/),527(,5 % B)26(N@-5MPLE

    !% ]!H % :( 1 ! ,4Y ZR 5 1 @ ,CH !j , , -.

    1 (29)

    1 (30)u

    u

    $

    $

    % %

    %

    R !% ]!H 1 & , !8 ZC & J! , -.

    (31)

    ! .

    !B! f9 15& -J , &1niu +&1nP +:9, , !A ," cW ;-- :*m

    u@C \Q --< ,5 / :9 & :( @J! \- , /.

    - , ? .;. 2% - M+ Q M ,".

    ,49! , .% % 1.

    9! 1 @ ," A$% & ,5 @ 7-C)26(!

    N@-5 1 ,".,! % ( eO9 :5

    !>/ ( .B! \Q % >2I ,"

    ,c@ ,"1u p$ $= 59 @,c@ % J! \Q !% B

    ! "# $%

    1.8 >" 2.:9 & :(3.>" ,*miu4.\Q !85.@C? B/6.. , .%7.% ;. B

  • & N%!< .,?- @ ( N/ B/!j .+ @

    , !. -)+ e W!-(. F@$ % 1k>/center cell !j ,4C @ / @ 5- ,c8 & B

    ,( B! 5- B.

    5- @ ")5W - !. (&-W,W G!" NA9 -W & G!" B!W \Q K&@ % A? @J

    G& ,! @ >2I )UDS (,C!. !g @ >H @- , & %

    !/ ," X G& ,! @ !

    (0 G% % .59 @G=0 @@ !8 ," A$ % ?@W @!( @- /-W ;& ,! I % @.J , ! ,22. ,

    H/2

    H

    L

    L/2

    SIMPLE NA9 K&@ X"- ,& :9 B!,( !j + K-.@+ B

    B, ,x & '& & @C &... B&@ ! >/!.

    !. !j % & B/ , !5( B/

    , : ," ]! 1 , -j B !% :( @ . !/ M@J B%@ ," @- 1 , 2I & % % ;. !/ @

    - . G& ,! @)UDS (% ;. !/ @

    @- ( )oldCDS UDSF F ," CDSF!-. !% @- , @ $.

    (m UDS CDS UDSF F G F F=,"G ZR !% ]!H )1%59 @ & - /-W G=1 !>/ % XJ ,MPLE ,( ," - B

    J! ( N/ B/!jB/?,J! ," ?B&@ /

    G!" NA9 1W B!? !/ .>/ ," ,-.

    !. & ,4C `& G9 B

    !. :( @ S8 >J /- .M9 ," B! ,(

    /-W . K&@ 1 :( \Q @8 &

    , \Q >2I - , :I @!( % &-

    ) ( ) 1m mUDS CDS UDSG F F +

    G& ,! " ,

    B/@!(m-1,m !! N/

    B!W \Q K&@

  • . N

    n

    e

    . S

    W . w

    s

    K&@ G>J G9 - /-W ;& B

    !j + B& B/ B/

    .i i ij jS S

    u d u ndS e ndS Pdt

    ( )+ =

    + + + +

    ( )1n np pud u ut t + ,)) -

    ,+

    ( )1n np pudt t ( (+ ,)) -

    ,+

    . c c c ce w n sS

    uv ndS F F F F = + + ++

    ( ) 0 1UDS CDS UDS olduF F G F F G= +

    . P . E

    ,! % @ M :9 I 1=>/ & - B ,22. @ N".

    K-.@+ ,( B&@! X"-!? B!

    .ndS Pd)

    * )+

    B & (

    B!W \Q K&@ % N":

    0 1uG% %

    ,4(< G-4/-R f29 /;-- & NA9

    ,22.,& B%-( N/

    Z5 (1M@" ) !?

    1.% ;!

    ?X:

    ?Y:

    2.A? ;!

    ?X:

