Une Methode de partition de domaine pour l'equation d'advection-diffusion
47
0
0
Texte intégral
(2) . .
(3). . . .
(4) .
(5). .
(6) . ! "# %$'& (*)+ (,) - + .0/1)2- + .436587,) 9 : !;' <>=@?2A2?2BDCFEHGIA2J2KLGM%N!O2J2G PHQSRUTWVYX[ZU\]Z^Q`_ aSbFcedZ!f gihjV@ZUf X[hHk ZU_ bFcml c6l#hjRURonWpqhrk ktsHX[nWu'Z^_wvxhyQYzSg|{'}w~ {i,vxnWehT QY_[hq6npyhjg ?%" &`"# = ;'&` ! &?%"# &` ! "#;<e .
(7)
(8) . Z!g \ Z^f _[enYV`Z gwV`Z V@Z!f Ron\]Snxgihq_[hqnWQ V`Z V`nW\ T hyQZ6nzeX XZ!f ginzSV`X Z pqZ!g2Zf z T _[hqnWQSg T!z V@ZUf X h ZUf Z!g6 T X[_ hyZUpqpyZ!gginQ`_ST!X[_ hRozepqhZU X ZU\]ZUQY_STVeT e_ZUf Z!gDT z RUT pjRozepW T X T!pypZU pyZxc PHpypyZ g g'nWQY_S TWgYZUf Z!g#gizeX pyZ V Z f RonWze TWZtV`z V`nW\ T hyQZ V`ZwR^T pR zepeZUQMg'nWzSg'V`n\T hqQeZ!g#epyzSgHSZU _ hy_ gx g'zeX#pyZ!g zeZ^pgrnQ XZ!f ginze_ V`Z!g#ginzSgi eX[nepZ^ \]Z!grhqQSV@ZUf SZUQSVT QY_ g#V`Z _ T hqpypqZ@XZ f V`zehy_ Zxc l#Z X T!eSnWX[_eXZ f giZUQY_[Z p ZUf _[zSVYZ2V zeQ8\ nYV ZU pyZ2pqhyQ Z f T hyX Z2V TWV x Z Ro_[hqnWQeV`h!zSg'hynQ Z^Q2zeQeZMezehg V`Z^z 2 V`hq\]ZUQSg'hynQSgV" Z!g'STWRoZ c{p#RonW\ 6nX[_ ZzeQeZ
(9) ZUf _[zSVYZ_[ ZUf nX[h# zeZMVYz X[n
(10) p ZU \]Z \]nYV"Z^ pyZwZU_ VYZ!g@XZ!f g'zepy_ T _ g QYze\ ZUf X h$x zeZ!g c.
(11) .
(12) . c b%n_[
(13) h W T! _[hqnWQ"!#!!$!!$!!$!!#!%!!#!%!#!!$!!$!!$!!!$!!#!%!#!! & c(' b Z^f _[enYV`Z g ZUf Q|ZUf X T pyZ g|V`Z V@Z!f Ron\]Snxgihq_[hqnWQV`Z V`n\T hqQeZ)!$!!#!%!#!! * c(+ sHXZ!f giZUQY_ T!_[hqnWQV`Z p ZUf _[zSVYZ,!!#!%!!#!%!#!!$!!$!!$!!!$!!#!%!#!! . /Y' c PH02351 _ 46zSV`37Z 4_ |ZUf n X[h$xze Z<48!3 !$9! : !$! 3!#0 !%!!#!%!#!!$!!$!!$!!!$!!#!%!#!! ; = Y' c c srn gihy_ hynQ2V`zeX n
(14) epZU \]Z"!!#!%!#!!$!!$!!$!!!$!!#!%!#!! = Y' c c(' P#RoX[hq_[zeX Z V`zg?> gi_ Z^ \]ZwZUQST!X[_[hq_[hqnWQ7!!$!!$!!!$!!#!%!#!! @ Y' c c(+ P T pyz T _[hqnWQ V`z X TWVYhyZUQY_"!#!%!#!!$!!$!!$!!!$!!#!%!#!! A Y' c cB& b ZUf _ enYV`ZVYZ VYZ!g[RoZ^Q`_ ZC!!#!%!#!!$!!$!!$!!!$!!#!%!#!! + Y' c(' {\]pUZUf \]Z QY_ T _ hynQ ZU_ XZ!f g'zepy_ T _ g QYze\ ZUf X h$xzeZ!gD!!$!!$!!!$!!#!%!#!! + Y' c(Y' c p WnWX hy_ e\]Z !!$!!#!%!!#!%!#!!$!!$!!$!!!$!!#!%!#!! + Y' c(Y' c(' QST!pE> giZ V`Z pTR nWQ xZUX ZUQSRoZF!#!!$!!$!!$!!!$!!#!%!#!! + G /Y+ c PH02351 _ 46zSV`3 Z _ | ZUf n 46X[h$x3 ze Z< ! !$ !3 !$0 !!#!%!!#!%!#!!$!!$!!$!!!$!!#!%!#!!C.H'IG+ Y+ c c b%nYV ZUf pqhg T _[hqnWQ V`zeX[nepZU \ ZJ!#!!$!!$!!$!!!$!!#!%!#!!C'I+ Y+ c c(' P#RoX[hq_[zeX Z V`zg?> gi_ Z^ \]ZwZUQST!X[_[hq_[hqnWQ7!!$!!$!!!$!!#!%!#!!C'& Y+ c c(+ ~Z!f ginpyze_ hynWQK!$!!$!!#!%!!#!%!#!!$!!$!!$!!!$!!#!%!#!!C'I* Y+ c cB& ~|ZU\T X zZ!gL!$!!$!!#!%!!#!%!#!!$!!$!!$!!!$!!#!%!#!!C+ A Y+ c(' {\]pUZUf \]Z QY_ T _ hynQ ZU_ XZ!f g'zepy_ T _ g QYze\ ZUf X h$xzeZ!gD!!$!!$!!!$!!#!%!#!!C+ A M N0 9 : O..
(15) . . . c ~|Z!Ronz YX[ZU\]Z^Q`_ !$!!$!!$!!#!%!!#!%!#!!$!!$!!$!!!$!!#!%!#!! * c(' s T X[_ hy_ hynWQ !%!#!!$!!$!!$!!#!%!!#!%!#!!$!!$!!$!!!$!!#!%!#!! 'Yc p WnX[hq_[e\]ZtV`Z XZ f ginWpqze_[hqnW)Q !#!%!!#!%!#!!$!!$!!$!!!$!!#!%!#!! & 'Y(c ' v R Z^f \T V Z^f _ T hqpypjT QY_@pTVYhg[R XeZUf _ hg[T!_[hqnW"Q !#!!$!!$!!$!!!$!!#!%!#!! * 'Y(c + l#n Q xZ^X WZ^QSRoZ pyhqQ|Z!f T hqX[F Z !!#!%!#!!$!!$!!$!!!$!!#!%!#!! * 'YBc & v nWpyz_[hynQ%_ nWzSg|pyZ!g V`h STWg V`Z _[ZU\ Sg !!$!!!$!!#!%!#!! 'Y(c *
(16) }n\ eX ZM V hq_ZUf X T _ hynWQ g ST!X hy_ZUf X T!_[hqnWQ V`Z] p T p WnWX hy_ e\]ZMV`Z VYZ!g[RoZ^Q`_ ) Z !%!#!!$!!$!!$!!#!%!!#!%!#!!$!!$!!$!!!$!!#!%!#!! 'Y(c - v nWpyz_[hynQ T 7!#!%!!#!%!#!!$!!$!!$!!!$!!#!%!#!! 'Yc v nWpyz_[hynQ T - )!%!!#!%!#!!$!!$!!$!!!$!!#!%!#!! = 'Y(c = PHX[X[Z^zeX !$!!$!!$!!#!%!!#!%!#!!$!!$!!$!!!$!!#!%!#!!C' A 'Y(c @ ovxnWpqze_[hqnWQ_[nWz g pqZ!g@V`h ]STgV`Z _ ZU\]Sg !!$!!!$!!#!%!#!!C' A 'Yc 9A }nW\ eX Zw V hy_ZUf X T!_[hynQSg !!#!%!#!!$!!$!!$!!!$!!#!%!#!!C' 'Yc v nWpyz_[hynQ T F!#!%!!#!%!#!!$!!$!!$!!!$!!#!%!#!!C' 'Yc ' v nWpyz_[hynQ T - !%!!#!%!#!!$!!$!!$!!!$!!#!%!#!!C'I' +Yc d nW\T!hyQeZ \]nY"V Z^ pyZ ZU_ RonWQ V`hy_ hynWQ g|T z pyhq\]hy_ Z!g !!$!!!$!!#!%!#!!C'& +Y(c ' l#nQSV`hq_[hynQSg T z pyhq\]hy_ Z!grZUQ 'd !#!%!#!!$!!$!!$!!!$!!#!%!#!!C'I@ +Y(c + l Tgi _[Z!g'_ l#enYRMa6l#nWQ V`hy_ hynWQhyQehq_[hjT pyZ !#!!$!!$!!$!!!$!!#!%!#!!C+I' +YBc & l Tgi _[Z!g'_ l#enYRMa6vxnpyze_ hynW Q SQST!pyZ T & !$!!$!!!$!!#!%!#!!C+I+ +Y(c * l Tgi _[Z!g'_ l#enYRMaeP xnWpqze_[hqnWQV`Z!g T pqZUzeX g T p hyQY_[Z^ X TWR Z !$!!#!%!#!!C+& +Y(c - l Tgi _[Z!g'_ l#enYR]aS}n\ X[Z V hy_ZUf X T!_[hynQSg@SnWzeXt p T!p nWX[hq_[e\ Z V`Z V`ZU g RoZUQY_[Z !!%!#!!$!!$!!$!!#!%!!#!%!#!!$!!$!!$!!!$!!#!%!#!!C+& +Yc l Tgi _[Z!g'_ l#enYRM!a T pqZUzeX V`#Z " SRoX hy_ Z^ X[ZtV`Z RonWQ xZUX ZUQSRoZ T $ !!C+I* +Y(c = l Tgi _[Z!g'_ l#enYRM!a T pqZUzeX V`#Z " SRoX hy_ Z^ X[ZtV`Z RonWQ xZUX ZUQSRoZ T $ ' !C+I* +Y(c @ l Tgi _[Z!g'_ l#enYRM!a T pqZUzeX V`#Z " SRoX hy_ Z^ X[ZtV`Z RonWQ xZUX ZUQSRoZ T $ + !C+I+Yc 9A l Tgi _[Z!g'_ %tT zSg g al#nQSV`hq_[hynQhyQehq_[hT!pyZ !!$!!$!!$!!!$!!#!%!#!!C+ . '.
