• Aucun résultat trouvé

Le schéma de MacCormack sur l'équation d'advection bidimensionnelle. Application au cas test C1 de l'ONERA

N/A
N/A
Protected

Academic year: 2021

Partager "Le schéma de MacCormack sur l'équation d'advection bidimensionnelle. Application au cas test C1 de l'ONERA"

Copied!
33
0
0

Texte intégral

(1)Le schéma de MacCormack sur l’équation d’advection bidimensionnelle. Application au cas test C1 de l’ONERA Romuald Carpentier. To cite this version: Romuald Carpentier. Le schéma de MacCormack sur l’équation d’advection bidimensionnelle. Application au cas test C1 de l’ONERA. RR-3076, INRIA. 1996. �inria-00073616�. HAL Id: inria-00073616 https://hal.inria.fr/inria-00073616 Submitted on 24 May 2006. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés..

(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. Le sche´ma de MacCormack sur l’e´quation d’advection bidimensionnelle. Application au cas test C1 de l’ONERA. Romuald CARPENTIER. N˚ 3076 de´cembre 1996 THE`ME 4. ISSN 0249-6399. apport de recherche.

(3)

(4) 

(5)     !

(6) "#$ &%(')* +! -,.

(7) /%(')* 0 '1 '1 

(8) * ')* * 

(9) ))32465 5$1')7 8%('93*  7 :%

(10) ;%<= >@?:ABDC4E2 #F GIH+JKILNMDO.PQF-RSTVUVW1SF X7Y[Z)\^]_3` acbd\3egfihkjlbimonQ])jpmoqgjlbi\rbds@hkjlbimtn u ]8slvcsljwZ1\^]1sx1mo\^qgfd]9yz]1s {|wmk}~])jaz€~‚a ƒhkq[q„mt|lj u ]8|w])x Y[]1|lx Y[]†n3‡Vˆo‰ Šk‹.` u[Œ x1])\3[|l]Ž‘ot‹` t’ rq“ht”o])s •-–c—™˜(š›–QœžŸ Œ jwe u ] q[| Œ sl]1n j Œ ] u htn[s¡x1]q“htqgbd]1|¢hqImoe[|/[egj¢fNŸ£htn“hkf¤vcsw] u Ÿ£e[ng] \ Œ j@Ygm u ]n>e[\ Œ |lbd¥>e[] egjlbdf¤bis Œ ] u htngs7fi] x)m u ] u ] \ Œ x1htngbd¥ceg] u ])s7¦“egb u ]1spac€~§/ƒpƒ

(11) ¨ u[Œ)© ])fdmoq[q Œ q[ht|¢fNŸ«ª&§¬ƒ

(12) ¨3­“®] slx Y Œ \#h u ]$“htsl]¯egjlbdf¤bis Œ q“hk|Vx)]Qx)m u ]$]1s°jfd]Qslx Y Œ \#h u ]¯±¯htx™²¢mo|w\#htx ³ u Ÿ´mo| u |w]¯’zµ]1n © ]1|lslbdmon¶]9yzqgf¤bdx)b¤j@] q[| Œ1u bdx)jw]1e[|px1mo|l|w])x)j@])e[|h © ]1xe[n[]&·¸mo|l\3egfihkjwbdmon u ] © mkfie[\^])s¹“ngbds

(13) swe[|

(14) \#hkb¤fdfiht”o]8¥>e“h u |@htn[”tegfºh»bi|l]t­ ¼ htngs.e[n›q[|l]1\rbi])|3j@])\^q[s1µ½n[moe[s.| Œ hkf¤bdswmon[s3e[n[] Œ j@e u ]Vfdbdn Œ h»bi|l]-swe[|f¾Ÿ Œ ¥>e“hkjlbimtn u Ÿ¿h ug© ])x)jwbdmonÀgb u bÂÁ \^]1n[s°bimtn[n[])f¤fd]])n$])n © bds@hk”o]™htn jpfi])sÃ¥>e“hkj@|l]8x1mong¹[”oe[|@h»jwbdmon[sÃqImosws°bigfd]1s u e swx Y Œ \#h u ]±¯htx‘²¢mt|w\#htx ³Ä­ §nÅq“ht|@h»fdfdZ)fd]tµ;ngmoe[s&x1mtng·¸|wmon jwmon[s&x1])s8| Œ slegf¤j hkjws8Æ-x1]1ecyÅmogjw]1n>e[s8q“ht|fd]rswx Y Œ \#h ugŒ x1])n j@| Œ^u ]^ƒ