    ,22. B!A? ;! B%

  • e . E

    0

    0P eUDS

    eE e

    U mF

    U m

    >====

  • ( )UDS CDS UDS oldvF F G F F= +

    0

    0P eUDS

    eE e

    V mF

    V m

    >====

  • ( )11 1 12 2 . d de we e ndS F F F F + = + + ++

    ( )11 1 12 2 1 11.dee

    F e e e ds ds S = + = =,+ +

    ( )11 1 12 2 1 11.( )dww

    F e e e ds ds S = + =+ +

    ( )11 1 12 2 2 12.dnn

    F e e e ds ds S = + = =,+ +

    ( )11 1 12 2 2 12.( )dsn

    F e e e ds ds S = + =+ +

    ( )21 1 22 2 . c c c ce w n se e ndS F F F F + = + + ++

    ( )21 1 22 2 1 11.dee

    F e e e ds ds S = + = =,+ +

    ( )21 1 22 2 1 21.( )dww

    F e e e ds ds S = + =+ +

    ( )21 1 22 2 2 22.dnn

    F e e e ds ds S = + = =,+ +

    ( )21 1 22 2 2 22.( )dsn

    F e e e ds ds S = + =+ +

    d dn sF F+ +

    1m m

    E P E Pe e

    E P E P

    U U U Us SX X X X

    = , +

    11

    m

    P W P Ww w

    P W P W

    U U U Uds SX X X X

    = , +

    +

    1m m

    P ne nwn n

    P ne nw

    U U v vs Sy y x x

    = , +

    12

    m m

    P S se sws s

    P S se swn

    U U v vds Sy y x x

    = , + +

    c cn sF F+

    1m m

    ne se E Pe e

    ne se E P

    u u V Vs Sy y X X

    = , +

    1

    21

    m

    nw sw P Ww w

    nw sw P Ww

    u u V Vds Sy y X X

    = , + +

    1m m

    P Pn n

    P P

    V V V Vds Sy y y x

    = , +

    1

    22

    mm

    P S P Ss s

    P S p sn

    V V V Vds Sy y y y

    = , +

    +

    ?X:

    1m

    W

    1

    1m

    W

    W

    VX

  • Pd * )+

    1 ,( ;& & N" : \c

    .i

    Pd Pe nds * )=+ +

    (1. e e w wPe nds P S P S = , ,+

    (2. n n s sPe nds P S P S = , ,+

    1m

    e w

    e w

    P PPdx x x

    )= +

    e e E p PP P P0 0= + wP =

    1m

    n s

    n s

    P PPdy y y

    )= +

    n e p PP P P0 0= + sP =

    @ -?& .B&@ G! , @ 7-C G! ,( G&N" .

    \

    ) 1mwS

    ,

    ) 1ms sS

    ,

    NA9 B&@ 1

    ,)

    p P w WP P0 0= +

    1

    ,)

    p P s SP P0 0= +

    4.,@C ;! B

    & @ & @C ;! , B!z>82 @ G! " ,

    Z5(\c B&@ G! , :

    ?X:

    ?Y:

    6(,G! N82 B

    ?X:

    ?Y:

  • ( ) ( )

    ( ) ( )

    ( ) ( )

    1 max ,0 min ,0 ( ) max ,0 min ,0

    max ,0 min ,0 ( ) max ,0 min ,0

    max ,0 min ,0 ( ) max ,0 min ,0

    n n m mp p e P e E e e E p P e P e E

    mn P n

    m mw P w W w p P w W w P w

    u u m U m U m U U m U m Ut

    m U m U m U U m U m U

    m U m U m U U m U m

    +,) +,

    + + + +

    +

    ( ) ( )max ,0 min ,0 ( ) max ,0 min ,0ms P s S s p P s S s P s S

    m me e e eE P e e

    E P E P E P

    m mw w w w P WW P w w

    P W P W p w

    mn n n n

    P

    m U m U m U U m U m U

    S SU U SX X X X X X

    S S U UU U SX X X X x x

    S SUy y y

    + + + +

    , ,= +

    , ,

    + +

    , ,+ +

    m

    P

    m ms s s s se sw e wS P s s

    P S P s se sw e w

    Uy

    S S v v p pU U Sy y y y x x x x

    , ,

    + , ,)

    1

    , , ,

    u m u m t m pP P l l

    l E S WA u A u Q Q Q Q

    =

    + = + + =

    ( )min ,0 e eE eE P

    SA mX X

    ,=

    ( )min ,0 w wW wP W

    SA mX X ,

    =

    ( )min ,0 n n n P

    SA my y ,

    =

    ( )min ,0 s sS sP S

    SA my y ,

    =

    X @ !% :( ,$.

    ( ) {

    ( ){( )

    min ,0 ( ) max ,0 min ,0

    ( ) max ,0 min ,0

    ( ) max ,0 min ,0

    m mP e E e e E p P e P e E

    m n n p P n P n

    mW w p P w W w P w

    m U m U U m U m U

    U m U U m U m U

    m U U m U m

    0 0

    0 0

    0 0

    + + +

    + +

    + +

    {( ){

    1

    1

    ( ) max ,0 min ,0mS s p P s S s P s Sm

    E Pe e

    E P

    m

    P Ww w

    p w

    m U U m U m U

    U USX X

    U USx x

    0 0

    + +

    + ,

    ,

    1

    1 1

    m

    ne nwn n

    ne nw

    m m

    se sw e ws

    se sw e w

    v vSx x

    v v p pSx x x x

    ,

    , ,)

    - :

    pQ Q+ =

    ? @ ;-- ,5 1!

