Computation of shoaling and breaking waves in nearshore areas by the coupling of BEM and VOF methods

6
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0 10 20 30 40 50 60 AB n r2 Γ z/h o h o h 1 Γ b Γ Γ r1 f x/h o s x l AP

Transcript of Computation of shoaling and breaking waves in nearshore areas by the coupling of BEM and VOF methods

!"# $ % &'

' () * +, - !# .//0 % &'

)0 1 2' -- . 1 3 , - , !! *

* 0' 4 5 6 3 '- 1 . /

0 0 - 1. 74 8

0 21 & 0 - /5 8 /

'' 10 1 3- 65/

- 4 3

!"#

3 . 0 93 :9; 3 . Æ'1 ''- 3 - 3- 1 ' 4 6. 60 -3. - 1 4 :-$ ""< "" ""!= $ > "" ""!; ,'3 '0 1. 74 3. ./'. . ,- 10 6 1' $? 1' ' 3-3/ 0 /- 1 63 3 6. -0. '3 0/' 0 1 1 3 :@; 6' 3. 0 3 1'. 16. 5 4 - - /A6 : 64; 9. 6. %0 334 3 '0 @ 6 74 8/ . '' '- 63 3 3 5/0' 1 1' 4 3- - 60 365- :1 43'3 4 3 ' - 31 1'; -3. 6. 3 1 0' 1 65 B 3 1 1' :- $ ""< "";&3 3 3 34 3 03 65 4 3 1 -- 8

3 0 1 9/@ /65- 4 3 3 0 1 C' 03 1 /

- 65- '0 3 03 . 1 :*; :- ""= 0 "" =$ > "" ""!= &- ; 3 ' 66 -. 10 ' 4 3 %0. 1 3 @61 3. - 3-3 '06 1 1' ' 6 :D66- E *;@3 * ' 4 3- 4 /0. '' 1 65 3 1 3 143'3 . 3 C 4 6 '' 3 @ @3 * 34 '' 4 ' 6 3 .' 3 65- 61 3. 3 * 3 -. :$ > "" ""!;

- 1- 0 . 8- 0 . 6- 0 . 4- 0 . 2

00.2

0 1 0 2 0 3 0 4 0 5 0 6 0

AB

n

r 2Γ

z / ho

ho

h1

Γb

Ω

Γ

Γr 1

f

x / ho

sx

l

AP

&- F 5'3 1 ' 4 3- '0 $ >? :""; )/9/@ 43 66- 6'3 :*; 66- :*; 3%0.

3 '3 * . /3.' 3 3 43 -6. 66- 4 -. 3. -. 3 4. '' 3-3 3 '06 '/ 1 '. 6' '. 43 3 7 0>' 1 4 3 50' 433 * 43'3 ' . 6 - D6'5 6%E 10- -. 6 1' 0' 0

00 '0 4 3 '.

3 03 '. 3 '0 /5 8/ - '- 3 43 0 6 ''/. 14 3 0 1 1 1' 1' 647 6. - 6 -- 1' 05 2&03 4 1 '5 1 6 43 3 70 1 ' 1 4 '3 10 3 0 '0/ 0 >' 3 03 . 10- 65- 4 - 60 H- $- ""! """= &- = 34 3 0 3 /3 0 6 '06 1 '5 1 3 4 F 3 0. 6 %0 1 060I 2& 03 34 '0. %/ J 10 0' J - C' 1 4 -. - ' 1 -

31.5 32 32.5 33 33.5 34

0

0.2

0.4

0.6

0.8

&- F 5- 1 . 4 F# 4/3 2& 0 H$- ""!I -3 -. 3 - 5 -. 3 4 - *4 '74 '

, 3 . 3 5. 1 - 1 639 2& 03 % 6. '- 3 03/ '. 4 3- '0 13 3 30' 1 65 B 3 1 1' 3 9 0300 @ 43 * ''. Æ'.0 4 3- - 60 61 65- '/' 3 2& 03 ' '' 65- /65-4 3 1 3 - 60 C ' -43 7 74 0 6- 63 G 3 ' 6. - 3 9/@ 3 '0 4 1 Æ' '' '0 1 34 - 10

- 1

- 0 . 5

0

0.5

0 5 1 0 1 5 2 0 2 5 3 0 3 5 4 0 4 5

z / ho

Hb

hb

ho

Ho

s

B P

xb

x / ho

&- F 3- - 1 . 4 1 3-3

H $ ""I

, 3 9A2& 0 '- . /

G 1 . 4 3- 65- 0 1

43'3 7' '' :- &- ; 3 3 0

' 43'3 1 6'5 '' 10 3 2& 0 3

9 0 9 '0% ' 43 ' 4 1

6'5 - 4 6 3 '1'

#!$ "$

$ :"!"; $ 60. :"" ; 0/0 Æ' '' 4/0 : ); 90 - 1. 74 8 :&&=&- ; '. 8

K L:; :;

3 1. 50' .0' 1 1' 6.'

