HİD 473 Yeralt ısuyu Modelleri - Hacettepeyunus.hacettepe.edu.tr/~tezcan/H473/Sayisal Model...

HİD 473 Yeraltısuyu Modelleri

Sayısal Analiz

Sonlu Farklar Yaklaşımı

Levent Tezcan2013-14 Güz Dönemi

Modelleme

Problemin Tanımlanması

Kavramsal Modelin Geliştirilmesi

Hidrojeolojik Süreçler Sınır Koşulları

Matematiksel Modelin Geliştirilmesi

Diferansiyel Eşitlikler Analitik & Sayısal Yöntemler

Modelin Kurulması Kalibrasyon & Veri Toplama

Sonuçların Elde Edilmesi

SAYISAL YÖNTEMLER

• Yeraltısuyu Akımını ifade eden Diferansiyel Eşitlik,  Cebirsel DoğrusalMatris eşitliklerine dönüştürülür.

• İki dönüştürme yaklaşımı yaygın olarak kullanılır:

• SONLU FARKLAR YAKLAŞIMI

• SONLU ELEMANLAR YAKLAŞIMI 

SONLU FARKLAR YAKLAŞIMI

dfdt

f t t f ttt

lim

( ) ( )

0

dfdt

f t f t 0 1( )

f t t f tt

f t( ) ( )

( )

f t t f t t f t( ) ( ) ( )

f t t f t t f t( ) ( ) ( ) t=0.1

0.20.1

t

0.0

0.30.40.50.60.70.80.91.0

f(t)

1.00000.90000.81000.72900.65610.59050.53140.47830.43050.38740.3487

0.0010.01

t

0.1

f(1)

0.34870.36600.3677

dfdt

f

f t e t( )

f e( ) .1 0 36791

f t t f t t f t( ) ( ) ( ) t 0

t 0 f tf t t

t( )

( )

1

f t t f tt

t( ) ( )

( )

( )

112

112

f( ) .1 0 3855

f( ) .1 0 3676

Taylor Seri Açılımı

f f x xdfdx

x xd f

dx

x xd f

dx

i i i i

i i

i i

1 1

12

2

2

13

3

3

12

13

( )

( )

!( ) ....

x x f x f x x fi i i i ( ) :1 1

Taylor Seri Açılımı

x x f x f x x fi i i i ( ) :1 1

f f x xdfdx

x xd f

dx

x xd f

dx

i i i i

i i

i i

1 1

12

2

2

13

3

3

12

13

( )

( )

!( ) ....

birincidfdx

türev:

dfdx

f fx x

x xx x

d f

dx

x xx x

d f

dx

i i

i i

i i

i i

i i

i i

1

1

12

1

2

2

13

1

3

3

12

13

( )

( )( )

!( )( )

....

dfdx

f fx x

xi i

i i

1

1

0( )

birincidfdx

türev:

dfdx

f fx x

x xx x

d f

dx

x xx x

d f

dx

i i

i i

i i

i i

i i

i i

1

1

12

1

2

2

13

1

3

3

12

13

( )

( )( )

!( )( )

....

dfdx

f fx x

xi i

i i

1

1

0( )

ikincid f

dx türev:

2

2

d f

dx

f f f

x xxi i i

i i

2

21 1

12

220

( )

dfdx

f fx x

xi i

i i

1

1

0( )

dfdx

f fx x

xi i

i i

1

1

0( )

d f

dx

f f f

x xxi i i

i i

2

21 1

12

220

( )

2D DENGELİ YAS AKIM EŞİTLİĞİ‘NİN SONLU FARKLAR ŞEKLİ

2

2

2

2 0x y

x

y

i,j

xi

yi i+1,j

xi+1

i-1,j

xi-1

i,j-1yi-1

i,j+1yi+1

xi

yj

i,j i+1,j

i,j+1 i+1,j+1

İleri Farklar Yaklaşımı

( ) ( ) ....

( ) ( )

x x x xddx

ddx

x x xxx

Geri Farklar Yaklaşımı

( ) ( ) ....