(17) +Yc +Yc +Yc +Yc +Yc +Yc. l Tgi _[Z!g'_%tT zSg g av nWpyz_[hynQ SQST pqZ !%!#!!$!!$!!$!!!$!!#!%!#!!C+I= '8l Tgi _[Z!g'_%tT zSg g aSP xnpyze_ hynWQV`Z g WT!pyZUzX g T p hqQ`_ ZUX TRoZ !!#!%!#!!C+I@ +8l Tgi _[Z!g'_ %tT zSg gwa`} nW\ eX[Z V hq_eZUf X T _[hqnWQSgHSnWzX|p T!pnWX[hq_[e\ Z|V`ZtV`ZU g RoZUQY_[Z !!%!#!!$!!$!!$!!#!%!!#!%!#!!$!!$!!$!!!$!!#!%!#!!C+I@ & l Tgi _[Z!g'_%tT zSg g a T!pyZUzeX V`Z#" SRoX[hq_ ZU X Z V`Z RonQ xZUXWZUQ RoZ T ! & A *8l Tgi _[Z!g'_ %tT zSg g a T!pyZUzeX V`Z#" SRoX[hq_ ZU X Z V`Z RonQ xZUXWZUQ RoZ T ' & A -8l Tgi _[Z!g'_ %tT zSg g a T!pyZUzeX V`Z#" SRoX[hq_ ZU X Z V`Z RonQ xZUXWZUQ RoZ T + &. +.
(18) .
(19) 6 . . 6 , 6
(20) .
(21) . . T "ZU QZU\]ZUQY_wVYZ!gwnWX VYhyQST!_[ZUzeX g ST!X T!pypZ^ pyZ!g T \ nW_[h Z f pyZ V@Z f xZUpqnWeSZU\ ZUQ`_tV`ZMQenWz xZ T z T p WnX[hy_ e\]Z!g V`ZXZ!f ginpyze_ hynWQ VYZ!g%Zf xzST _ hynQSg T z V@ZUf X[h Z^f Z!g T X[_ hyZUpqpyZ!g cSd zQ R nW_Z f 6 pqZ!gwT p W nX[hy_ e\]Z!g|R pTWg gih# zeZ gnWQY_2ZUf _Zf TWVT e_Z!f g T z QenWz xZ^pypyZ gT!X R ehy_ Z!Ro_[zX[Z!g VYZp T!ze_[X ZnWQ V@Z f x ZUpqnWeSZ V`Z QnWz x ZUpqpyZ!g|\ ZUf _ enYV`Z!g6hqQ`_ X[hqQSgZ xzeZU\ ZUQx_|ST X X T!pyp^Z^f pyhg' Te pyZ g VeT QSgHp Z!g'6nhyX V`Z@XZ!f ginzSV`X Z|ZUQ pqZ!gHV Z!f R nW\]Snxg T QY_rZ^Q zeQeZ g'zehy_ Z|V`Z|X[n
(22) p ZU \]Z g pyzSg|g'hy\]epqZ!gHSnWzeXwpqZ!g x zeZUpjg@V`Z g@\ZUf _[nYV`Z!g _ X Z! g@Z RUTRoZ!g@Z Y hg'_[ZUQY_Uc Z!g\ ZUf _ enYV`Z!gVYZ%V Z!f RonW\ 6n gihq_[hynQ
(23) V`ZV`nW\T!hyQeZg'nWQY_ zeQ
(24) V`Z g T` Z!gMV`ZRoZU_ _[Z X Z!R eZUX R eZxcPHpypqZ!g RonWQSg'hg'_[ZUQY_ ZUQzQ4V@Z!f RonzeSTW ZV`z V`n\T hqQeZ]VYZ]RUT!pRozpHZUQ4g'nWzSg' VYnW\T!hyQeZ!g#g'zeX@pqZ!g x zeZUpjg nQXeZ!f g'nWzSV`X TV`Z!g ginWz gi eX[ne pZU \ Z!gHhyQSV Z^f 6Z^QSVeT QY_ g V`Zw_ T hypqpyZ XZ!f V`zehq_[Zxc Z!g T T QY_ T Z!g|Z!gi Z^f XeZ!f g|g'nWQY_|QenW\ e X[Z^z % a P QV@Z!f RonzeST QY_VYZ X[nxg X[n
(25) p ZU \]Z gS nWQ4SZUze_ Z gi ZUf X ZUX XZ!f g'nWzSVYX[Z V`Z!g X[n
(26) p ZU \]Z g R nW\]epqZ Y Z!gHenWX gV T _ _[ZUhqQ`_ ZwSnWzeX pyZ!g@nX V`hqQST _ ZUzeX g|g[RUT!pT hqX[Z!g|TRo_[zZUpg c Z T hy_ V`Z2XZ!f ginzSV`X[Z V`Z!g X[n
(27) p ZU \]Z g epyzSgM6Z^_[hy_ g T!\ZUf pqhynWX ZpyZ2R nWQSV`hq_[hqnWQe QeZU\]ZUQY_HZU_ V`nWQ R TRURZU pqZUX[Z pyZ g Y hy_[Z g[giZ g@V`Z R nWQ x ZUX ZUQSRoZtV`Z!g|T!pW nX[hq_[e\]Z g VYZ XeZ!f g'nWpyz_[hynQV`Z!g]Zf x zST _ hynQSgT!z V Z^f X[h ZUf Z!g#ST X _[hqZUpypqZ!goc Q SZUze_XZ!f ginzSV`X Z@VYZ!gwZf x zST _ hynWQ gV`h!tfZUX ZUQ`_ Z!gSgizeX R STWRozQ V`Z!gg'nWzSg'V`n\T hqQeZ!g ZUQ nWQSR _[hynQFVYZ!gwRUT!X TWR _eZUf X hgi_ h$x zeZ!g|e >eg'h$x zeZ!gwV`z eX n
(28) e pZU \]Z ST!X[_ hy_[hqnWQ2ST!X \]nYV ZU pqZwe >eg'h$x zeZ! c. &.
(29) . '. . rh WzeX. Z c ae~|Z!Ronz `X ZU\]ZUQY_ QZ gi ZU X Z@SnWz xnWhyX Z `pynWhq_[ZUXpqZ!gHV`h tfZUX[ZUQY_ geX nYRoZ!g[g'ZUzeX gHV`Z!gr\ TWR ehyQeZ gST X X T pqpZU pqpyZ!g #ST X|Z `ZU\ epyZtb%ZUh x n V`Z \T Q h ZU X ZZ RUTRoZxc.
(30) .
(31) . . v nWhy_ zeQ V`nW\ T hyQZ nz xZUX _wV`Z V`Z X[nWQY_[hZU X[Z c Q RonWQ gihV"ZU X[Z pyZ eX[nepZ^ \]Z g'zehT!Q`_ a ! # VeT!QSg " ! n"z Z!g'_|zeQ%n|ZUf X T _[Z^zeXwVYh!tfZUX[Z^Q`_ hyZUp$#2zeQ_[Z^X[\]Z g'nWzeX RoZ V`nWQQ|Z f ZU_ " p hqQSRonWQQ`zeZ c QV`nhy_@X T u'nWz_[ZUX T!z X[n
(32) p ZU \]Z|XeZ!f RZ f V`ZUQY_@VYZ!g|RonWQ V`hy_ hynWQ g|T z Mpyhq\]hy_ Z!gxT!QSgih zZ VYZ!g|RonWQ V`hy_ hynWQ g hqQehy_ hT pqZ!goc sHT!X[_ hy_[hqnWQenQSg T pynX g Z^Q%VYZUz g'nWzSg'V`n\T hqQeZ!g|SnWzeXtgihq\]epyh S ZUX^a {pZ Yhg'_[Z V`Z^z ]\ ZUf _ enYV`Z!g#eX[hqQSRohqST pqZ!goa ZwX[Z!R nWz YX[ZU\ ZUQ`_ i l WzX[Z ! n"z pqZ!g#V`ZUz V`n\T hqQeZ!g @ ZU_ ZU\ ehZU _[ZUQY_|p zeQgizXp T z_[X[ZtZU_|n"z T pynX g% Z!g'_|zeQeZ gizX TWR Zxc *.
(33) . '. . . Z c ' aSs T X[_ hy_ hynWQ T T X[_ hy_ yh nWQ 'l zeX[Z c 'Mn"z8 pqZ V`nW\T!hyQeZ Z!g'_V Z!f R nWze Z2f Z^Q `V ZUz ST X _[hyZ |g V`hg'_[hyQ Ro_[Z!g ZU_ V`Z X[nQ`_ h ZU X Z RonW\ \ zeQZ% c rh WzeX.
(34) !"# $%& $
(35) (' *) +,* -.