(15) mc] q[| Œ x)bdsÆrfNŸ´mo| u |l]’zµ[]1n © ])|ws°bimonQ]9yzqgf¤bix9bdjw].h © ])xegn[]&bin j Œ ”o|@h»jwbdmon$jw]1\^qImo|w]9fdfd] u ]ƒpe[ng”o]Ç8ezjwj h#’z­ ¼ htngs7e[nsw])x1mon u jw]1\^q[s)µ[n[moe[s7ht„mt| u mongs7e[nx™h»fix)egf;n[mtn-fdbdn Œ h»bi|l] swe[|¡fi] x1hts7j@])sljp²Ž u ]f¾Ÿ¿ª&§¬ƒ

(16) ¨ È qg|wmo”o|wht\^\^]V¨ a[a[±ÊÉ8moË;µswe[|8fd]V\^m u Z)fd] u ])s Œ ¥ce[hkjwbdmon[s u Ÿ¿§egfd]1|)µ½ngmoe[s © moegfdmon[s|w])n u |w]Vx1mo\^qgjw] u Ÿ´e[nÌqgY Œ n[mt\#Z)n[] u ] j@mte[|wgb¤f¤fimongs u[Œ j htx Y Œ s u htn[s#e[nÌ| Œ ”tbd\^]Qbdn[slj@hkjwbdmon[n“h»bi|l]Qq Œ |°bim u bd¥ceg] Œ j@htgf¤b¾­ mte[sÃn;Ÿ£htn“hkf¤vcsw]1|lmon[spq“hts7fd]1s

(17) x™hke[sw])sq[Y vcslbd¥>e[]1s u ]&x1]8q[Y Œ n[mo\^Z)n[]tµÄ\#hkbdsÃx Y[]1|lx Y[]1|lmon[s Æ3b u ])n>jlbd¹[]1| fih8n[hkj@e[|l] u e#| Œ ”kbi\^]Ãmoslx)b¤fdfihtn j¢qg| Œ1u bdj¬])n#·¸mongx)jwbdmon u erj!vcq„] u ])s¬]1|w|l]1e[|ls/bdn j@|lm u ezbdjw]1s¬q“ht|fNŸ¿hkq[q[|wm™ycbÂÁ \#hkjwbdmon;­ ÍÏΓÐї9Ò@Ó ÔՖœÌ±Qhtx‘²¢mo|l\#htx ³Á u bdswqI]1|ws°bimtn$Á u bdsws°biq“h»jwbdmon$Á¬jwmoe[|wzbdf¤fimtn Ö¤×Ø!ÙÛÚiÜNÝ)Þ~ÚàßkákÚàâÛã.

(18)     (

(19)  * %(%   '1 

(20) * ')*$  p,. 

(21) "V &%(')* 2¯4 5 5Q)'17 &%(')* % %(  = %

(22) ;% 7 ®  ?:A B C4E2  —) Ð

(23) “ÓtÐ œX7Yg]slj@e u v›q[|l]1sw])n j@] u bdnÀjwYgbdsrq“htqI]1|3bds.·¸mzx)e[slbdn[”žmon jwY[] htn“h»fdvcslbds^mt·hÊn>e[\^]1|lbdx™h»f swx Yg]1\^]8e[sw]&bdn-j@Y[]² ¼Ïx)m u ]&az€~§¬ƒƒ

(24) ¨ u ] © ])fdmoqI] u hkjpª&§¬ƒ

(25) ¨3­“X7Y[]&[htslbdx&swx Y[])\^]egsw] u bdn-j@Ygbds x1m u ]bds¢jwY[] ]9yzqgf¤bdx)b¤j

(26) q[|w] u bix9j@mo|¢x1mo|l|w]1x9j@mo| © ])|wslbdmon$hkjÃsl]1x)mon u mo| u ]1|Ãhkx1x1eg|@htx9vmt·®jwY[]8±¯hkx‘²¢mo|l\Vhkx ³ swx Yg]1\^] Ãb¤j@YQh.¹“ngb¤j@] © mtfde[\^]8·¸mo|w\egfºh»jwbdmonQmtnQh^¥>e“h u |whtn[”oezfºht|Ã\^])swY;­ ½bd|ws°j™ µ ¡]¯|l]™hkf¤b )]Êhžfdbdn[]1ht|s°j@e u v mon j@Y[] j ¡m u bd\#])n[slbdmon“h»f ¢h © ]Ê])¥ce[hkjwbdmon; ­ ]Qx)mon[s°b u ])|j@Yg] ·¸moe[|rqImoslslbdgfi] x)mong¹“”oeg|@hkjlbimongsrmt·&±Qhtx‘²¢mo|l\#htx ³ swx Yg]1\^]t ­ ]x1mo\^q“ht|l]$hkfislmžj@Y[])sw] |w])swegf¤j@s Ãb¤j@Y j@Ygmosw]&mozj hkbdn[] u Ãb¤j@YjwY[]&sw])x1mon u Á!mo| u ]1|