( ) ( )

x x x xddx

ddx

x x xxx

Orta Farklar Yaklaşımı

ddx

x x x xxx

( ) ( ) 2

xi

(x)

x

B

xi+1

x+x

(x+x)

xi-1

(x-x)

x-x

İleri Farklar

Geri Farklar

Orta Farklar

ikincid

dx türev:

2

2

d

dx

x x x x x

xx

2

2 2

2

( ) ( ) ( )

2D DENGELİ YAS AKIM EŞİTLİĞİ‘NİN SONLU FARKLAR ŞEKLİ

2

2

2

2 0x y

2

2

2

2 0x y

i j i j i j i j i j i j

x y

1 12

1 12

2 20, , , , , ,

x y

i j i j i j i j i j

, , , , ,

14 1 1 1 1

2D DENGESİZ YAS AKIM EŞİTLİĞİ‘NİN SONLU FARKLAR ŞEKLİ

2

2

2

2x yST t

Zamana göre türev

t tt k t

k k

1

İFY

t tt k t

k k

1

GFY

İleri ve Geri Farklar Yaklaşımı

i jk,

xx

y

y

i jk1,

i jk, 1

i jk, 1

i jk1,

t

t

i jk,1

i jk,1

t=(k+1)t

t=(k-1)t

İleri Farklar Yaklaşımı (t)

i jk

i jk

i jk

i jk

i jk

i jk

i jk

i jk

x y

ST t

1 12

1 12

1

2 2, , , , , ,

, ,

i jk

i jk

i jk

i jk

i jk

1 1 1 1, , , , ,,, , , i jk,

1

Açık=Belirtik (Explicit) Çözüm

Geri Farklar Yaklaşımı (t)

i jk

i jk

i jk

i jk

i jk

i jk

i jk

i jk

x y

ST t

11 1

11

211 1

11

2

1

2 2, , , , , ,

, ,

i jk,

i j

ki jk

i jk

i jk

i jk

11 1

11

11

11

, , , , ,,, , ,

Kapalı=Örtük (Implicit) Çözüm

Açık ve Kapalı Çözümler

k

k+1

x

t Bilinenleri

k i+1ki-1

k

ik+1 Aranan

k

k+1

x

t Bilinenleri

k i+1ki-1

k

ik+1 Aranani-1

k+1 i+1k+1

b

Örnek

L R

R

(t>0)

ki

ki+1

ki-1

x

=sbt =sbti i+1i-1

xi xi+1

1 2 3 4 5

Başlangıç ve SınırKoşulları

b=1.5 mx=3 mK=0.5 m/gS=0.02

L= 1= 6.1m t

R= 5= 6.1m t

R= 5= 1.5m t

2= 3= 4= 6.1m t

Örnek

i j

ki jk

i jk

i jk

i jk

x

ST t

1 1

2

12, , , , ,

i j

ki jk

i jk

i jk

i jkT

St

x, , , , ,

1

2 1 12

i j

ki jk

i jk

i jk

i jkT

St

x, , , , ,

1

2 1 12

TS

t

xt

2

12

0 1

. gün

i j

ki jk

i jk

i jk

i jkT

St

x, , , , ,

1

2 1 12

i jk

i jk

i jk

i jk

i jk

i jk

i jk

i jk

i jk

i jk

, , , , ,

, , , , ,

. ..

.

.

12 1 1

11 1

0 5 150 02

0 1

32

0 416 2

Çözüm

k i=1 i=2 i=3 i=4 i=50 6.10 6.10 6.10 6.10 6.101 6.10 6.10 6.10 6.10 1.502 6.10 6.10 6.10 4.18 1.503 6.10 6.10 5.30 3.86 1.504 6.10 5.77 5.04 3.48 1.505 6.10 5.60 4.69 3.30 1.506 6.10 5.43 4.49 3.13 1.507 6.10 5.32 4.32 3.02 1.508 6.10 5.23 4.19 2.93 1.509 6.10 5.16 4.10 2.86 1.50