K :

M ; K K N :; : ;

K M

N :; :;

'. 43 3 ' 3 1 1' 3 - '' 3 ' ' 3 3 1 1' 3 7 .= /74' 3 60

K N :<;

43 3 'C . ' 6 N N ' %

$ > :""; 00 '' -

6 1 ' 4 3 9 0 /

)/@ '6 3- 4 9

'C'. 3 @ '06 F :; 3-3/ 9 /

1 &. &4 :&&; 8= :;

%' - 1 C 0 ' 4 :

; 3 4 %0. :N;= :; !

" :*; 3 1 1 3 5 :1- 63 1

1' 6 N ' 6 N= &-

; *' 34 3 1 6 1

4 '0 3 @ '3 #

1 43'3 7' 10 3 * 4 . 0 ) ' 6

1 3 6/1'

$- :""!"""; 0' 0 10- 0/1' 4/3 :A4; ' '0/

5 8 63 7 43 ' 3 .:/'06. 03= - ""#= - ""!;* ' - 43 6 03 '- 63 7 /C - 3 ' ,1' 3 0 0/ - 4 -- 03 1 /2& 03 :$- ""!; , 3 03 /1' 0 4 4. F :; 1' C 43'3 ' 1 3 2& - 3 1' : ; 1 3 ' '' 6. 3 7 :'' 2& '';= 3' .1' 3 ' ' 3 ' 1 /1' 3 '= :; -0 1 3 1' C 6 3 1 3 ' 1' ''- '4 ,1' ' '' :- ""#;

,1' -0 ' 1' 1 0 14/

- 3 '. C 6 10 3 2& 1 /

5 8 *1 3 ' 4 1 3 '

1' '0 5- '' 3 4 1

3 -0 ) ' 6 1 3 6/1' /

-1.5

-1

-0.5

0

0.5

1

22 24 26 28 30 32 34 36 38 40x/h

o

η/ho

xg

A P

A B

xl

(a)

a

-1.5

-1

-0.5

0

0.5

1

22 24 26 28 30 32 34 36 38 40x/h

o

η/ho (b)

xg

VOF

a

&- < F ' 1 9A2& 0 '- :; 3-

6 3 9/@ 43 * : *; /

-

1 . 4 43 ' 3-3

0 & ' ''

' -- :6; 0 '0 3 2& 0

G 43 4 - 6. '

10 :;

$ ? )/@ '6 6 0 3 -1 6. 1. 4 '0% 60 -/3 . 1 4 74 0 :'. '/' ; . 6 3 = 1 1 3 0 C ' 6 '0 '/C $- :""!; 3 @ - 3 2& 0 1 3 -1 - . 4 ' 3 ,

'. - ' 1 - J'6. 0' J 43'3 C' ' /-. 4 3 4 - * 6'1 3 - 7 0 '3 2& '0 %0.0- 0 1 '0 ' , 1' 3 '0/ ' . 6 10 6 0 6.- 6/0 43 - - /. ''- 3 - 1 . 4 36/0 10 6/0 3 %

, 3 43 1 3 9/@ $ :""; '' 3- 1 . 4 0 ' 365- : &- <; > 34 4 - * 'C 3 1 3 9 '' - ' 1'1 0 3 ' 6. ' 32& 0 :&- <6;

9 'C'. C '0 3 @ 43/ 3 * :- &- #; ' ' ' 3 :' ; C '' '/- 3 2& 0 - 03 ' 3 C 2& '0 :- &- <6; *' '0 3 3 @ 1 3 0 4- 3 * 66 ' 4 -. :- &- < #6;, 3 ' 0' 4 -- 'C ' 3 /' 1 3 6'3 43'3 63 6. C '' 3 ' ' 1 2& - '/ 1' 1 0 3 0 1 '. 4 C. 3 2& 0 6. ' :- &- ;

. '- 3 4. 3 '6 1 63 9 2& 03 '06 6 , 4 C /0 6. '' 3 @ '/C 3 2& 0 J' 6. 0' J3 2& 0 . 3 -' 3' 63 '' Æ' 1 /65- 4 43'3 6. 3 '3 1 3 9/@ 9 1 0 0 - 3 % '

-1

-0.5

0

0.5

1

24 25 26 27 28 29 30 31 32 33 34 35 36x/h

o

η/ho

da b c

(a)

e f

-1

-0.5

0

0.5

1

24 25 26 27 28 29 30 31 32 33 34 35 36x/h

o

η/ho

da b c

(b)

e f g h

&- # F 3- 65- 1 . 4 43 K

0 10 3 3 ' 4 ' K K # KF 6F ! 'F << F <! F # 1F # -F 3F !"

C. 3 3 0 1

3 1' 3 3 ' 63 0 .