    ( ) ( ) }

    ( ) }( )

    1

    1

    ax ,0 min ,0

    min ,0

    min ,0

    m

    e P e E

    m

    n

    w

    m U m U

    m U

    m

    }( ) }

    1

    1in ,0

    m

    W

    m

    s S

    U

    m U

    ,"!% :( , @ $ -

  • ({({({

    ({1

    ( ) max ,0 min ,0

    ( ) max ,0 min ,0

    ( ) max ,0 min ,0

    ( ) max ,0 min ,0

    e e E p P e P e E

    n n p P n P n

    w p P w W w P w W

    s p P s S s P s S

    m

    E Pe e w w

    E P P

    Q m U U m U m U

    m U U m U m U

    m U U m U m U

    m U U m U m U

    U US SX X X

    0 0

    0 0

    0 0

    0 0

    = +

    +

    +

    +

    + , ,

    1m

    se sw e ws s

    se sw e w

    v v p pSx x x x

    , ,)

    * *

    , , ,

    * *

    , , ,

    :

    :

    u m u m uP P l l

    l E S W

    u m u m uP P l l

    l E S W

    x A u A u Q

    y A u A u Q=

    =

    + = 3

    + = 3

    > )":

    * * * * *e w n s pm m m m m

    + + + =,

    $ G!" NA9 -

    ( ) ( )1* * mee e E Pu

    p e

    Su u P PA

    = 333

    @!( @ ," m-1 ,-.

    ) ( ) }) ( ) }) ( ) }

    ) ( ) }

    1

    1

    1

    1

    ,0 min ,0

    0 min ,0

    ,0 min ,0

    0 min ,0

    m

    e P e E

    m

    P n

    m

    P w W

    m

    P s S

    P W

    P

    m U m U

    U m U

    U m U

    U m U

    U UX

    1 1

    1

    m m

    ne nwn n

    W ne nw

    m

    w

    w

    v vSX x x

    + ,

    ,)

    ? y ,22. M-.

    !% & ,N@:

    3

    33

    z&M5 7-C % $ @7 -< ,5

    5

    BJ! >" *u&*v-?& B&@!, , ,w s n e NA9

    `&@ `- 3&33 F> !% @- , @.

    333

    &@J ,>+ ,4>? /

    ? @ @- 1>/ ,

    ,22. % X< 1!, B%

    J! B/*u&*v$

    !? B/@ ,"*m

    >"

    BJ!*u&*v ,

  • *u P

    le

    p

    Q Q A uu

    A

    =

    ( )( ) 1* * mnn n P

    P n

    Sv v P P VA

    = 3

    v;!? 2< - \Q m mp P P=!. ," ]4c 1 , ,?- &

    ( )

    ( )

    mm m ee e E pu

    p

    mm m nh e pv

    p

    Su u P PASv v P PA

    =

    =

    N@.

    ( ) ( )' e

    e e E pup e

    Su u P PA

    # # #=

    *u

    m L L Le e e

    p

    A uu u u

    A## = =

    *ul lA u

    M - !% @- , -:

    V3

    N@-5 SIMPLE \H-)J! B/*u&*Z! *mu u u #= +)*mv v v #= +&1m P #+

    " 7 !% ,c@ @ N ,.

    (5)

    (6)

    )5(&)6(J! \Q `&@ , N" N"

    (7)

    N:

    $ @ ,"

    ]! 1>/ , *nv@

    @-5 $!C @ ," @-c>/z8I - H@.@- >/ ,J! @!( @ @ @C & /m

    !. G9)3(&)4(% @

    ,"

    B! ]! 1>/ , &vN@

  • ( ) ( )e

    nn n pvp n

    Sv v P PA

    ## # #=

    ( ) ( ) ( )m m m me w n s

    Su Su Sv Sv +

    ,5 %5 !% ,5 ,N@:

    ( ) ( ) ( )m m m me w n s

    Su Su Sv Sv m # # # # +

    @C \N@.

    *. .p P

    p pp p L LA P A P m m#

    # #+ =, ,

    SIMPLE%.

    pm#

    ,e! !gN":

    2

    2

    P P PE W u

    p e

    P P pE p pu

    p e

    SA A AA

    SA A A L E A

    = =

    = =

    !" e!S! B! ," , :( 1

    ( )1

    * * 1 me e ue

    p e

    Pu uA x x

    = ,)

    (8)

    mv 7 -< ,5 @ ":

    ( ) 0ms

    Sv =

    *mv v v #= + & 7-C ,5 @ @!I &

    ( )*

    mP

    sSv m

    # =,

    )7(&)8( @Q B! !% ,5 , 7-C ,5

    v #d8 B!N@-5 3S 2 ;-4 ,2>/LE

    2 2

    , , ,

    Pu u

    p pw n

    pp

    l

    S SAA A

    A L E W S

    =

    =

    -)#

    " @ -?& @C A!c G>9 )(

    1m

    e e

    px

    J! 1 ! & J B/mu&m

    C! G9*mu u u #= +&

    @!I ,"eu #&nu # %

    $ % ," Q ," ?u #&

    #./ +& 012# 213

    ,N/ ,( % :5(@- :>J !%N":

  • \Q @8 !% @- , M J!

    1e e e E pu

    ep e

    PuA x A

    # # =,) =

    B/( ) `- ! .1>/ , &8 ]!

    ( )1 E pup e

    P PA

    # #

    ,"e,) 9 J & G-4 NA w -: