Optimized Schwarz Algorithms for Coupling Convection and Convection-Diffusion Problems

Proceedings Chapter

Reference

Optimized Schwarz Algorithms for Coupling Convection and Convection-Diffusion Problems

GANDER, Martin Jakob, HALPERN, L., JAPHET, C.

GANDER, Martin Jakob, HALPERN, L., JAPHET, C. Optimized Schwarz Algorithms for Coupling Convection and Convection-Diffusion Problems. In: 13th International Conference on

Domain Decomposition Methods . Cimne, 2001. p. 253-260

Available at:

http://archive-ouverte.unige.ch/unige:8284

Disclaimer: layout of this document may differ from the published version.

1 / 1

!

" # $

% %

$ $ & $ " #

$ " $" %

" $ "

$ '()*

(+*,

- . # #

/ 0 $ (1*

(2 3* & # " 4

" /(5*

6 $"

$"$ /

#! "

4 4

' ,7 8' ,8 9 :

' , 9 :

';2,

# : "Ê

$

;$;9' ,

'

½

':,,

$0#

½

':,8Æ; 6

# #

"

4 $$$ :

" : :9:

  :

# :

  :

9 $ < "

#:

  :

$ # " :

6

';2,## " 4 $ :

" 4

',78',89 :

#

',',89 :

#:

::

:#

<

!!"#""

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

0 / # / " : 9 Ê

#

# 0 $

.# $ .#" $

6 # /# / " $

$0 " $

! # / # / "

(+*

: 9 Ê

:

  9 Ê

Ê

:

9Ê

Ê <9' , Ê 9; & ".# $

<

=

> """0 $

=

',9

#

' , 9 ; :

9 <

0$

&" Æ "

# $ " =

- " 6$ $ #

" $

88'

88,9;

6'

=

, <" 4

:

'(1*, &"# # /

'

,9 :

'

,9 '  

,<

'

,9 :

=

'

,9

=

'  

,<

';),

" :

:

#"#

', 9 :

9 <

', 9 :

9

<

';+,

0 ';+,

0$ 6

$"

# 4 $"

4 $$/ 6

" (+*" "

## #?

0 "

6 " :

# / ';),

# "

6 # =

$

!$4 # #

9

# ; ; Æ /

" # / # " 4

(5* 6/# / " "

$

'

,9 :

'

,9 '  

,<

'

,9 :

'

,9

'

,<

';1,

'

,

:

@ ##

(+*(3*

':

¦

, 9 ':

¦ ,

'<,

'

,

':

  ,

':

, A

" :

"

#

!

! " #

9

9

&$

# $""

9 < $ "

6 $ $

::

$ $

',9 :

# " " '(+*,

0$

', 9 :

9 <

0<

9<

<

9 < # <

<

9 <

<

9< #

- ;2

:

:

<

<

- ;2B @ #.# .# 0 "

/# /

'

, 9 :

'

, 9 '  

, <

9  

<

'

, 9 :

'

, 9

<

';5,

@ "#

$ #

':

  ,

':

,

$ " " ';5, !

# '

,"/# /';5,

' ,"

', 9 :

9 <

', 9 :

9

<

:9Ê

:

  9Ê

Ê:

9Ê

Ê

<9' , Ê 9; "4

Ê

> ()*" 9;

9 ;

7 9 ;

9

9;

',

¾

Ê

¾

9;'

, ',

¾

Ê

¾

·

9;''

,

¿

¾

,

-

7 9 ; 9 9;

9 ;

9

9;

',

¾

Ê

¾

9;''

,

¿

¾

, ',

¾

Ê

¾

·

9;''

,

½

¾

,

## 0$ !

! " /4

/ # / $ # 0 4

" 4

/ 9 2);; #

$ 0 .#

$ " $

# /# /

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x

y

- ;)B 0 $" .# $

/# /';1,# 92;

9';2 ;2,

92;

6 $# - ;) "

9;)

C " - ;+ #

$/# /" 9;;2" )

C "- ;+##

" (+*$ / 6$

$

8

9 ',  

<

9  

<

';3,

" "$ $ " "

- ;+

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x

viscous solution optimized Schwarz

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x

viscous solution coupling with (7)

- ;+B D " $

" $ / # /

"

(+* $ 9;)

# /# /

# 9 2;

9 ';5 ;5, 9 2;

$

- ;1 6 "9;)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x

y

- ;1B 0 $" $

$/# /" +

- ;5# 9;25'.#

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

x

viscous solution optimized Schwarz

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

−0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

x

viscous solution optimized Schwarz

- ;5B D " $ " 9 ;25 # /

(; ;5*(; ;5* 9;E 6

/# /

$ ,9;E' .#" $

, 6 "

<

C <

? "

$0#$&

- ;3## # ';3," (+*

" + <

? #

<

? " 6 /

" # # $

$ $

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

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

x

viscous solution coupling with (6)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

−0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

x

viscous solution coupling with (6)

- ;3B - ;5 " #

';3," (+*

-$##- ;F "" "

$ 6 0 $ " ()*

1 0 1 #!

23 !)! 4"5 ) " +

6)7

89:9;<:--9

23 )7 &

& --

23 07"5 ) $= )> +

7 ?) " ) (@!

!

" ;:& --.("

23 $) A "57) +6) ?) #

#89;<-<:

293 ! * =4 B+/ " +6)7+

(& ,CD B !

$ ! <;<-

--<

2:3 0%

%

#01 04 +6)

>4

9EF:8;---9

10 ⁻³ 10 ⁻² 10 ⁻¹ 10 ⁻²

10 ⁻¹ 10 ⁰

ν

log(max(error on the interface))

ν ^1/2 optimized Schwarz coupling with (6)

- ;FB @$ " $

" "

½

¾

/ # /

" # ';3,