(27) htx)x1e[|whkj@]8ƒ

(28) mc] e[q Ãbin u slx Y[]1\^]kµI] yzqgfdbdx)b¤j © ])|wslbdmon;µ 

(29) Yg]1n$h ƒ

(30) e[n[”o]Ç&egjwj@h#’.jw]1\^qImo|@hkf®bdn j@])”o|@hkjlbimtn bds

(31) e[sw] u ­ az])x1mon u µ ¡]3qI]1|°·¸mo|w\h^n[moncÁÛf¤bin[]1ht|px™hkfdx1egfihkjlbimonQmonQjwY[]3²Žrª&§¬ƒ

(32) ¨ jw]1s°j x™hksw] È ¨&aga[±q[|lmo”o|wht\VÉ 

(33) Y[])|w]tµmon jwY[]+\^m u ])f3mt·^§egfd]1|1Ÿ´sž]1¥>e“h»jwbdmon[s1 µ ¡ ] 7hkn>jÊ|w]1qImo|°jÊmonÏh q[Y[]1ngmo\^]1n[monÏmk· © mo|°j@]9y swYg] u[u bdn[”$binh$I]1ngx Y+qI]1|lbdm u bix^e[ngslj@]1h u v slj@hkj@]k­ +] u m n[mtjhtn“h»fdvcsw]#q[Y vcslbdx™hkf¡q[|°bin[x9biqzfi]#mt·/j@Ygbds q[Y[])n[mo\^]1ngmon;µÃ[egj ¡]¯sw])]1³›j@m b u ]1n jwb¤·àvÀj@Y[]$n“hkjwe[|w]$mt·&moslx)b¤fdfihkjlbin[”|wegfd]1sVq[|w] u bdx)j@] u bdnÌ|w]9fºh»jwbdmon Ãb¤j@Y j@Y[]&j!vcq„]mt·½]1|l|wmo|ls7bin j@|lm u e[x1] u  vj@Y[]htqgq[|wm™ycbi\#hkjlbimtn;­ Ò .Î (—tœ ±¯htx‘²¢mt|w\#htx ³-Á u bdswqI]1|ws°b © ]Á u bdsws°biq[hkjwb © ]8Á © mo|°j@]9y. "!# %$  '&.

(34) ˆ. 

(35)     

(36)  ! "#

(37) $%. = ,.-/,. +4  B. '&. ?)(<B < ( B 4. +*. 021436587:9<;>=#?A@CBD?8E$FHG#I.J. moegs © moegfdmon[sp| Œ swmoe u |w]8f¾Ÿ Œ ¥>e“hkjlbimtn u Ÿ£h ug© ]1x9jwbdmonž’t¼ swx1hkfihkbi|l]8swegb © htn j@]LK. È Ž‘É moËeQ/]1sljfd]Ã\^m u egfi] u ]7fºh © b¤j@]1slsw] u Ÿ£h ug© ]1x)jlbimtn;µ`Yswmtn^bdn[x9b u ])n[x1] © e[] u htngse[nr|w])q„Z)|w]Ã])jfMÌfºh © hkfd]1eg| swx1hkfihkbi|l]h ug© ])x)j Œ ]t­ acb&ngmoe[sswq Œ x9bd¹[mon[s$e[n Œ j h»jbingb¤jwbihkfgKhMji4kb c>l!mHl!npoqb Mri4mHlsn>ohkfdmo|ls-fºh slmtfiezjwbdmon u ]tivuo])slVj K Mri4m2wRQk>SxUXWZYyl!njwRQkyW!]_^$YLo

(38) s°bi”tngbd¹“htn j&¥>e[]3fNŸ Œ j hkjbingb¤jwbihkf © hsw]j@|whtn[slfihkjw]1| hkeÊx1moeg|ws u e¯j@])\#qgs&Æ e[n[] © b¤j@]1slsw] u ]8x1mo\^qImos@htn jw]1s igQTSxUXWZYylQzW!]_^{YXo9­ MON PRQTSVUXWZY[MO\8PRQTW!]_^:Y`MOa:bdc. ,.-}|. ~9A=vG/G#9.€AI.J.  moegsegjwb¤f¤bislmon[se[nr\#hkb¤f¤fºht”t]¢| Œ ”oegf¤bi])|¥>e“h u |whtn[”oezfºhkbd|w] u ]7\#htngbdZ1|l]ÃÆn[]/·Õhkbd|w]7hke[x1e[ng] u b_ Œ |w]1ngx1] ]1n jw|w]/e[n3x1hkfix)egf6‚ x1]9fdf>x)]1n j@])|w] u ‚¬])j{‚ © ]1|ljw]9yx)]1n j@])|w] u ‚¬])j(n[moegs½x)mon[slb u[Œ |wmon[s½n[mtjw|w] u mo\#hkbdn[]/x1mo\^\^] q Œ |lbdm u bi¥>e[]Vq„mte[| Œ)© bdjw]1|fi])sx)mon u b¤jwbdmon[s u ]VImo| u s1­(mte[s·¸])|wmongs| Œ · Œ |l]1n[x)]-ƄƒÊq„mte[|fd]#q„mtbdn j u ] x™h»fix)egf]9j&†Æ qImoe[|psw]1s © mtbdslbdn[s)­®{ht|hkb¤fdfd]1e[|ls1µIx1])s q„mkbin j@ssw])|wmon j |l]1q Œ | Œ s q“hk|pfd]1spbin u bix)]1s u bdswx)|w]9j@s ‡zˆŠ‰ ‹