(36) .. / . . . . 0 21 . Z g \ ZUf _[nYV`Z!g VYZ%V Z!f RonW\ 6n gihq_[hynQ4V`ZV`n\T hqQeZ nQ`_Z^f _eZf T epyh$xz ZUf Z gT2 V`ZQen\] X[ZUz eX n
(37) epZU \]Z!g pqZ]X[Z RonWz YX[Z^\]ZU\_ SST!X Z YZU\]pyZ SZ!gi_Z^f _[zSV`h^Z f T% p {'}w~{'1ST!X 3 l dws @ '54o pT@ T X[_ hy_ hynWQ TZUf _Z f _[X T!hy_ZUf ZHSnWzeX V`Z!geX n
(38) epZU \]Z!geZUpqpyhy_[h$xzeZ!geST!X 3 %ts#d = +54 Z^_ 36 zST @ 4c sHT!X RonWQY_[X Z SnWzeX pqZ!g2Zf z T _[hqnWQSg zeh#QeZMg'nWQY_ STWg V`ZM_ >`SZZUpqpyhy_[h$x zeZ epjT]pyhy_ _ZUf X T!_[zeX Z Z!gi_ S Z!T!zSRonWz%epqzSg@ST z ` X Zxc }nzSg@T x nQSg@V`nQSR RonW\]\ ZUQSRZ#f ST!X]ZUf _ zSV`hyZ^X zQ eX n
(39) e pZU \]Z|\]nYV"ZU pyZ axnWQ T R enWhjgih p Zf x zST!_[hynQV TWV x Z Ro_[hqnWQeV`h!zSg'hynQV TS nWX V8T x Z!RzeQeZ2VYhy\]ZUQ gihynQV Z!gi TWRoZezehg VYZUz c Z!g|n
(40) e u'Z Ro_[h g@ginQ`_ pyZ g@gizh T QY_ g a. -.
(41) c srZUze_ nQXeZ!f g'nWzSV`X Z@zeQZZf z T _[hqnWQ QenWQe ZUpqpyhy_[h$xzeZ#ST!XHzeQMT p WnX[hy_ e\]Z V`Z ST X _[hy_ hynQ 'Yc 6 zZUp_ >Y6Z V`Z Ron Q xZ^X WZ^QSRoZwne_[hqZUQ`_ nQ +Yc srZUze_ nQ _ hyX ZUX|eX[n S_t V zeQZ T X R ehq_[Z!R _[zeX ZwST X T pqp ZU pqZ. .
(42)
(43) 6 .
(44) L "
(45) .
(46) . . Q. . 21.
(47) . . . 1.
(48) "!$& # %'$. xZUze_XZ!f g'nWzSVYX[Z@pqZHeX n
(49) epZU \]ZD\]nYV ZU pqZ#gizeh T QY_#a!R
(50) Z!g'_zeQZMZ f zST!_[hqnWQ V TV xZ!Ro_ hynQe VYh!zSgihqnWQ4T x Z!RVYZ!g RonWQSVYhy_[hqnWQSg T z S nX VFV`ZM_ >`SZ dhyX hR epyZ^_ZU_ nz4V`ZM_ >`SZ }ZUze \ T QeQ
(51) ZU_zeQ_[Z^X[\]Zg'nWzeX RoZ)(xc Q
(52) V@Z!f g'hyX[ZzeQeZ ginWpqze_[hqnWQ pyn
(53) T pyZ gizeX p hqQ`_ ZUX T!pypyZ 3 A+*9 4c Zg?>gi_ ZU \]Ztg Z!f RoX[hq_|T!pynWX g a. A. Q%Snxg'ZT!pynWX g. . 0 1 354602798;:<0=7>7 ?( ,-- 2 . A@CBD@ -- 3 -/ 3. YV Z!g|RonWQ V`hy_ hynWQ g|T z SnWX Veg B A UZ _ B ,zQeZ RonWQSVYhy_[hqnWQhyQhy_[hjT pqZ " BE* A V`nWQ|Q Z f 021. . 0GF6H. . ' !. . . 8I0GF. Z^_ nQFX T!\ ZU QeZ pT]XZ f ginWpqze_[hqnWQ V`zFeX n
(54) epZU \]Z RonW\]pyZU_ T zeQZ]g'zSRURoZ!g gihqnWQ V`Z X[n
(55) pZU \]Z!g T R T
(56) xzeZSTWg V`ZM_[ZU\] goc Q QeZM g hyQY_Z^f X[Z!g giZhR h xz $T] pjT XZ!f ginpyze_ hynQFV`Z RoZ X[n
(57) p ZU \]Z c Z g >eg'_ ZU \]Z zeh V`nWQQeZJ0GFKH L0 Z gi_ T pqnWX g pqZ g'zehT!Q`_ a MLN O 0 354602798;:<0=7>7 3. # A. *P "@CB
(58) @. ,V`Z g|RonWQSVYhy_[hqnWQSg|T!z SnWX Vg ZUQ. =. B. A. ZU_|ZUQ B. . ' !('.
(59) n"z . dwT!QSg Ro Z ZU _%ze#hDg' zehy_ `nQ2R enWc hjgihy_ V Z^f _[zSV`hqZUX@pqZ N. 1. ?(3. N 0GF. eX[nepZU \ Z '`c(+ c. . 0 3 4 027985: 027>7 ,-- N I . 0 -- 0 -/ @CBD@. A. A $ $ A. #. ' !(+. ) $ " 9 + $&# %'$ $ Q xZUze_XZ f ginWz V`X[Z g`ZUf ST!XZUf \ ZUQ`_g'zeXrp hqQ`_ ZUX T pqpyZ 3 A * 4xZU_DgizeX 3 *9 4c! Q hqQ`_ X[nYV`zhy_pT T!pyZUzeX T p hyQY_[Z^ X TWR Z B c Q XZ!f ginze_DT pqnWX gpyZ gV`ZUz ginzSgi eX n
(60) epZU \]Z!gg'zehT QY_ gHa ,-- N 0 354607
(61) 8I: 07> 7 # -
(62) . 0 A 0 ' !B& -- 0
(63) --/ . ZU_. A. @CBD@. ,-- N 0 -. 0 -- 0 --/. . . 35460 7 . A. . 8I: 0 7>7. #. ' !(*. @?B @. T nQSRo_ hynWQ)0 V`nWQY_ 0
(64) ZU_90 ginQ`_ pyZ!g@X Z!gi_ X[hjRo_[hqnWQSg|T!z hyQY_[ZUXWT!pypqZ!g 3 A+* 4 Z^_ 3 *9 4 X Z!giSZ!R _[hxZ^\]ZUQx_|Z!g'_RonQ`_ hyQYzeZZU_ g T _[hjg T!hy_ p Zf xzST!_[hynQ V`h!fZUX ZUQY_[hyZ^pypyZ ST!X \ nWX R Z!T z c`l#ZwQ Z!g'_@R ZUSZUQSVeT!Q`_ STWg#zeQeZ g'nWpyz_[hynQ[pqhg giZ V`z]eX n
(65) epZU \]Z|hyQhy_[hjT p T \ nWhyQ g x zeZwpTV ZUf X[h ZUf Ztginhy_|ZUpqpyZU \ZU \MZ|R nWQY_[hyQYzeZxc Q]Z!gi_ VYnWQSR T \ ZUQ|Z f T R eZUX R eZ^X pjT T pyZ^zeX V`Zx zeh\]hqQehy\ hyg'ZpqZ RoX hy_ Z^ X[Za ' !( 0 7
(66) 28I0 7 . rs nzeX|R ZUpT nQ]hy_ ZU X[Z g'zeX ZU_ T QV`Z RonQSgi_ X[zehqX[Z zeQeZw\ ZUf _[enYVYZ V`Z V`Z!g RoZUQY_[Z hyp R nWQ `hqZUQ`_ V Z f T!pyzeZUX xpyZ WX TV`hyZ^Q`_ DRoZ zehSZ!g'_ T!hy_ VeT Q g@pT g'Z!Ro_ hynWQ gizeh WT!Q`_ Zxc. @.
(67) ) !> " $ sDnWze
(68) XM Z f T pqze ZU X#pyZ X TV`hyZUQY_ V`Z WnQ SZUX _[zeXSZwpyZ RonQ`_ X n pyZ V`Z ZU_#nWQ
(69) Z f T pyzZ 00
(70) Z^ _ 0 0 ZU _ giSnWQSQYT!_ pypyZUZ!\ g|ZUg'Q`nW_pyz _[#hync QSg|V`Z!g V`ZUz g?>gi_ ZU \]Z!gHpyhqQ|Z!f T!X[hgYZ!f g@g'zehT!Q`_ a. ,-- N 0
(71) 354 07
(72) 8I: 07>
(73) 7 A - . 0 A $ A ' ! -- 0 $ --/ . . . A. ZU_. @?B @. A $ $ A . ,-- N . ---/. X enQ2T]a
(74) . . 0. 354. 0. 0 7. 8I:. 0 7>7. ' !(=. 0. @.
(75) '. B @. ' 0 7
(76) ' 28 0 7 ' {pDRonQ YhyZUQY_|VYnWQSR V Z YeX hy\]ZUX 0 7
(77) ZU_ 0 7 @ZUQ nQSRo_[hqnWQ V`Z 6csrnWzeX R ZUpTnWQ4ze_[hqpyhjgiZ]pjT%_[Z!R eQeh# zeZ RopjTWg[g'h$xzeZV
(78) ZUf pyhq\]hmQST _ hynQST!Xp Zf z T _[hqnWQ4TV u'nW hq Q`_ Zxc Q]hqQ`_ X[nYV`zhy_@zQ Z^f _ T _ TWV u'nhyQY_ B T 0 ZU_@zeQ ZUf _ T _ TWV u'nhyQY_ B T 0 c Q ZZ Ro_[zeZ|pqZ@eX nYV`zehq_@g RUT pjT hqX[Z V`Z '`c DST X B ZU_ V`Z 'Yc DST!X B Z^_HnWQMhyQY_ Z X[Z T X ST X _[hyZ eRoZ xzehV`nQeQeZ a . 0 7. 28;0 7. .
(79) . . . . A. .
(80) M Q H0 Z! Nf RoX 0hy_ pyZ XZ! f g'ze0 3 py_ T _ V` Z 31 p46 hyQY3 _Z .f WX T!_[hqnW QV`Z R ST
(81) xzeZ _[Z^X[\]Z a
(82) hjV`ZU\
(83)
(84) .
(85)
(86) .
(87)
(88)
(89) A
(90)
(91) A.
(92)
(93) . QX[Z X[nzeSZRoZ!g@Z `eX Z!g[g'hynQSgwa "
(94)
(95). A A QR nWhg'hy_ T!pynWX g _[ZUp xzeZMa A A A $ A QT T!pynX g a
(96) ' $ ' . 0. 0 7. 0. 8. 8. 0 7>7. 7. 3. :. 3O:. 0 7. 0 7. 7>7. 28. 7 8. 7. 3. 0 7. N 854. 4. 28. 0. 3. 0 7. 0. 0. 8. 8. 7. 0 7. 7. +7. 3. 7>7. 8I:. 7>7. 0. 0. 7. 0. 0 7. 0 7. 854 ,-- N A. -. 7G8I:. 7>7. .. --. -/. ' !(@. J@CB
(97) @. 0 7. 4. :. I. 93. 7. ' ! 9A.
(98) M Q H0 Z! Nf RoX 0hy_ pyZ XZ! f g'ze0 3 py_ T _ V` Z 31 p46 hyQY3 _Z .f W X; T!_[hqnW QV`Z R ST
(99) xzeZ _[Z^X[\]Z a
(100) hV`Z^\ .
(101)
(102)
(103)
(104). .
(105)
(106)
(107)
(108)
(109)
(110).
(111)
(112)
(113). QX[Z X[nzeSZRoZ!g@Z `eX Z!g[g'hynQSgwa
(114). " .
(115). . .
(116) A QR nWhg'hy_ T!pynWX g #_[Z^p xzeZMa A $ A $ QT T!pynX g a ' $ ' . 0. 0 7. 0. 8. 8
(117) . 0 7>7. 8. 0 7. 7. 854. :. 3. 4. 3I:. 7. 28. 7 8. . 7. 0. 93. 7>7. 7>7. 0. 0. 0 7. --, N. 0 7. 854 7G8I: 7>7. -. ' !. --. @?BD@. 4. 0 7. 354 3. 7>7. 0 7. 8;:. -/. T!zeX T!hy_ n
(118) e_ ZUQYz. 0 7. B. .. . 0 7. 3. 3. 7. 28. 0. 8
(119) . N. 0. 0 7. 8. 0. 7. 8. 8
(120) . 7. 93. :. vxhHnQFT T hq_why\]Sn giZUXwzQeZMRonWQ V`hy_ hynWQ VYZM}Z|\T!QeQ%ZUQ 4. . E3I:. 7. A. R nW\]\]Z R nWQSV`hq_[hqnWQT z 6nX V6nzeX pyZ g?>gi_ ZU \]ZtTWV u'nhyQY_ZUQ Dc. '. ' ! '. 7. B. . nWQ.
(121) HP QX[ZUSnX[_ T!Q`_ pyZ!g#XZ!f g'zepy_ T _ g@V`Z '`c 9A #Z^_ 'Yc ne_[hqZUQY_ a. VeT!QSg@p xZ YeX[Z g[gihqnWQVYZ
(122) nWQ. '.
(123)
(124)
(125) ' ! + l#Z!R h6Z^X[\]ZU_ V hV`Z^Q`_ h S ZUX#pqZ X TV`hyZUQY_ Z f xT!p T c - . T RonWQeQ T hg g[T!QSRoZMV`Z pTMV@ZUf X[h Z^f Z V`Z RonWQ V`zehy_ TM RonWQSg'_[X zehyX Z pyZ QenWz xZUphy_ZUf XZ f T!z%\]nx> ZUQ V`Z pT nX[\MzepyZ a ! ' ! & b ZUf _[enYVYZ VYZ } Z |_[nQ2T epyh# z Z^f Z T A c
(126) 1 1 1 +. T eX[nWX T!\]\T!_[hynQ T%ZUf _Z f Zf Z!R _[z Z#f ZUQ nX[_ X T QMg'zeXDzeQ]v w
(127) }FZU_DX[ZUXeZ!f g'ZUQ`_ Z#ZUQ YhyX nWQ + A A pyh WQeZ gV`ZMR nYV`Zxc" T p WnX[hy_ e\]Z hy\ ep^ZUf \ ZoQY_Z f Z!gi_ V@Z!f RoX hy_tgizeXwpjT WzeX Z `' c `' c c T]XZ!f ginpyze_ hynWQ VYZMR ST zZMginWz gig?> gi_ Z^ \]ZMgiZ T! hy_wZUQ VYh!tf ZUX[Z^QSRoZ!g QehyZ!gtRoZUQY_[XZ^f Z!g T p nX V`X Z%VYZUz c Z2R^T pR zep@QYze\ ZUf X h$xzeZMV`Z xzeh T2zeQeZhy\]SnX[_ T!QSRoZ X[hy\ nWX VYhT pqZZ gi_|Z YepyhjRohy_Zwf g'Z!Ro_ hynWQg'zehT QY_[Z c 8;0 7. 0 7. . $ . $. $. $ . 0 7. 28. 0 7. $ $. FKH. F. F 8. F. . . . !. . . %'$. 7. . +
(128) ! . $. $. !. . . . $ . . 8. $ . . $. 7. 4 3 3 0
(129) : 3 0:0 3 TR nWQ xZUX ZUQSRoZ V`Z p T p WnWX hy_ e\]Z V`Zt}Z |_ nWQ xzeh ZUf Q ZUf X T!pyZU\]Z^Q`_HZ gi_ z TWV`X T _[h# zZ g'ZV@Z f WX TWV`ZpqnWX g zZ]pyZ ZUf X[n V`Z R eZUX R ZMf Z!g'_MT zSg gih|zeQ ZUf X n2V`Z c l Z!gi_ pqZ!T!g_ T! pyZU\]zeX[Z^Z!Q`g _# R `' Z c + z hY' gicB& Zte X[ nYY' V`c(* z#Zhy_|^_ SnW `'zecX #npT Q2nWQSRoRn_[QShygin_ QeT ZU_[pqZ pyZ ze Q`' Z c - R #ZnWUQ Q xZUxX ZUX[ZU_ QSz]RoZwV`Z pqhyQ '`Z f c T hy+ X Zxc c vx zeT X Yhy_ Z!g[g'Z V`Z RonQ xZUXWZUQ RoZwZ!g'_ V ZUQ YhyX[nQ M+ V Z!f R^TWV`Z!g@SnzeX A hy_ZUf X T!_[hqnWQSg c + .
(130) l T!pRozpV`zSTWg V`Z _[ZU\ Sg. ~ Z!f ginpyze_ hynWQ dw{'~ P l ~Z!f ginpyze_ hynWQ wd " t{'} srnzeX R
(131) T xzeZ ginWz giV`nW\T!hyQeZ }wP t } l t } P#~ t% P } l P } t}
(132) t{ l t } P#~ t% P } l P } t}
(133) w{ rh WzeX. Z#'`c aSp WnWX hy_ e\]ZtV`Z XeZ!f g'nWpyz_[hynQ. &.
(134) A. . '. } 3 'W} } n\ eX ZwVYZ SnhyQY_ g V`Z `V hg RoXZUf _ hg T _[hqnWQc. A. #'`c '. rhzeX[Z. 3. '. aSvYR |ZUf \T V@ZUf _ T!hypqpT QY_@pjTV`hg RoXZ^f _[hg T _ hynWQ. Courbe d’erreur semi-logarithmique 0 "fort.4" "fort.7" "fort.10" -2. Log(J/J0). -4. -6. -8. -10. -12. -14 1. 2. 3. 4. 5 6 Nombre d’iterations. 7. #'Yc(+a wl#nWQ xZUX ZUQSRoZwpqhyQ Z f T hyX Z. rhzeX[Z. *. 8. 9. 10.
(135) Solution globale tous les 10 Delta T 1 "fort.2". Solution U. 0.8. 0.6. 0.4. 0.2. 0 0. 0.2. rh WzeX. Z'`c &%a. 0.4. . 0.6. 0.8. 1. Abscisse X. v nWpyz_[hynQ_[nWz g pqZ!g|V`h STWg V`Z _[ZU\ Sg. Nombre d’iterations de gradient pour chaque iteration en temps 10 "fort.8". 9. ITER GRADIENT. 8. 7. 6. 5. 4 0. DhWzX[Z. VYZ!g[RoZ^Q`_ Z. 10. 20. 'Yc(*0a
(136) ]}nW\. 30. 40 50 60 ITER EN TEMPS. 70. 80. 90. 100. eX Z%V" hy_ZUf X T!_[hqnWQSgST X hy_Z^f X T _ hynQV`Z2p T p WnX[hy_ e\]ZVYZ. -.
(137) T=1*Deltat T : evolution de la solution a chaque iteration 1 "fort.15". Solution U. 0.8. 0.6. 0.4. 0.2. 0 0. 0.2. 0.4. 0.6. 0.8. 1. $Z 'Yc(-]a
(138) vxnpyze_ hynQ T T T pqZUzeXHhqQ`_ hT!pyZ|VYZ|p hqQ`_ ZUX TRoZ T2ZUf _Z f R enhg'hyZ Z f xT pqZ Tw pTwV`Z^\]heg'nW\]\ Z@VYZ!gT pqZUzeX g VYZ!g|RonWQ V`hy_ hynWQ gT!z ]pyhq\]hy_ Z!gHV`Z dhyX hR epyZ^_Uc Abscisse X. rh WzeX. .