10 6.10 5.11 4.02 2.81 1.50

k

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

0 5 10 15 20 25 30 35 40 45 50

i=4

i=3

i=2

t=0.1 gün

k

t=0.15 gün

i=4

i=3i=2

-1.00

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

0 5

10 15

Geri Farklar DenklemiKapalı ‐ Örtük Çözüm

i j

ki jk

i jk

i jk

i jk

x

ST t

1

1 111

2

12, , , , ,

i j

ki jk

i jk

i jk

i jk

x

ST t

1

1 111

2

12, , , , ,

i jk

i jk

i jk

i jk

ST

x

t

ST

x

t

11

21

11

2

2, , ,

,

b

Örnek

L R

R

(t>0)

ki

ki+1

ki-1

x

=sbt =sbti i+1i-1

xi xi+1

1 2 3 4 5

Başlangıç ve SınırKoşulları

b=1.5 mx=3 mK=0.5 m/gS=0.02

L= 1= 6.1m t

R= 5= 6.1m t

R= 5= 1.5m t

2= 3= 4= 6.1m t

i jk

i jk

i jk

i jk

ST

x

t

ST

x

t

11

21

11

2

2, , ,

,

i jk

i jk

i jk

i jk

11

21

11

2

20 02

0 5 1530 1

0 020 5 15

30 1

, , ,

,

.. . .

.. . .

i jk

i jk

i jk

i jk

1

1 1114 4 2 4, , , ,. .

k+1=1t=(k+1)t=0.1

i=2 2 11

21

2 11

204 4 2 4 . .

10 1

20 1

30 1

204 4 2 4. . .. .

11

21

31

204 4 2 4 . .

6 1 4 4 2 4 6 121

31. . . .

i jk

i jk

i jk

i jk

1

1 1114 4 2 4, , , ,. .

k+1=1t=(k+1)t=0.1

i=2 11

21

31

204 4 2 4 . .

i=3 21

31

41

304 4 2 4 . .

i=4 31

41

51

404 4 2 4 . .

i

i

i

2 4 4 2 4

3 4 4 2 4

4 4 4 2 4

11

21

31

20

21

31

41

30

31

41

51

40

. .

. .

. .

6 1 4 4 14 64

4 4 14 64

4 4 1 5 14 64

21

31

21

31

41

31

41

. . .

. .

. . .

4 4 1 0 20 74

1 4 4 1 14 64

0 1 4 4 16 14

21

31

41

21

31

41

21

31

41

. .

. .

. .

4 4 1 0

1 4 4 1

0 1 4 4

20 74

14 64

16 14

21

31

41

.

.

.

.

.

.

21

31

41

6

5 8

5

m

m

m

.

Gauss Yoketme Yöntemi

a a a

a a a

a a a

x

x

x

b

b

b

110 120 130

210 220 230

310 320 330

1

2

3

10

20

30

E

E

E

10

20

30

a a

a a

x

x

b

b

Ea

Ea

Ea

Ea

a x bEa

Ea

221 231

321 331

1

2

21

31

10

110

20

210

10

110

30

310

332 3 3221

221

31

331

E

E

E

21

31

32

Gauss Yoketme Yöntemi

a a a

a a

a

x

x

x

b

b

b

ba

b aa

b a aa

110 120 130

221 231

332

1

2

3

10

21

32

332

332

221 231 3

221

310 120 2 130 3

110

0

0 0

x

xx

xx x

Gauss Yoketme Yöntemi

4 2 1

3 6 4

2 1 8

12

25

32

11

21

31

X

X

X

Gauss Yoketme Yöntemi

Crank‐Nicholson Yaklaşımı

Orta Farklar YöntemiTek Yönlü Akım

12

2 211 1

11

1 12

1

( ) ( )

( )

( )

ik

ik

ik

ik

ik

ik

ik

ik

x

ST t

Crank‐Nicholson Yaklaşımı

( ) ( )( )

( ) ( )( )

, , , , , ,

, , , , , ,

, ,

i jk

i jk

i jk

i jk

i jk

i jk

i jk

i jk

i jk

i jk

i jk

i jk

i jk

i

x

y

ST

11 1

11

1 12

11 1

11

1 12

1

2 1 2

2 1 2

jk

t

0<<1

Duraylılık

TS

t

x

t

y

2 2

12

b

Örnek

L R

R

(t>0)

ki

ki+1

ki-1

x

=sbt =sbti i+1i-1

xi xi+1

1 2 3 4 5

Başlangıç ve SınırKoşulları

b=1.5 mx=3 mK=0.5 m/gS=0.02

L= 1= 6.1m t

R= 5= 6.1m t

R= 5= 1.5m t

2= 3= 4= 6.1m t

Crank‐Nicholson Denklemi

12

2 211 1

11

1 12

1

( ) ( )

( )

( )

ik

ik

ik

ik

ik

ik

ik

ik

x

ST t

k+1=1t=(k+1)ti = 2

1

2

2 231

21

11

30

20

11

2 21

20( ) ( )

( )( )

x

S

T t

i=21

2

2 231

21

11

30

20

10

2 21

20( ) ( )

( )( )

x

S

T t

i=3 1

2

2 241

31

21

40

30

20

2 31

30( ) ( )

( )( )

x

S

T t

i=41

2

2 251

41

31

50

40

30

2 41

40( ) ( )

( )( )

x

S

T t

1

2

2 6 1 6 1 2 6 1 6 1

3

0 02

0 0756 13

121

2 21( . ) ( . . . )

( )

.

.( . )

x

1

2

2 6 1 2 6 1 6 1

3

0 02

0 0756 14

131

21

2 31( ) ( . . . )

( )

.

.( . )

x

1

2

15 2 6 1 2 6 1 6 1

3

0 02

0 0756 14

131

2 41( . ) ( . . . )

( )

.

.( . )

x

1

2

2 211 1

11

1 12

1

( ) ( )

( )

( )

ik

ik

ik

ik

ik

ik

ik

ik

x

S

T t

(( )

)

( )

ik

ik

ik

ik

ik

ik

S x

T t

S x

T t

11

21

11

1

2

1

2 1

2 1

ik

ik

ik

ik

ik

ik

11 1

11

1 16 8 2 8. .

31

21

11

30

20

106 8 2 8 . .

41

31

21

40

30

206 8 2 8 . .

51

41

31

50

40

306 8 2 8 . .

ik

ik

ik

ik

ik

ik

11 1

11

1 16 8 2 8. .

31

216 8 6 1 6 1 2 8 6 1 6 1 . . . . . .

41

31

216 8 6 1 2 8 6 1 6 1 . . . . .

1 5 6 8 6 1 2 8 6 1 6 141

31. . . . . .

31

216 8 6 1 29 28 . . .

41

31

216 8 29 28 . .

1 5 6 8 29 2841

31. . .

6 8 1 0 35 38

1 6 8 1 29 28

0 1 6 8 30 78

21

31

41

21

31

41

21

31

41

. .

. .

. .

6 8 1 0

1 6 8 1

0 1 6 8

35 38

29 28

30 78

21

31

41

.

.

.

.

.

.

Birinci ve ikinci satırlar birinci elemanına bölünür:

1 0 147 0

1 6 8 1

0 1 6 8

5 203

29 28

30 78

21

31

41

.

.

.

.

.

.

Gauss Eliminasyon

Birinci satırdan ikinci satır çıkartılarak yeni ikinci satır elde edilir:

1 0 147 0

0 6 653 1

0 1 6 8

5 203

34 483

30 78

21

31

41

.

.

.

.

.

.

Gauss Eliminasyon

Gauss Eliminasyon

İkinci ve üçüncü satırlar ikinci elemanlarına bölünür:

1 0 147 0

0 1 0 150

0 1 6 8

5 203

5 183

30 78

21

31

41

.

.

.

.

.

.

Gauss Eliminasyon

İkinci satırdan üçüncü satır çıkartılarak yeni üçüncü satır elde edilir:

1 0 147 0

0 1 0 150

0 0 6 650

5 203

5 183

35 963

21

31

41

.

.

.

.

.

.

1 0 147 0

0 1 0 150

0 0 6 650

5 203

5 183

35 963

21

31

41

21

31

41

21

31

41

.

.

.

.

.

.

41

31

41

21

31

35 9636 650

5 408

5 183 0 150 5 994

5 203 0 147 6 084

..

.

. . .

. . .

m

m

m

İterasyon Tekniği

x y

x y

3

2 4

x y

yx

3

42

Jacobi ‐ İterasyonİterasyon

No x y

1 0 0

2 x = 3 - 0 = 3 y = (4-0)/2 = 2

3 x = 3 - 2 = 1 y = (4-3)/2 = 1/2

4 2.5 1.5

5 1.5 0.75

6 2.25 1.25

n 2 1

Gauss‐Seidel ‐ İterasyonİterasyon

No x y

1 0 0

2 x = 3 - 0 = 3 y = (4-3)/2 = 0.5

3 x =3 - 0.5 =2.5 y=(4-2.5)/2 =0.75

4 2.25 0.875

5 2.125 0.9375

6 2.0625 0.9687

n 2 1

3D Sonlu Farklar Akifer Modeli

Akifer Modeli

Hücre Merkezli Grid Sistemi

(Block Centered Grid Sys.)

i,j i+1,j

i,j+1

i-1,j

i,j-1

xi

yj

xi+1/2xi-1/2

xx x

yy y

ii i

jj j

1 21

1 21

2

2

/

/

3D

i,j i+1,ji-1,j

2D Yeraltısuyu Akımı

y

x

i

j

2D Yeraltısuyu Akımı

x

Tx y

Ty

W Stxx yy( ) ( )

x

Qy

Q W Stxx yy( ) ( )

Q

x

Q Q

xi j i j i j

i

, / , / ,

1 2 1 2

x

Tx x

Tx

Txxx

ixx

i jxx

i j

1

1 2 1 2 / , / ,

11 2 1 2

1

1 2

1

1 2 xT

xT

xixx

i jk

i jk

ixx

i jk

i jk

ii j i j/ , / ,

, ,

/

, ,

/

yT

y

yT

yT

y

yy

jyy

i jk

i jk

jyy

i jk

i jk

ji j i j

11 2 1 2

1

1 2

1

1 2 , / , /

, ,

/

, ,

/

2D YAS Akımı Sonlu Farklar Eşitliği

1

1

1 2 1 2

1 2 1 2

1

1 2

1

1 2

1

1 2

1

1 2

xT

xT

x

yT

yT

y

ixx

i jk

i jk

ixx

i jk

i jk

i

jyy

i jk

i jk

jyy

i jk

i jk

j

i j i j

i j i j

/ , / ,

, / , /

, ,

/

, ,

/

, ,

/

, ,

/

W St

ki j

i jk

i jk

,, , 1

yT

xx

T

y

yT

xx

T

y

yT

xx

T

y

j

xx

ii jk

i

yy

ji jk

j

xx

ii jk

i

yy

ji jk

j

xx

ii

yy

j

i j i j

i j i j

i j i j

1 2 1 2

1 2 1 2

1 2 1 2

1 21

1 21

1 21

1 21

1 2 1 2

/ , , /

/ , , /

/ , , /

/,

/,

/,

/,

/ /

yT

xx

T

y

x y W x yS

t

j

xx

ii

yy

ji jk

i jk

i ji j

i jk

i jk

i j i j1 2 1 2

1 2 1 2

1

/ , , /

/ /,

,, ,

B xT

y

D yT

xF y

T

x

H xT

y

i j i

yy

j

i j j

xx

ii j j

xx

i

i j i

yy

j

i j

i j i j

i j

,/

,/

,/

,/

, /

/ , / ,

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Veriler

xi yj Sij Txij Tyij N ij

50 100 3050 100 3050 100 30

250 80 0.02 200 100 0.01 26250 240 0.01 300 150 0.01 29250 100 0.02 200 100 0.01 27300 80 0.03 350 175 0.01 20300 240 0.04 400 200 0.009 27300 100 0.02 200 100 0.01 25400 80 0.01 310 155 0.01 19400 240 0.01 290 145 0.01 22400 100 0.03 180 90 0.01 19

50 100 1850 100 1850 100 18

N=0.01 m/günQw=-100 m3/sW=N+Qw

i j T xi-1/2 T xi+1/2 T yj-1/2 T yj+1/21 1 1.143 0.949 0.000 0.8331 2 1.500 1.263 0.833 0.7691 3 1.143 0.727 0.769 0.0002 1 0.949 0.931 0.000 1.2072 2 1.263 0.939 1.207 0.9092 3 0.727 0.537 0.909 0.0003 1 0.931 1.117 0.000 0.9213 2 0.939 1.064 0.921 0.7233 3 0.537 0.735 0.723 0.000

Dij Fij Bij H ij Eij Qij91.43 75.93 0.00 208.33 -775.69 -10600.00

360.00 303.16 208.33 192.31 -1663.80 -18000.00114.29 72.73 192.31 0.00 -879.32 -13750.0075.93 74.51 0.00 362.07 -1232.51 -14640.00

303.16 225.43 362.07 272.73 -4043.38 -78380.0072.73 53.73 272.73 0.00 -999.19 -15300.0074.51 89.37 0.00 368.44 -852.32 -6400.00

225.43 255.41 368.44 289.20 -2098.48 -22080.0053.73 73.47 289.20 0.00 -1616.40 -23200.00

1 2 3 4 5 6 7 8 91 E11 H11 0.00 F11 0.00 0.00 0.00 0.00 0.00 Q11-D1112 B12 E12 H12 0.00 F12 0.00 0.00 0.00 0.00 Q12-D1223 0.00 B13 E13 H13 0.00 F13 0.00 0.00 0.00 Q13-D1334 D21 0.00 B21 E21 H21 0.00 F21 0.00 0.00 Q215 0.00 D22 0.00 B22 E22 H22 0.00 F22 0.00 Q226 0.00 0.00 D23 0.00 B23 E23 H23 0.00 F23 Q237 0.00 0.00 0.00 D31 0.00 B31 E31 H31 0.00 Q31-F3118 0.00 0.00 0.00 0.00 D32 0.00 B32 E32 H32 Q32-F3229 0.00 0.00 0.00 0.00 0.00 D33 0.00 B33 E33 Q33-F333

1 -775.69 208.33 0.00 75.93 0.00 0.00 0.00 0.00 0.00 -13342.862 208.33 -1663.80 192.31 0.00 303.16 0.00 0.00 0.00 0.00 -28800.003 0.00 192.31 -879.32 0.00 0.00 72.73 0.00 0.00 0.00 -17178.574 75.93 0.00 0.00 -1232.51 362.07 0.00 74.51 0.00 0.00 -14640.005 0.00 303.16 0.00 362.07 -4043.38 272.73 0.00 225.43 0.00 -78380.006 0.00 0.00 72.73 0.00 272.73 -999.19 0.00 0.00 53.73 -15300.007 0.00 0.00 0.00 74.51 0.00 0.00 -852.32 368.44 0.00 -8008.658 0.00 0.00 0.00 0.00 225.43 0.00 368.44 -2098.48 289.20 -26677.439 0.00 0.00 0.00 0.00 0.00 53.73 0.00 289.20 -1616.40 -24522.45

1.00 -0.27 0.00 -0.10 0.00 0.00 0.00 0.00 0.00 17.200.00 7.72 -0.92 -0.10 -1.46 0.00 0.00 0.00 0.00 155.440.00 192.31 -879.32 0.00 0.00 72.73 0.00 0.00 0.00 -17178.570.00 -0.27 0.00 16.13 -4.77 0.00 -0.98 0.00 0.00 210.000.00 303.16 0.00 362.07 -4043.38 272.73 0.00 225.43 0.00 -78380.000.00 0.00 72.73 0.00 272.73 -999.19 0.00 0.00 53.73 -15300.000.00 0.00 0.00 74.51 0.00 0.00 -852.32 368.44 0.00 -8008.650.00 0.00 0.00 0.00 225.43 0.00 368.44 -2098.48 289.20 -26677.430.00 0.00 0.00 0.00 0.00 53.73 0.00 289.20 -1616.40 -24522.45

1.00 -0.27 0.00 -0.10 0.00 0.00 0.00 0.00 0.00 17.201.00 -0.12 -0.01 -0.19 0.00 0.00 0.00 0.00 20.140.00 4.45 -0.01 -0.19 -0.38 0.00 0.00 0.00 109.470.00 -0.12 60.06 -17.94 0.00 -3.65 0.00 0.00 802.060.00 -0.12 -1.21 13.15 -0.90 0.00 -0.74 0.00 278.690.00 72.73 0.00 272.73 -999.19 0.00 0.00 53.73 -15300.000.00 0.00 74.51 0.00 0.00 -852.32 368.44 0.00 -8008.650.00 0.00 0.00 225.43 0.00 368.44 -2098.48 289.20 -26677.430.00 0.00 0.00 0.00 53.73 0.00 289.20 -1616.40 -24522.45