(39) Œ /‰pŽ sljwbdq[egfihtn j^fi])e[|ws^x)mzmo| u mon[n Œ ]1xs Kmb‘i4’P”“pov•jmÌ]9e j nRb‘i—–ePd˜™ov•en h © ]1„x •jm¶]9j •en fi])s bdng¹“ngb¤j Œ slbd\Vhkezy^swq[hkjwbihtezy„­opmoe[sx)mon[s°j@|wezbislmon[ssweg|e[n3j@]9f[\#hkb¤fdfiht”o]¡fºhx)])f¤fiezfi{] šf›¬htslswmcx)b Œ ]

(40) hterngmz])e u ƒ ugŒ ¹“ngbd]8q“ht|7fd]&x1mon jwmoe[: | œZšf›‘µ“| Œ h»fdbds Œ q“ht|¡f¾Ÿ´e[ngbdmon$swe[x)]1sws°b © ] u ])s

(41) \^b¤f¤bi])ezy u ]1s

(42) sl]1”o\^]1n jwspf¤bºhkn>{j ƒÆ htezy [ht|lvcx1])n j@|w])s u ]1sp¥ce[h u |@hkn[”tfd]1s È © mtbi|ù“”te[|w ] v€ r—­ u‘É9­ Sj,k+1 J2 ∆x S. S. j,k. j-1,k. J3. I. ∆y. - ∆ y C j,k = C I - ∆x. Sj,k-1. J4. žŸ¡ 8¢Ž$£¤¥ L¦¡¡_ ¨§yª©V«p [L/ L¬`§X. ­H­¯®.°8±

(43) ²¨³´. Sj+1,k J1.

(44) _. h «p L_  

(45)  ,.-. :?pB 7hGv9;>=v?A@DIH@.?AGv7$BDI @$=TJ. moegs¡bdn>j Œ ”o|lmon[s ivu oswe[|/fºhx1]9fdfdegfd]šf›7])j¢]1nVegjwb¤fdbds@hkn>j¢fºh8·¸mo|w\egfi] u ]8ƒp§/§¬µcngmoe[s¢mtgj@])n[mon[sxK  MN![m"n b w $#% i& i}M o%')(z\fP+* i}M o,'-( ao/.. h © ])xLK &i M o b QTSxUXWZY M ])j0* i}M ob QTW!]_^:Y M]9j i1(z\Xl2(zaVofd]1s^x1mo\^qImos@hkn>jw]1s u e © ])x)j@])e[|^fimcx™hkf e[ngb¤j h»bi|l]mt|lj@Ygmo”omon“h»fÆeœ šf›Ñµ[x)mon j@moeg| u ]8fihrx1]9fdfdegfd] šf›‘­ ,.-13. 465758y?9:=vB)9;>=#?@:5$9+57>36E$=;Z;>IH7tIT;<;z?/>I;Z;yIH77 J. ® ]x1hkfix)egf u ]8fºh^n[moe © ])f¤fi] © hkfi])e[| u bdswx1|lZ)jw] u ] M› hte$j@]1\^q[s{kAb i=(P u o/•jk µÄs1Ÿ´mogjlbi])n jq“hk|pegn[] q[|l]1\rbiZ)|w]7])sljl‰Bbi\#A hkjlbimon µkn[mkj Œ ]?M> › u htn[s(e[n[] Œ j@htq„] u ]/q[| Œ)u bix9jwbdmonrswezb © bd]¢q“ht|(e[n[] Œ j@htq„] u ]/x1mo|l|w]1x9jwbdmon u mongn“htn jM7› @ ­ £D{| Œ)u bdx)jwbdmon K • k \ a M> ›fb'M› @ w. £. ²¢mo|l|w])x)jwbdmon. •jm •enDC2E. i&GFi}M› @ o%' •. P<*HF<i M› @ o%' • o. K u •jk M7› @ B‰ A b i&GF<i/M > ›

(46) o,' • \ P+*GF<iMM> ›

(47) o,' • a oN M > › P  M ›@ w •jm • nLC E IKJ. © bd]1n j u ]f¾Ÿ£hkbd|w] u ]fºh3x)])f¤fiezfi]&]9jªig• \ l• a o/fd]1s7x)mzmt| u mongn Œ ])s u e © ])x)jw]1e[|