(139) T=6*Deltat T : evolution de la solution a chaque iteration 1 "fort.3". Solution U. 0.8. 0.6. 0.4. 0.2. 0 0. 0.2. 0.4. 0.6. 0.8. 1. #'Yc a wvxnpyze_ hynWQ T - Abscisse X. rhzeX[Z. dwT!QSgHRoZ RUTWgD\]nWQenYVYhy\]ZUQ gihynQeZUpn"zM nWQ R ZUX R eZ T XZ f ginWz V`X[Z zeQeZ|g'ZUzepqZ]Zf xzST _ hynQ g RUT pjT hqX[Z A 6nQ2SZUze_ TRohypqZU\]ZUQx_ RonWQY_[nzeX[QeZ^XwRoZ^_[_[Z V`h Rozepq_Z f ZUQ V`nWQeQZUQ`_ T!z2RoX hy_ ZU X[Z pTQenWz xZUpypqZwV Z f SQehy_ hynQ%g'zehT!Q`_ Z a 0 7
(140) 28;0 7 ' ! * pqnWX gST xZ!RpjT \ ZU \]Z V Z f SQehy_ hynQ%VYZ!g|g?>gi_ ZU \]Z!g TWV u'nhyQY_ genQT a
(141) 0 7
(142) 28 0 7 A. ' ! ZU_ pT RonWQ xZUX ZUQSRoZ Z!gi_ xzSTWV`X T _ h$xzeZxc l#n\]\]Z$"wZ!g'_rZ^Q T hy_ zeQeZ nQSRo_ hynWQMT S QeZ VYZ MpTRonQ xZUXWZUQ RoZZ gi_tT _[_ ZUhyQY_[ZtZUQZ eTRo_[Z^\]ZUQY_ ' hq_ZUf X T _ hynWQ goc 4 3 3 0 3 } nWzS gwT xnQSg Z g[g[T9> Z f _ X[nWhjgwT eX[nYhy\T!_[hynQSg V`Z pjT V Z^f X[h ZUf Z SnWzeX RUT pjRozepyZ^X c =
(143) +7. 7. 8.
(144)
(145) QeZ V`h!tfZUX ZUQSRoZR ZUQ`_ XZUf Z xzeh TWg[g'zeX[Zp nWX V`X[Z SnWzeXpjT%V Z^f X[h ZUf Z RoZ zeh Z!gi_ RonWQSg'hg'_ T QY_ T xZ!RpqZ g R ZUf \T T p nWX VYX[Z#' c
(146) QeZ V`!h fZUX ZUQSRoZ RoZUQY_[XZ^f ZwV nWX V`X[Z#' T T pqZUzeXZ `pyhR hy_[Z xzeZ# p nWQ R^T pR zepyZ#T!QST p >`_ h$xzeZU\]Z^Q`_ T@ T X[_ hyXDV`Z N * : * 4 c PHQ Z ZU_|pyZ!g|VYZU z g >eg'_ ZU \]Z g TV u'nWhqQ`_ gg'nWQY_|enW\
(147) n Z^ QeZ!g@ZU_|pqhyQ Z!f T!hyX Z!goc } nWzSg]T xnQSg]RonQSgi_ T _Z2f zQeZ RonWQ xZUX WZUQSR Z xzSTV`X T!_[$h xzeZ giZUzepqZU\]ZUQY_ SnzeXpyZ%X[ZU \ hyZUX RUTWg 6ZUQZ ZU_ pyZ!g V`ZU z T!ze_[X Z!gg'nWpqze_[hqnWQSgwV Z f ZUf Q ZU X[ZUQY_ xZUX g@zeQeZMRon Q xZUX WZUQ RoZ pqhyQ Z f T hyX Zxc. 3 3 4 3 3 3 0: Z RUT!pRozp nWX[\ ZUp nWzeX Qehy_ a
(148)
(149) ' ! ' T xZ!R
(150) "& QFSnxg'Z ZU_ Q4X[Z^\T X zeZ xzeZ 0QZ V ZUf SZUQSV xzeZ V`Z c 6 zST!QSV !T pynX g
(151) A c!V`nQSR 0 N 3 3 3 3 3 31 3 0 E 3 0 3 3 0 3 c 3 9$0 3 QXZ f ginWz_pqZw\ ZU \]Z|X[n
(152) p ZU \]Z zeZteXZ!f RZ!f V`ZU\]Z^Q`_ W\T hjg hjRohT xZ!R
(153) ' ' TR nWQ xZUX ZUQSRoZ|Z!g'_ T pynX g xzSTWVYX T _ h$xzeZ a l WzeX Z!g `' c(= `' c @ Y' c I HZ^_ Y' c ' c . 28. 0 7. 0 7. (. :. 4. 3. . . . N : N * 4 * :. (. . . ?0 7. @. 28I0 7.
(154) Courbe d’erreur semi-logarithmique 0 "fort.4" "fort.7" "fort.10". -2. -4. Log(J/J0). -6. -8. -10. -12. -14. -16 1. 1.2. 1.4 1.6 Nombre d’iterations. 1.8. 2. #'Yc(=]a PHX X[ZUzeX. rhzeX[Z. Solution globale tous les 10 Delta T 1 "fort.2". Solution U. 0.8. 0.6. 0.4. 0.2. 0 0. 0.2. rh WzeX. Z'`c @ a. 0.4. 0.6. vxnWpqze_[hqnWQ_[nzSg|pyZ!g|V`h 'A. 0.8. Abscisse X. TWg V`Z _[ZU\] g. 1.
(155) Nombre d’iterations de gradient pour chaque iteration en temps 2.2 "fort.8" 2.15. ITER GRADIENT. 2.1. 2.05. 2. 1.95. 1.9. 1.85. 1.8 0. 10. 20. rh WzeX. 30. Z#'`c A a. 40 50 60 ITER EN TEMPS. }nW\. 70. 80. 90. 100. eX ZwV hy_ZUf X T!_[hynQSg. T=1*Deltat T : evolution de la solution a chaque iteration 1 "fort.15". Solution U. 0.8. 0.6. 0.4. 0.2. 0 0. 0.2. 0.4. 0.6. #'Yc a '. vxnpyze_ hynWQ T . Abscisse X. rhzeX[Z. 0.8. . 1.
(156) T=6*Deltat T : evolution de la solution a chaque iteration 1 "fort.3". Solution U. 0.8. 0.6. 0.4. 0.2. 0 0. 0.2. 0.4. #'`c 'a . 0.6. vxnWpqze_[hqnWQ T . Abscisse X. rhzeX[Z. 'I'. 0.8. - . 1.
(157)
(158) 6 .
(159) L
(160) "
(161) .
(162) .. 21. . .
(163) . - G $ !> QXZ!f g'nWze_tgizX a. . . . ". 1. "!$& # %'$. 0273 0 8I: 027>73I0!$ A
(164) 1 T pynX g90GF6H 0 Z!g'_wg'nWpyz_[hynQV`Z +`c ' . + !. 0213. nQ%Snxg'ZJ021. 027 3 08I: 027>73I0 $# * P 8 @CBD@ 0 8 * $ P 8 @ @ 0 BE* 8 $L0 BE*9 $ A P 8 @CBD@ 027 * A P 8 @ @ 1 ZU%_ # N 0 F BE* #ZU_|ST!X|Z `Z^\]epyZ a ,- $ 0 g'h @ A . 0 g'h AJ@ -/ $ Z Y 8
(165) P 8 @J@ . ,-- N 0C3 .. --/. n"z N. . 'I+. * P 8. J@. @. + !(' + !(+.
(166) F. ". ". A . F. ". . A. " F. A. #+`c. DhWzX[Z. aSdnW\T!hyQeZt\]nYV ZU pqZwZU_ RonQSV`hy_ hynQSg|T z pqhy\]hq_[Z!g ) $ " 9 + $&# %'$ $ _[hy_ X[Z#V" Z YZU\]epqZ 'nWQV Z!f RonWz6Z#pqZ#V`nW\ T hyQZ ZUQ V`ZU z ginWz giV`nW\T!hyQeZ gg?>Y\ZUf _[X h$xzeZ T X#X T!eSnWX[_ Tw p T`Z B A c vxzeX#pqZ ginWz giV`nW\T!hyQeZ -&- B * 3 8 * A 4 3 8 *9 4 nQ%XZ!f ginze_ a ,-- N " 3 " 7
(167) 3 "
(168) 85: " 7>
(169) 7 3 "
(170) $# * P BE* 3 8 * A 4 3 8 *9 4 -
(171). " 8
(172) * * P 3 8 *9 4 .
(173) . -
(174) " B * $ A * P B 33 8 * A 4 " BE* 8 --/ " A+* $ * P 8 *9 4. + !B&. '&.