1.00 -0.27 0.00 -0.10 0.00 0.00 0.00 0.00 0.00 17.201.00 -0.12 -0.01 -0.19 0.00 0.00 0.00 0.00 20.14

1.00 0.00 -0.04 -0.08 0.00 0.00 0.00 24.580.00 502.14 -150.06 -0.08 -30.55 0.00 0.00 6730.430.00 -10.09 109.89 -7.61 0.00 -6.22 0.00 2354.620.00 0.00 -3.79 13.65 0.00 0.00 -0.74 234.960.00 74.51 0.00 0.00 -852.32 368.44 0.00 -8008.650.00 0.00 225.43 0.00 368.44 -2098.48 289.20 -26677.430.00 0.00 0.00 53.73 0.00 289.20 -1616.40 -24522.45

1.00 -0.27 0.00 -0.10 0.00 0.00 0.00 0.00 0.00 17.201.00 -0.12 -0.01 -0.19 0.00 0.00 0.00 0.00 20.14

1.00 0.00 -0.04 -0.08 0.00 0.00 0.00 24.581.00 -0.30 0.00 -0.06 0.00 0.00 13.400.00 10.59 -0.75 -0.06 -0.62 0.00 246.660.00 -1331.66 4793.42 -0.06 0.00 -259.37 82499.640.00 -0.30 0.00 11.38 -4.95 0.00 120.890.00 225.43 0.00 368.44 -2098.48 289.20 -26677.430.00 0.00 53.73 0.00 289.20 -1616.40 -24522.45

1.00 -0.27 0.00 -0.10 0.00 0.00 0.00 0.00 0.00 17.201.00 -0.12 -0.01 -0.19 0.00 0.00 0.00 0.00 20.14

1.00 0.00 -0.04 -0.08 0.00 0.00 0.00 24.581.00 -0.30 0.00 -0.06 0.00 0.00 13.40

1.00 -0.07 -0.01 -0.06 0.00 23.300.00 3.53 -0.01 -0.06 -0.19 85.250.00 -0.07 38.07 -16.61 0.00 427.840.00 -0.07 -1.64 9.25 -1.28 141.640.00 53.73 0.00 289.20 -1616.40 -24522.45

1.00 -0.27 0.00 -0.10 0.00 0.00 0.00 0.00 0.00 17.201.00 -0.12 -0.01 -0.19 0.00 0.00 0.00 0.00 20.14

1.00 0.00 -0.04 -0.08 0.00 0.00 0.00 24.581.00 -0.30 0.00 -0.06 0.00 0.00 13.40

1.00 -0.07 -0.01 -0.06 0.00 23.301.00 0.00 -0.02 -0.06 24.160.00 530.59 -231.45 -0.06 5986.930.00 -23.04 129.94 -18.08 2013.870.00 0.00 -5.40 30.03 480.55

1.00 -0.27 0.00 -0.10 0.00 0.00 0.00 0.00 0.00 17.201.00 -0.12 -0.01 -0.19 0.00 0.00 0.00 0.00 20.14

1.00 0.00 -0.04 -0.08 0.00 0.00 0.00 24.581.00 -0.30 0.00 -0.06 0.00 0.00 13.40

1.00 -0.07 -0.01 -0.06 0.00 23.301.00 0.00 -0.02 -0.06 24.16

1.00 -0.44 0.00 11.280.00 5.20 -0.78 98.680.00 -3289.78 18295.24 292800.32

1.00 -0.27 0.00 -0.10 0.00 0.00 0.00 0.00 0.00 17.201.00 -0.12 -0.01 -0.19 0.00 0.00 0.00 0.00 20.14

1.00 0.00 -0.04 -0.08 0.00 0.00 0.00 24.581.00 -0.30 0.00 -0.06 0.00 0.00 13.40

1.00 -0.07 -0.01 -0.06 0.00 23.30

1.00 0.00 -0.02 -0.06 24.161.00 -0.44 0.00 11.28

1.00 -0.15 18.975.41 107.97

1 2 31 27.14 22.60 20.882 28.77 26.52 21.983 27.95 25.66 19.96