(48) n[mo|l\#hkf„bdn j Œ ”o| Œ ­ ®]1s7bdn u bdx1])spsle[q Œ |lbd]1eg|wsj‚PO‚px1mo|l|w]1slq„mtn u ]1n jÆ3fih3·ÕhRQ1mon u mon jÃfi]¦[ezy])slj

(49) x™h»fix)egf Œ q“hk|7|@htqgq„mo|°jÃÆ3fih x1]9fdfdegfd]7x1mtn[slb u[Œ | Œ ]Kz‚PS ‚¬hte u ])fiÆ u ]¡f¾Ÿ bin jw]1|l·Õhkx1]¢]9jh‚@Áx‚])n u ]TQ1Æg­»€Ûfg])n.| Œ swegf¤j@]¢fd]1s¥ce[hkj@|l]¢qImosws°bigb¤f¤bdj Œ s swezb © htn j@])Vs K q[| ‰ Œ)u bdx)j@])‰e[| x1mt|w|w])x)jw]1e[| ²¢¨&a & * &V‰U *V‰U € & ‰U * U & * ‰ ²¢¨&a & * ‰U & ‰U * €w€ & U * & * U az])egfis)µ fd]1s x1hts€

(50) ])j€w€ © mon j8sw] u _b  Œ |w])n[x)bd]1| u htn[sfd].x1h u |w]fdbdn Œ h»bi|l].¥>e[].n[moegs htImo| u mon[s1­ §nÊx] „])j1µ n[moegs#q[ht| © ]1n[mongsÆÊe[n L\ W1\^] | Œ swegf¤j hkj#¥>e“htn jVÆÊf¾Ÿ´]9yzq[|l]1slslbdmon u e›¦“ezy u bislx1| Œ jwbds Œ q„mte[|.fi])s u ]1ezy q[|l]1\rbiZ)|w])spf¤bi”tn[]1s u e j htgfd]™hke$]9jpn[moe[s÷Õhkbdswmongs

(51) fd]8L\ W1\^]x)mon[s°j hkjpqImoe[|7fd]1s u ]1ezy u ]1|lngbiZ)|w])s1­ •jm • nq[|lm. B * ( B ( B 4 Y 4[Z]\„^\ B moegs$slmoe[Y“h»bdjwmon[s$htq[|lZ1s u bdswx1| Œ jlbiswhkjwbdmon u eD¦“ecy µ7jw|wmoe © ]1|fNŸ£] yzq[|w])swslbdmon u eD”ohkbin moe ·Õhtx9j@]1eg| u Ÿ£ht\^qgf¤bd¹“x1hkjwbdmon$])j u mongn[]1|

(52) sw]9fimtnQfd]1s

(53) x™hts È €¢moe €w€°É¢fd]1s

(54) x1|°bdjwZ1|l]1s u ]8slj hkgbdf¤b¤j Œ8u Ÿ´e[nQjw])fswx Y Œ \#hg­ X. _a`O­_=b.

(55) 

(56)     

(57)  ! "#

(58) $%.  {½moslmon[s A. |-/,. 0jI 79 E =M;B>3T;>=y3.J. bQx•jmhW!]_^$Ycµ[bdf © bd]1n j¨K. bdQ

(59) • nSxUXWZYr])j. ²¢¨&a€. Mˆ@ Œ  ‰BA. ²¢¨ a €l€. . M —ˆ @ Œ S N \ a.  .  A i M ˆ @ U A}Œ  wtM ˆŠ@ ‰BA}Œ  o6P  i}M ˆ@ Œ U A w M ˆ—@ Œ!‰BA o

(60) S   \  N  a . w I i A P A OP  osM ˆ@ Œ. w I i A w A P   osM ˆ—@ Œ P A i A P oxi}M ˆŠ@ ‰BA}Œ  P M ˆ @ U A}Œ  o P A i A woVi M ˆŠ@ ‰BA}Œ P M ˆ @ U A}Œ o Pi A P oxi}M ˆ@ Œ/‰BA P M ˆ@ Œ U A o w i A woVi M ˆ@ Œ!‰BA P M ˆ@ Œ U A o w A  i}M ˆ @ U A}Œ/‰BA P M ˆŠ@ ‰BA}Œ  U A o