(175) ZU_ g'zeX pyZ g'nWzSg'V`n\T hqQeZ#' -&- BE* 3 A+*9 4 3 8 * 4 enQXeZ!f g'nWze_ a --, N " 3 " 7 3 " 8I: " 7> 7 3 " $ # * P B * 3 A *9 4 3 8 - A+* *CP 3 8 * 4. " . . - " . BE*9 $ A * P2B 33 A+*9 4 " BE* 8 --/ " 7 * $ A * P 8 * 4. 94 *. + !(*. T Qenz xZ!T zzeQZ Wn Q Ro_[hqnWQeQeZ^pypyZ _[ZUpqpyZ xzeZMa + !( ' " 7 8 " 7 A * pqnWX g@pyZ WX TWV`hqZUQ`_ VYZ WT! ze_ a
(176) " 7
(177) 8 " 7 " 7
(178) 8 " 7 A+* + ! T nQSRo_ hynWQ " V`nQ`_ " ZU_ " ginQ`_MpyZ g X[Z!g'_[X[hjRo_[hqnWQSg T ZU_ X[Z giSZ!Ro _ hxZU\ ZUQ`_ Z!g'_RonQ`_ hyQYzeZ D
(179) R Z gi_ zQeZginpyze_ hynQ pqhg giZ V`z4eX[n ep ZU \ ZMV`ZV ZUf T X[_Mg'h@ZU_ g'ZUzepqZU\]ZUQY_#gihpT V@ZUf X[h Z^f ZQenX[\T!pyZ T p hyQY_[ZUX TWRoZ|Z!g'_ RonWQY_[hqQ`zZxcY{ pg Thy_ T Qenz xZ!T!z VYZ|_[X[n z xZUX V`Z|\T!Qeh ZU X Z Tw XZ f T pyhjgiZUX RoZU_ _[Z RonQ`_ hyQYzehy_Zxf c s T XDRonQ`_ X[Z|hR h !nWQMhy_ Z^ X[Z@QnWQ pyzSg|g'zeXzQeZ QenW\ eX[ZtXeZ f ZUf p\T hjg@g'zeX|zeQeZ nWQSRo_ hynQ c. QhyQY_[X nYV`zehy_. . . . . . . . . . $ !>G .
(180) Z^_ ginWQY_ pyZ!g|g'nWpyz_[hynQSg|V`Z!g V`ZUz g?>gi_ ZU \]Z!gHpyhqQ|Z!f T!X[hgYZ!f g@g'zehT!Q`_ a "
(181) "
(182) " "
(183) "
(184) $ A 3 3 A 4 3 9 4 $ A 9 4 "
(185) " "
(186) 9 $ A 33 9 4 " A $ 9 4 + !(= 0. 0. --, N. 3. --. .. . --. 7. 3. 8I:. 7>7 3. 8. BE* 8. --/. *. ZU_. 'I*. * BE*. +*LP +*LP +*LP *IP. 8. BE*. 8. *. 8. *. 8. *. *. 8. *.
(187) ,-- N .. ---/. --. " " " " " A A $ " $ " 9 $" A 3 9 4 " A 3. 3. 7. 8I:. BE* 8. 7>7 3. * * P 7. BE*. 8. 38. 3 +* 4 * 4. 38 *. BE*. *. *. A9 9 94. . +*LP *CP +*LP. 94. 38 *. + !(@. ~Z!f g'nWpqze_[hqnWQV`Z +Yc(= c Q%
(188) hyQY_[X nYV`zehq_@pT nWQ Ro_[hqnWQgize
(189) h T QY_[Z a T X hTpyZ|TV u'nWhqQ`_ Z V`Z " nQSRo_[hqnWQ V`Z BE* 3 8 * A 4 3 8 *9 4 '`c Q]\ zpy_[hqepyhqZ T pynX g +`c = ST X Z^_@nWQ hyQY_ Z X[Z gizX@pyZtginzSgiV`n\T hqQeZ c N "
(190) 3 " 7
(191) 3 " . + ! 9A
(192)
(193) B A 8 : " 7> 7 3 " +`c QhqQ`_ Z WX ZMT pynX gwST!X ST!X[_[hqZZU_ nWQ gihq\]epyh SZ ZUQ _[ZUQST!Q`_ Ron\]e_ ZV`Z!g RonWQ V`hy_ hynWQ gT! z ]pyhq\]hy_ Z!gren\]
(194) n ZU QeZ!gwa N
(195) 8 7
(196) 8
(197) 8I: 7>
(198) 7 3
(199) "
(200) B
(201).
(202). 3 : 8 * " 7 8 * .
(203) .
(204) .
(205) . 3 3 3O: 4 BE*9 $ " BE*9
(206).
(207).
(208). 8 3 3O: 4 BE* 8 B " BE* 8 . .
(209) . .
(210). 3 8 : A * " 7 A+* E3 3 3I: 7 4 A * A + ! &ec%rhyQ T pyZ^\]ZUQY_ WnQ%Snxg'Z
(211) 0: 5351 463 H 9 . . . . . . ---. . . . . ,-- N. . . . . . .
(212) 8 7
(213) 8
(214) 85: 7>
(215) 7. 3
(216) $ A+*LP B *
(217) 8 * $ A+*LP 3 8. .
(218) 3I :
(219) B * 8 $ A+*LP2B 3 8
(220) A+* $ "3O7 : 8 " 7 BE *9 $A * A+*L* P2PB 33 88. 38. 4 A4 A4 4. *. .. -/. --. --. --. *. 'I-. A4 . *. *. *. + ! '. 38. 4 *.
(221) ZU_|nWQn
(222) e_ hyZUQY_|pyZtXeZ!f g'zepy_ T _ gizhT QY_ a :. .
(223) A A " " 8. 7. 0 7. *. 7. *.
(224) . . . 3I:. 7.
(225) . A + ! + +*. . ~Z!f g'nWpqze_[hqnWQV`Z +Yc(@ c Q% hyQY_[X nYV`zehq_@pT nWQ Ro_[hqnWQgizeh T QY_[Z a T X hTpyZ TWV u'nhyQY_[Z V`Z# " V`Z BE* 3 A *9 4 3 8 *9 4 '`c Q]\ zpy_[hqepyhqZ|T!pynWX g +Yc(@ ST X Z^_@nWQhqQ`_ Z WX Zwg'zeX@pqZ ginzSgiV`nW\ T hyQZ '`c N " 3 " 7 3 " . + ! & B A 8 : " 7> 7 3 " +`c QhqQ`_ Z WX ZMT pynX gwST!X ST!X[_[hqZZU_ nWQ gihq\]epyh SZ ZUQ _[ZUQST!Q`_ Ron\]e_ ZV`Z!g RonWQ V`hy_ hynWQ gT! z ]pyhq\]hy_ Z!gren\]
(226) n ZU QeZ!gwa N 8 7 8 8I: 7> 7 3 " B . 3 3 3I: 7 4 * " * . . . 3 3 3I: 4 BE*9 " BE*9 . . 8 3 3O: 4 BE* 8 B " BE* 8 . . 3 : A+* " 7 A * 28 3 3O: 7 4 A * A + ! * &ec%rhyQ T pyZ^\]ZUQY_ WnQ%Snxg'Z 0: 5351 463 H 9 ,-- P BE* 3 A+*9 4 3 8 *9 4 - $ A+* -- N 8 7 8 8;: 7> 7 3. - . . 3O: 7 * $ A+* P 3 8 *9 4 + ! -- 3I: BE* 8 3I: BE*9 $ A A. -- A+* " 7
(227) 8 " 7 A * --/ P 3 8 *9 4.
(228) . . . . . . . . . . . . . . . '.
(229) ZU_|nWQn
(230) e_ hyZUQY_|pyZtXeZ!f g'zepy_ T _ gizhT QY_ a 7 8 7 A * 0 7 A+* : " 3O:" 7 A+* . . . T X[_ hyX V`Z +`c. . +. . ZU_ +Yc e nQ2RUT!pRozpyZwpjT WT!pyZUzX V`Z#
(231) 4a 7
(232) 8 7 7
(233) 8 7 A * " " " " 3I: 7
(234) A+* . 8 7 8 7 3I : A+7 * A+ * . . . . + ! . . . . . . . . . . + ! =. .
(235) $ A . . 8. 7. 7. +*. + ! @. Z!gi_|hjRohpyZ g T ze_ VYZ V ZUf X[h ZUf ZtQenWX \T pqZ -&- pTMV`h!tfZUX ZUQSRoZ ZUQY_[X Z pqZ!g T pqZUzeX g gizeX Z^_ c T hyQ gih xzeZ p Z `eX Z!g[g'hynQV`Z p T pnWX hy_[\]ZwVYZ VYZ!g[RoZ^Q`_ Za + !(' A nWQn
(236) e_ hyZUQY _ T pqnWX g . 8. 'I=.
(237) s X n
(238) epZU \]Z VYhyX[Z Ro_waSV`Z^z ginzSgiV`n\T hqQeZ!g P zST!_[hqnWQ ZUf Q ZUf X[h# zeZ a N 0C3 0273 0 8I: 027>73O0 #. $ A. BE* 8 0. . . $ . 0 8. *. BE* 8 0. . A. . $ A 8. "3O:. *. . BE* 8. rh WzeX. A $
(239). *. 0 7. A. 8I0 7. A. $ A. * 8. . 0 7. *. . 'I@. . Z$+Yc(']al#nQSV`hy_ hynQSgT!z pyhq\]hy_ Z!grZUQ W' d. A B *. . A $
(240). A. A+*. A. . B 0. BE*. A. s X n
(241) epZU \]Z TV u'nWhqQ`_ aSVYZUz g'nWzSg'V`n\T hqQeZ!g c P z T _[hqnWQ H ZUf Q Z^f X[h$xzeZa N A8 7G8 8I: 7>7 3 3I: . 9 $ A. "3O:. *. 027. . . 0. . A. $ A. B . . ! A. "3O:. 8I0 7. 7. *. A+*. "3I:. . BE* 8. $ A. A *.