>' 3-3 9/@ 1 3 2&

0 3 1 6'5 10 3 0 3 9/@

@ 4 3 1 . 4 3 1' J'

& ' 4 34 43'3 4 6

' - 1 6'5 4 6 '. 4 8 3

00 1 -30

"$ ! " !#$

!" # $ #!%# &' ( )*+ ( , -+ . !" / $001' . . !" ( ( $ ' 2 $013' 4 / $00*005' 4 !" 6 *+ )) ** 6 7

( 7 ( )+ 7 ( 7

( ))*+,

8 77

( )*

98 +)) " & * 8%: #+ 3 8 $ / ; 003' < 3) !" 3)) = 8%:

-0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

-0.75

-0.5

-0.25

0

0.25

0.5

z/ho

u '

(a)

ab

cd

e

f

g

h

-0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04

-0.75

-0.5

-0.25

0

0.25

0.5

z/ho

w '

(b)

a

bc d e f gh

&- F 0 ' &- # )0 ' '/

'' 3 9/@ 43 3 * :&- #6;

' --

K # 10 60 1' :&- <; F :;

3G '= :6; ' '

!"

( 1* $ % >' .

# * < !" 6 # + !" !" 6 +)) ** 0 6 7

( )* 7 ( ))*+, 8 )* " &* 8%: # + 1 $1)' &

( +35 $# *' ?@#

8 # + # + A

" # + !" = B (

?@# $ > ;' # 3 6 (

*

$# +'

# * ?@# !" > (

6 ( +3 ( )3 8 6 !" # +

< ?@# 1+ & 6 6 7 ()) 1) 6 7 ( ))+ (

?@# 8 )0 $/ 001' !" 1+>1) ?@# " 7 ( ))) 8%: & 31 !" # )))+ ?@# 5+) & ?@# = *1 98 +))

6 ?@# > $# 3' !" C # 5 !" # 5 ! > / $00*005' > A D E !" > F C $001' $ / 001' = !" E ?@#

< # 5 & ?@# < A ?@# $'

&

-0.5

0

0.5

1

29 30 31 32 33 34 35 36x/h

o

η/ho

b

c d e

(a)

-0.5

0

0.5

1

29 30 31 32 33 34 35 36x/h

o

η/ho

edc f g hb

(b)

&- F 0 ' &- # '' F :; 3 9/

@ :0 &- #;= :6; 3 2& 0

0 G 3 2& 0 3 0 1

' 6. ' 'C K #

- 3 9/@

9 $' ?@# E

E = ?@# 9 E E &

/ $001' ?@# > ( ) +3 $# ' 1)) 1) 6 7 ( ))* 7 )) ( 8%: & +)3 9 . / # 5 $ # ' A A > . ?@#

< ?@# Æ ?@# 9

+

$#

-?@# ? @ # ?@# .

9 Æ ?@# +) A A G $' ?@# 6 ?@# , $' ?@# Æ

< ?@# & ?@#

?@# . ( < > ?@# >

%$"&

F; : 3)5 8!C; :H ? # : C < :; F;2

0 * :"" ; - 1 4 *66- . / 1 ) 0/0 0 1 & 1'$. @ $ % & "/#

:""; 0' 0 1 @ 3 ' ! " ' :<; /

$ > O :""; 0' $ *6 1 &. ' @ $ ' :; / "

$ > O :""!; 0 1 ' 43- 6/6'3 1. 0'4 5 , ' ,2"! :9 9.""!; : 3- O 2- 9 P0 > P/.0 @; ,,, "</

$ > O :"""; 0 1 1' 4 3- 0 1. 0' 4 5 $ :60;

$ 5 O ,* :"!"; * Æ'6. 0 03 1 4 4 ' ! " ' : ; "/

$ 60. :"" ; 0' 0- 14 65- ' 6. C% 0- 6 % </"

$ 60. ,* 0. O:""<; 3- 1 . @ '3 $ & % ( ' : ; "/ !

$ ,* 60. :""; 5/- 3'' 1 . @ $ & % ( ' :; /

$ ,* 60. :""!;5- 3'' 1 . @ Q $ & % ( ' : ; /#

$- 9' . P31 3 & 3:""!; . @ 5- - '3 F ) 4/3 &4 0' 0 6. /2& 93 '$ :60;

$- 9' . :"""; 4 2& 931 0 1 @ J' &)(&'** % : &';

> '3 :"!; 0 1 & 93 1 3 )./0' 1 & $ % & /<#

- :""!; 8 ? '0 / ' ? 1' + '/3 *

O :""#; '4 ,1' ' % ! & :,, 6; "/"

R '3 & :""!; 5- ' '3'/' 1 . 4 Q )' $ & % ( ' : ; "/

5 9 :"! ; 3 6. 1 . @ & , / #

> :""#; *. 1 /'06. .01 '06 '06 74 % , - :; #/ ##

3