(61) P A  i}M ˆ @ U A}Œ U A P M ˆŠ@ ‰BA}Œ!‰BA o

(62). . |-}|. 0jI 9 ;Z;yIH77 E 1™9AB 5 Gv=8;T9;>=v?A@ J.  moegs ugŒ1u egbdswmtn[s u ]&f¾Ÿ´]9yzq[|l]1sws°bimtn u e¦“ezy u bislx1| Œ jwbds Œ µ“fi] ·Õhtx9j@])e[| u Ÿ£ht\^qgfdb¤¹“x1hkjwbdmon *i A lso¢q“hk| fNŸ´bdn j@|wm u e[x9jwbdmon u ]1sp\^m u ])s u ] Ämte[|lbd]1|Ã])n Œ x1|lb © htn jx Y[ht¥>e[]eM ˆŠ@ ‰ ‹Œ!‰pŽ x1mo\^\^]LK moË(# . .    "!$#/i “% A PR˜&'o 1] x,+<])j (Åfd]1spn[mo\3g|w]1s u Ÿ£mtn u ]1s|w])swqI]1x)jlb © ]1\^]1n j I*) • m$+  *) * i A l so@ Vm 8b I • nL+ ( h©. b+w  u ])j A b ]1n†mÊ]9jp]1n„n„­“{½ht|

(63) hkb¤fdfd]1eg|ws1µÄn[mte[s

(64) slbd\#qzfdb¤¹“]1|lmon[sn[mtj@|l]. Œ jwe u ]]1n$x1mon[s°b ugŒ |@hkn>jVK. •jm†b •en b • N µgbdfslegb¤j¨K. ])jpn[mte[s u[Œ ¹“nzbi|lmon[s.- x)mo\^\#]&fd]8|@htq[qImo|°j0/  £ ²¢¨ a €K P2- 43 wªu{w £. ²¢¨ a €l€K. 1-  '  3 5 2#:;. * i ylsYyl A l so<b u W!]_^hYSxUXWZYpi#uPRSVULW i A w o!o6P ™i SxUXWZY{PRW/]—^hYXoxi™SVULWZYSVUXW A P W!]_^$YSVUXW so w SVULWZYW!]_^ A P W!]_^:YW!]_^. ; 8. 6. * i1y- lsYyl A l's o<b u 4  3 P2- wªuPRW!]_^hYSVUXWZY>ivuPRSxUXWi A P'so!o6Pdi4SVUXWZY w W/]—^:YLoVi™SxUXWZYSVULW6 A w2#:- 3 SVULWZYW!]_^; A P W!]_^:YW!]_^; 8. ­H­¯®.°8±

(65) ²¨³´. 7' 98 7' 98. w W!]_^$YSVUXW so. È ’tÉ È ˆoÉ.

(66) ‹. h «p L_  

(67)  |-. 0j9 [;y9 =vG/= ;y3.J. moegs © moegfdmon[sÃjw|wmoe © ]1|Ãn>e[\ Œ |°bi¥>e[])\^]1n jfih © hkfi])e[|7\#h»ycbd\Vh»fi] u en[mt\3[|l] u ]8²¢moe[|whtn j- hkswswm»Á x)b Œ ]Ærx Y“ht¥>e[] u bd|w])x)jwbdmonqYrn[mo\^\ Œ ] - / i™YXo7¥>egb ©oŒ |lb¤¹“]qImoe[|7jwmoe[s7fd]1s

(68) \^m u ]1s u ] “moe[|lbd]1|ªi A l 'o¡fih x1mtn u b¤jwbdmonQx)|lb¤jwbd¥>e[] u ]¬mtnQp]1e[\#htngn K - / i™YXo¢j@]9f®¥>e[L] K 

(69) Π r ΠL*i:- / igYLo

(70) lYl A l'soAb'u mte[sphkfdfdmon[sphkbdn[s°b½qImoe © mtbd|

(71) jw|@htx)]1|

(72) ]1n ·¸mon[x9jwbdmon u ]&f¾Ÿ bingx)b u ]1n[x)]jYr])j u ]8\#htngbdZ1|l]qImtfihkbd|w]tµ[fih.fdbd\rbdjw] u e n[mo\[|w] u ]²¢mte[|@htn jphte u ]9fºÆ u ] A fiht¥>e[]9fdfd]&fi]&slx Y Œ \#hVn Ÿ£])slj

(73) qgfde[s

(74) slj@htgfd]t­Ämte[s7j@|wRh Q1mongs u ]&qgfde[s fd]ngmo\3[|l] u ]²¢moe[|@hkn>j u ] © hkfd]1e[|  ¥ceg]n[mte[s