(242) . . . $&%. & 9. $ . cwvxnWhq_ ez QeZ Wn Q Ro_[hqnWQ T T!pyZUzeX|Sn gihy_ hxZ YpTV Z f SQehy_ hynQa 8 + !(' RonQSV`zehq_Z f xT!pyZU\ ZUQ`_ T
(243) 8 #c 'Yc T \ ZUf _ enYV`Z V`ZtV`Z!g RoZUQY_[Z|eX nWSnxgYZUf ZwhjRoheQ Z!gi_H TWg zQeZ\ ZUf _[enYVYZ V`Zw} Z|_[nQ RUT X p hy_Z^f X T _ hynQ]Z!gi_|zQeZT!eepyhjRUT _ hynQ%"V zeQZ!giSTRoZ nWQSR _[hynQeQeZUpDVT QSg HZU_ QenWQzeQ
(244) SnWhyQY_ `Z V zQ0Z!g'STWRoZVeT!QSg pqzehy \ ZU \]Z cDdnQSR%pT RonQ xZUXWZUQ RoZ V`Zw p T p WnWX hy_ e\]Z Q Z!g'_@STg xzSTV`X T!_[$h xzeZwZ^Q ZUf Q ZUf X T p `hyQ V@ZUf SZUQSVeT!\]ZUQY_#V`Z pT V`h Rozepq_eZ f pyh^Z^f Z T z WX TV`hyZ^Q`_|QYzep T Ron Q xZUX WZUQ RoZxc . 1 1 1 QXZ!f ginze_]pyZeX[nepZ^ \]ZV`hyX Z!Ro_ZU_]pqZ%eX n
(245) epZU \]ZTWV!u'nWhyQY_]ST!X]zeQeZ\ZUf _ enYV`Z2VYZ xnpyze\ Z!g S Qehjgoc Z!g g >eg'_ ZU \]Z gpyhqQ|Z!f T hqX[Z!g g'nWQY_ XZ f ginWpqzSg T X pjT \ Z^f _[enYV`Z V`Z %tT zSg gi v ZUhV`Z^pc
(246). M. . . . 3 4 3 3 N : 3 3 3 N 3 c T RonQSV`hq_[hynQT z SnX V Z gi_ V`hjg[RonQ`_ hyQYzeZxc6l +Yc(+ 'Yc Z|QenW\ eX[Z V hy_ZUf X T!_[hynQSgDV`Z@p T p WnX[hy_ e\] ZHZ gi_DZUQSRonX[Z SZ!T!zSRonze _ X[nhy\]SnWX _ T QY_ V`Zp nX V`X ZMV`Z 9AIA SnWzeX A cdZpyzSgwhypDQ Z!gi_w TWg V@Z!f RoX nWhjg[g[T!Q`_. T z2R nWzeX g|V`z%_ ZU\]Sg c l +`c +Yc z eX[Z^\]h ZU X Z!g hq_ZUf X T _ hynWQ gSp T!pnWX[hq_[e\ Z V`ZVYZ!g[RoZ^Q`_ Z n g[RohqpypqZ eezehjg qh pHT zQ RonW\]SnX[_[Z^\]ZUQY_ T xnX T epyZxc T4RonWQ xZUX ZUQSRoZZ!gi_X T ehjV`Zxc|b2T!hg]V"Z g x zeZ pyZ WX TV`hyZ^Q`_|_ ZUQSV xZUX g ZUf X[n `pTR nWQ xZUX ZUQSRoZ g'Z V@Z f WX TWV`Z cl +Yc &c $ ' @pjTRonWQ xZUX WZUQSR ZZ!g'_X T ehjV`Zxcml +`c = *Yc $ + @pjTRonWQ xZUX WZUQSR ZZ!g'_X T ehjV`Z Y\T hjg ZUpqpyZwn g[RohqpypyZ c l +Y(c @. +A.
(247) M. 3 . 4 3 3 N : 3 3 3 0 3 c T RonQSV`hq_[hynQT z SnX V Z gi_ V`Z _ >`SZ xT!zSg[g'hyZUQQeZxcl +`c A 'Yc Z QnW\ eX[Z V" hy_ZUf X T!_[hqnWQSg V`Z p T!pnWX[hq_[e\ Zwg'Z V Z f WX TWV`ZxcSd Z pyzSg@hqpQ Z!g'_@STg. V@Z!f RoX nWhg g[T!Q`_ T!z2RonzeX g|T!z2RonzeX g V`z_[ZU\ SgocSl +`c + Y+ c T V Z f RoX[nhg[g T QSR Z VYz%R X[hy_ZUf X[#Z Z gi_|_[X Z! g@pyZ^Q`_ Zw\T hjg XZ f WzepqhZU X Zxc. +.
(248) Wed Jun 24 18:25:36 1992. 1.5 1. 1.25. U(X,Y). 1.75. 2. Advection diffusion : partition. 0. Y. 0. 0.15. 0.333 0.3. rh WzeX. 0.667 1. X. Z#+`c(+al TWg' _ Z!gi_ l#enYRMal#nWQSV`hq_[hqnWQhyQehq_[hjT pyZ. +I'.
(249) Wed Jun 24 18:25:09 1992. 1.5 1. 1.25. U(X,Y). 1.75. 2. Advection diffusion : partition. 0. Y. 0. 0.15. 0.333 0.3. #+YcB&al TWgi _[Z gi_. rhzeX[Z. 0.667 1. X. l#enYR avxnpyze_ hynQ SQ T pqZT $. +I+. & .
(250) 2 "fort.91" "fort.92" "fort.93" "fort.94". 1.9. Profil de l’interface. 1.8 1.7 1.6 1.5 1.4 1.3 1.2 1.1 1 0. 0.05. 0.1. #+`c *]al TWg' _ Z!gi_. rhzeX[Z. 0.15. 0.2. 0.25. 0.3. 0.35. l#enYR aSP xnpyze_ hynWQV`Z g WT!pyZUzX g T p hqQ`_ ZUX TRoZ Y. 160. Iterations de l’algorithme de descente. "fort.200" 140. 120. 100. 80. 60. 40. 20. 0 1. DhWzX[Z. g RoZUQY_[Z. 1.2. 1.4. 1.6. +`c -Fa l TWg' _ Z!gi_l#enYR a#}nW\. 1.8 2 2.2 Iterations en temps. 2.4. 2.6. 2.8. 3. eX[Z V hy_Z^f X T _ hynQSg SnWzX p T p WnX[hy_ e\]Z V`ZV`ZU. +&.
(251) 2 "fort.101" 1.8 1.6. Valeur de J. 1.4 1.2 1 0.8 0.6 0.4 0.2 0 0. #+`c . rhzeX[Z. 20. 40. 60. 80 Iterations. 100. 120. 140. al Tgi _[Z!g'_ l#nYR a T pqZUzeX|VYZ" SR X[hy_ ZU X[Z V`Z RonWQ xZUX ZUQSRoZ T . 160. . 0.0002 "fort.102". 0.00018. Valeur de J. 0.00016. 0.00014. 0.00012. 0.0001. 8e-05 1. #+`c =. DhWzX[Z. 1.5. 2. 2.5 Iterations. 3. 3.5. aSl TWgi _[Z gi_ l#enYRMa! T pqZUzeX V`Z#" SRoX hy_ ZU X[Z VYZ R nWQ xZUX ZUQSRoZ T $. +I*. 4. ' .
(252) 0.0009 "fort.103" 0.0008. 0.0007. Valeur de J. 0.0006. 0.0005. 0.0004. 0.0003. 0.0002. 0.0001. 0 0. #+`c @. DhWzX[Z. 2. 4. 6. 8 Iterations. 10. 12. 14. aSl TWgi _[Z gi_ l#enYRMa! T pqZUzeX V`Z#" SRoX hy_ ZU X[Z VYZ R nWQ xZUX ZUQSRoZ T $. +I-. 16. + .
(253) Wed Jun 24 19:13:49 1992. 0.5 0. 0.25. U(X,Y). 0.75. 1. Advection diffusion : partition. 0. Y. 0. 0.15. 0.333 0.3. #+`c 9A. rhzeX[Z. 0.667 1. X. a6l Tgi _[Z!g'_%tT zSg g al#nQSV`hy_ hynQ%hyQhy_[hjT pqZ. +.
(254) Wed Jun 24 19:29:55 1992. -3.96 -8.92. -6.44. U(X,Y). -1.48. 1. Advection diffusion : partition. 0. Y. 0. 0.15. 0.333 0.3. rh WzeX. 0.667 1. X. Z$+Yc I aSl TWgi _[Z gi_%tT z g[g avxnWpqze_[hqnWQ S QST!pyZ. +I=.
(255) 1 "fort.91" "fort.92" "fort.93" "fort.94". 0. Profil de l’interface. -1. -2. -3. -4. -5. -6 0. 0.05. 0.1. #+`c 'al TWgi _[Z gi_ %wT!zSg[g. DhWzX[Z. 0.15. 0.2. 0.25. 0.3. 0.35. aSP xnpyze_ hynQV`Z!g T pyZ^zeX g T p hyQY_[ZUX TWRoZ Y. 1000 "fort.200". Iterations de l’algorithme de descente. 900 800 700 600 500 400 300 200 100 0 1. DhWzX[Z. g RoZUQY_[Z. +Yc +. 2. 3. 4 5 Iterations en temps. 6. 7. 8. al TWg' _ Z!gi_%tT!zSg[gaS}n\ eX Z V hy_Z^f X T _ hynQSg SnzeXwp T p WnWX hy_ e\]Z V`Z V`ZU. +I@.
(256) 0.7 "fort.101" 0.6. Valeur de J. 0.5. 0.4. 0.3. 0.2. 0.1. 0 0. 100. 200. 300. 400. 500 600 Iterations. 700. 800. 900. 1000. Z$+Yc %& al Tgi _[Z!g'_ t% T z g[g a @T!pyZUzX V`Z#" eRoX hy_ Z^ X[Z V`Z RonQ xZ^X WZ^QSRoZ T . rh WzeX. 0.022 "fort.102" 0.02. Valeur de J. 0.018. 0.016. 0.014. 0.012. 0.01. 0.008 1. 2. 3. #+Yc *a6l Tgi _[Z!g'_%tT zSg g. rhzeX[Z. 4 5 Iterations. 6. 7. a T!pyZUzeX V`Z#" SRoX[hq_ ZU X Z V`Z RonQ xZUXWZUQ RoZ T . &A. 8. ' .
(257) 0.1 "fort.103" 0.09 0.08. Valeur de J. 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0 0. 20. 40. #+Yc -a6l Tgi _[Z!g'_%tT zSg g. rhzeX[Z. 60. 80 Iterations. 100. 120. 140. a T!pyZUzeX V`Z#" SRoX[hq_ ZU X Z V`Z RonQ xZUXWZUQ RoZ T . &. 160. + .
(258) .
(259) 6 . "
(260) :0 . TwXZ f ginWpqze_[hqnWQ ST XHzQeZ@\ Z^f _[enYV`Z V`Z@ T X[_ hy_ hynWQMVYZ|V`n\T hqQeZ|V`Z p Zf z T _[hqnWQ V" TWV xZ!Ro_[hqnWQeV`h z gihynQ Z!g'_HVYnWQSR#XeZ!f T!pyhg TepqZxc b2T!hgSST X RoZ xzeZ@p nQ Q TSTgrR eZUX R Z f T ne_[hq\]hg'ZUXHpjT Y hy_[Z g[giZ VYZ RonWQ xZUXWZUQSR Z V`ZwpTw\ Z^f _[enYV`Z `R ZUpypqZUR h`Z!g'_ SZ!T!zSRonWz]_[X nW T!T!phenWpqX[ZxhqcY_[e}%\ Z!f T!Z QeV`\]Z nWV`hqQSZ!gg RoZ^ZUpyQYpyZ _[ZwSSnWT!zeXX X zT!Q%hy_ T!RopZU X nW_ X[T!hqhy_[QeeZU\ \ Z ZUQ`V`_Z ZUW _[X X TWZ V`T hqZU\ Q`Z^_ f pyhyR nnWXQWZUf u'Z|z Z^ Q]z|Zxf X[c ZU\ epTRU T QY_#p dZ ST X _Hg TwRonQSRoZUe_ hynQ ! RoZU_DT!pW nX[hq_[e\]Z Z!gi_ T hjg`ZUf \]Z^Q`_ST X T pyp^ZUf pyhjg[Te pyZxc ZH_[Z^\]Sg VYZ R^T pR zepV`Z gZUf _ T _ g|V`hyX Z!Ro_ g@Z^_ TWV u'nhyQY_ g@SZUze_ ZU _ X[Z V`hY hgYZwf ST X pyZtQenW\ e X[Z V`Z eX[n R Z!g[g'ZUzeX g#V zeQeZ|\TR hyQeZ[ \]hq\V ` c! QMSZUze_ V`nWQ R Z!g'|ZUf X ZUXHzeQ nWX _ T hqQV`Z|_[Z^\]Sg g'zeX zeQeZ \TWR ehqQeZ T X T!pypZU pyZxc dZpyzSg6 pjT XZ!f g'nWpqze_[hqnWQ V`ZMg'nWzSg' eX n
(261) e pZU \]Z!g T \ ZUf pyhqnWX[Z pqZRonQSV`hy_ hynQeZU\]ZUQY_ V`Z!g g >eg'_ ZU \ Z!g@pyhqQ|Z!f T hqX[Z!g c vxhp T!pW nX[hq_[e\]Z V`ZMVYZ!g[RoZ^Q`_ Z R nWQ x ZUX Z X T!hg'nWQSTe pyZU\ ZUQ`_ Y hy_ Z nQ TW QZUX TMT pqnWX g V`z_[ZU\] g \ZU \]Z gizXzeQZ \ TWR ehyQeZtg[R^T pT!hyX Zxc / 3 3
(262) 3 c Z2eX[ne pZU \ ZV ne_[hq\]hg T _ hynWQ4Q TSTg0ZUf _Z f ZUf _[z V`h^Zxf c {p|Z!gi_ V`nWQSR2R ZUX[_ T hyQZU \]ZUQY_wSnxg[g'he pqZV T \ ZUf pqhynX[ZUXwpjT%RonQ x Z^X W Z^QSRoZ T x Z!RMV`Z!g eXZ f RonWQSVYhy_[hqnWQeQZUzeX g n"z V" T z_[X[Z g|T p nWX hy_[\]Z!goc 'Yc }%Z!f T Q\]nWhqQSgrpyZ|X[n
(263) p ZU \]Z eX[hqQSRohqST peZ gi_#pT Y hy_[Z g[giZ VYZwRonQ x Z^X W Z^QSRoZxc P QZZ^_ pyZ T hq_ x zeZ A T z \]hyQehq\ze\ V Z f W X TV`ZhyX XZUf \ Z!f V`hTe pyZ^\ Z Q`_ pTRonQ x ZUX W ZUQSR Z]T x Z!R pT nQSRo_ hynWQZUpypqZ zSTV`X T!_[h# zeZ R enWhjgihyZ c Q eX[n6n giZV`nQSR VYZ RUT pjRozepyZ^X e T!QST pqn
(264) zeZMV`z2R^TWg\]nQenYV`hq\]ZUQSg'hynWQQeZUp x zeQ RoX[hq_ ZU X ZFpqnYRUT p asrnWzeX R ST zZwQenxZUzSV X[nQ`_ h ZU X Z a 0 7
(265) 8I0 7 . &'.
(266) T pynX g !. !. 1. n"z 1 !Z g'_rzQeZ nWX \]Z@pqhyQ Z!f T!hyX Z|ginpyze_ hynQMV zeQX[n
(267) p ZU \]Z TV u'nWhqQ`_Hne_[Z^Q`zMT xZ!R zeQeZ RonSQ V`hq_[hynQ T p hqQ`_ ZUX TRoZ Z f T pqZ T zeQ V`hyX TWRepjTWRZtf T zSnWhqQ`_[c QT T!pynWX g a !
(268) 1 T xZ R ! ! ! !. !9!9! ZU_
(269)
(270)
(271)
(272) cc
(273) l#Z xzehDT!\ ZU QeZ T XZ!f ginzSV`X Z pqZ g?> gi_ Z^ \]Z a ! n"z2 nQT SnxgYZ]f a cc l Z!g'_@zeQg?>gi_ ZU \]Z pyhqQ|Z!f T hqX[Z epyZ^hyQMQenWQg?Y> \ ZUf _ X[h# zeZ zZwp nWQ]SZUze_|XZ!f ginzSV`X Z ST X zeQeZ \ ZUf _ enYV`Z VYZ _ >YSZ%tb2~ P@vSc F. F. 1. 8. F. +Ycwl#ZU_[_ Z\. Z^f _[enYV`Z|Z gi_@ T X[_ hRozpyhZ^ X[ZU\]Z QY_ehqZUQ TWVeT!e_ZUf ZtT zRUT!pRozpeST X T pqp ZU pqZ|n"z nWQFSZUze_ eX[nWX T \]\]Z^X pjT]XeZ!f g'nWpyz_[hynQ4gihq\ zpy_ T!Q|ZUf ZMV`Z g g?>gi_ ZU \]Z!gtV`hyX Z!Ro_ gwZU_ TWV u'nhyQY_ goc. &+.
(274) . . % . dws @ '4bl c6l#hjRURonWpqh "x cedZ!f g'hV Z^f X[h YT!QSV "ecesZUf X[hjT z ce{QY_[X nYV`zSRo_ hynWQ n V`nW\T!hyQ V`Z!Ron\]Snxg'hy_[hqnWQ4_[Z R eQh$xzeZ!g hqQ0 >`SZUXSnWpyhjR]ST X TSnWpqhR n eX n
(275) epqZU\g c " ) ,* ,* ) $ ,*
(276) ,*
(277) !,* '#, +,* & $ $
(278) * ) -( ,*, @ @I'`c 3 %ts d = + 4 ~ c %pqn |hyQSg `h "ecsZUf X[hjT z "T!QSV 6 c cd hyQecDdn\T hqQ V`Z!Ron\]Snxg'hy_[hqnWQ \]ZU_ enYV`Z nWXHQnWQepqhyQeZ!T!XrX[
(279) n pyZU\gShyQ SzehV 5V >YQST \]hjRUgoc ,* ' * ) " ,
(280) '*' !
(281) ! " # $
(282) * ) O& A (a ' A 9A @ @I= +Yc 3 6 zST @ 4 p n 6 zST!X[_[Z^X[nWQhc dnW\T!hyQ V`Z!Ron\]Snxgihq_[hqnWQT!QSV0ST!X T pqpyZUp|X[nYRoZ!g gihq Q ,*nW Xw _ eZ " QYze \]Z^+X[hR^T p, g'nWpq ze $_[
(283) *hqnW 5Q2 n ST!@ X[@ _ hT c p V`!h ZUX ZUQ`_ hT!pZ z T _[hqnWQc ) ) ) 3l. &I&.
(284)
Documents relatifs
To test whether the vesicular pool of Atat1 promotes the acetyl- ation of -tubulin in MTs, we isolated subcellular fractions from newborn mouse cortices and then assessed
Néanmoins, la dualité des acides (Lewis et Bronsted) est un système dispendieux, dont le recyclage est une opération complexe et par conséquent difficilement applicable à
Cette mutation familiale du gène MME est une substitution d’une base guanine par une base adenine sur le chromosome 3q25.2, ce qui induit un remplacement d’un acide aminé cystéine
En ouvrant cette page avec Netscape composer, vous verrez que le cadre prévu pour accueillir le panoramique a une taille déterminée, choisie par les concepteurs des hyperpaysages
Chaque séance durera deux heures, mais dans la seconde, seule la première heure sera consacrée à l'expérimentation décrite ici ; durant la seconde, les élèves travailleront sur
A time-varying respiratory elastance model is developed with a negative elastic component (E demand ), to describe the driving pressure generated during a patient initiated
The aim of this study was to assess, in three experimental fields representative of the various topoclimatological zones of Luxembourg, the impact of timing of fungicide
Attention to a relation ontology [...] refocuses security discourses to better reflect and appreciate three forms of interconnection that are not sufficiently attended to