(75) q[|w])n u |wmtn[s

(76) q„moeg|

(77) f¤bd]1:| Qx•jk7Æ •­ REPRESENTATION POLAIRE DE NU(THETA) 1 CAS I .5 0.8. REPRESENTATION POLAIRE DE NU(THETA) 1 CAS II .5 0.8. 0.6. 0.6. 0.4. 0.4. 0.2. 0.2. 0 1. 0 1. 0.2. 0.2. 0.4. 0.4. 0.6. 0.6. 0.8. 0.8. 1. 1. !#"$%"&(')*'+($#&(-,.-/ 021436587:9;'<=,.>"$@?:&A+B&("!C2'<D):+EFDG!#"$#&(H!IF@">+(KJLNMPOQ6"+(JLNM)OO R M.&E" S<$%"&('),UTE&B."$@?:&A+B&("V.$@=C W<'<&EXP6X.C6+AS.H&(YZ,:S[JLNMPOQ'S\,:S]JLNMPOHO R. mte[sÃn[mtjwmon[s

(78) hkfdmo|ws¢¥ceg]8fd]&swx Y Œ \#h u ]±¯htx‘²¢mt|w\#htx ³ u hkn[sÃe[n[]&x)mong¹“”oeg|@hkjlbimon u mtn[n Œ ] È ²¢¨&a-€/moe ²¢¨&až€w€°Én Ÿ£])sljq“hts&slj@htgfd]^q„moeg|8jwmoegjªY-\#hkbds8¥ce Ÿ´b¤f/h-fºh·Õhtx1ezfdj Œru ]rf¾Ÿ)W)jw|w]^slbfNŸ£mtn qI]1ezjx Ygmtbis°bi|8fd] ²¢¨&ar€(q„moeg|e[n[]Ãbdn[x)b u ]1ngx1]psw])fdmonrfd]pqg|w]1\rbd]1|¬])jjw|wmtbdslbdZ1\^]

(79) ¥>e“ht|°j u e^x1]1|lx)fd]

(80) moerfi]p²¢¨ a^€l€½qImoe[|egn[] bdn[x)b u ]1ngx1] sl])fdmonfd] u ])ezycbiZ)\^]&¥ce[ht|lj¡])j u ]1|lngbd]1|¢¥>e“hk|lj u ex1])|wx9fi]k­“acbIn[moegs¢h © mtn[s7x1]9jwjw]qImtfdv © hkfd]1n[x)] u Ÿ£htq[q[|lmzx Yg].]1nÊ·¸mongx)jwbdmon u j] YqImoe[|

(81) fi]3swx Y Œ \Vh u ].±¯htx™²¢mo|w\#htx ³Äµ®hkfdmo|ls1µÄfi] u mo\#hkbing] u ]3s°j htzbdf¤bdj Œ sw])|@h&b u ]1n jwbd¥>e[]Æ&x)])fdegb u[Œ jw]1|l\^bdn Œ q„mte[|fi]

(82) slx Y Œ \#h u ]pƒpmc]Ãswe[|¬x)]pL\ W)\#]

(83) \#hkb¤fdfiht”o]Ã¥>e“h u |@htng”oegfihkbi|l] h © ])xe[ng]8bdn j Œ ”o|@hkjlbimtn$jw]1\^q„mt|w])f¤fd] u ]ƒ

(84) e[n[”o]8Ç&egjlj h#’z­ {hk|Ãhkb¤fdfd]1e[|ls1µzslb;ngmoe[s7n[] u[Œ s°bi|lmon[sÃq“hts7htn“hkf¤vcsw]1|¡f¾Ÿ bingx)b u ]1n[x)] u ]fih © bdjw]1swsl] u Ÿ¿h ug© ])x)jwbdmon;µgn[moe[s7qImoezÁ © mtn[s.hkf¤j@])|wn[])|3Æ$x Y“ht¥>e[]#bdj Œ |@h»jwbdmon;µ®fi]-²¢¨&aŀ ])jfi]²¢¨&aŀw€ ­(moegs3mogjw]1n[mtn[s.hkfdmo|lsegn[] )mon[] u ] slj@htgb¤fdb¤j Œ qgfde[sp| Œ)u egb¤j@] u mon j

(85) fi])s|l]1q[| Πsl]1n j hkjlbimtn[sqImtfihkbd|w]1s

(86) slmon j¨K _a`O­_=b.

(87) Š. 

(88)     

(89)  ! "#

(90) $% REPRESENTATION POLAIRE DE NU(THETA) 1 ROE RK2 .5 0.8. REPRESENTATION POLAIRE NU(THETA) 1 ALTERNANCE CAS I CAS II .5 0.8. 0.6. 0.6. 0.4. 0.4. 0.2. 0.2. 0. 0. 1. 1 0.2. 0.2. 0.4. 0.4. 0.6. 0.6. 0.8. 0.8. 1. 1. V<:'#HH&B?:&B+A&("-,.-"$@?:&A+B&("N$@S.H>:'S. "'S<" 3:H! F@"H$%"&(')*'+E$#&BV,.>/ 0214365 3 ),+.-0/12-436578 9( :;& $ <%$=>?  :@ A $!: 

(91) ! B  

(92)   !"#

(93) %$&'(  * |-13. {IHB 5 G#IE 1g=v@7[;y9 =vG/= ;y3.J. C 9. { fºhRQ)mon[s ngmoe[s u hkn[sfihx1mtng¹“”oe[|whkjwbdmon u eŲ¢¨&aQ€Ã]9j q[|l]1n[mtn[sYebDw D ­ ²7hkfdx1egfdmon[s hkfimt|wsFEE *GEE  Ærq“ht|°jwbd| u ]i I oK  - D wªuP SVUXWi A w5oN  È _ É   EE *GEE b uP w uPRSxUXW i A w5'o NP W/]—^  A w W/]—^ 'N  P J H?J I J     ²¢mon[s°b ugŒ |wmtn[s3fd] È s@Éx™hkVs K  A b  imoJ e I  o8]9,j  bKI  imoe  o ­¼] i H o9Lµ EE *MEE  u ] © bi])n jre[n[] © hkfd]1eg| swegq Œ |lbd]1e[|l]3ÆŽs1Ÿ Œ x1|°b © htn Vj K  EE *GEE. b uP. -. D. ²¢])jlj@]žs°bdjwe“hkjwbdmon qgfihtx)]Åhkfimt|wsfd]Êswx Y Œ \#h ])n slb¤j@e“h»jwbdmon u Ÿ bin[s°j htzbdf¤bdj ŒÅu Ÿ¿hkegj htn jqzfie[s”t|@htn u ]Ê¥>e[] fd]Vn[mt\3[|l] u ]²¢moe[|whtn j3x Y[mkbis°b¢])slj Œ fi] ©oŒ ­pmtj@mongs¥>e[]#fi])s3\^m u ]1s u ] “moeg|lbd]1| u[Œ x9fi])n[x Y“htn jrx)])jwjw] bdn[slj@htgb¤fdb¤j Œ swmon jq„])ex)mo\^\3e[n[s3])j™µ u htn[sx1])j3]9yz]1\^qgfd]tµ u ]^j@|lZ1sY“htegjw]1s8·¸| Œ ¥>e[])n[x1])s1­²¢]1qI]1n u hkn>j1µ \ W1\^]slb¢n[moe[srng]j@|wh © hkb¤f¤fimongs.q“htsrh © ]1x u ]-jw])f¤fi])s.·¸| Œ ¥>e[])n[x1])s1µfNŸ¿hkq[q[|wm™ycbd\Vh»jwbdmon›n>e[\ Œ |lbd¥>e[]·Õhkb¤j L ¥>e;Ÿ´])f¤fi])s ]9ycbdslj@])n jj@mtet}~moe[|ls]9jslmon j])n¯\^]1sle[|w] u ]sl] u[Œ9© ]9fimoqgq„])|q“ht|°·¸mtbdshte$Imoegj u Ÿ£egnQj@|lZ1s

(94) fimtn[” j@])\^q[s u ]¡x™hkfdx1ezfgx)mo\^\#]¢n[moe[s(q„mte[|w|lmon[s½fd]/x1mon[s°j hkjw]1| u htn[s(fi]¡q“ht|@hk”o|@htqgY[]¢h»fdfdmoe Œ htezy3htq[qzfdbdx™hkjlbimtn[s n>e[\ Œ |°bi¥>e[])s1­ B * ( B ( B Y BDCCB * C[Y A *  BDC \POD* B Y {ht|fi]#gbihkbds u ])s Œ ¥>e“h»jwbdmon[s Œ ¥cezb © hkfd]1n j@])s1µx1hkfdx1egf Œ ])s}~e[sw¥>e;Ÿ£ÆQfNŸ£mt| u |l]V_[µn[mte[s.hkf¤fdmon[s3qImoe © mtbd| Œ)© hkfde[])|$fd]1s$x™ht|whtx)j Œ |°bis°jwbd¥ceg]1s u bdswqI]1|lslb © ])sž])j u bdswslbdq“hkjlb © ]1s u e swx Y Œ \#h u ]+±¯htx™²¢mo|w\#htx ³ ]1nDfi])s x1mt\#q[ht|@htn jÆrx1]9fdfd]1s u e$swx Y Œ \Vh u ]ƒpmc] J ‹ N¾­ N. ­H­¯®.°8±

(95) ²¨³´.

(96) h «p L_  

(97)  {-/,. 0jI 36587:9;p=#?A@7 36587h=9AGvIH@.;>IzJ. moegs

(98) ·Õh»bislmon[sÃ| Œ · Œ |l]1n[x)]bdx)bÆ Š NNµ[q„mte[|Ãx™hkfdx1ezfi])|h»bis Œ \^]1n j

(99) fi])s Œ ¥>e“hkjlbimongs Œ ¥>egb © hkfd]1n jw]1s1µ u Ÿ´moËbdf |w])swslmo|lj

(100) fd]1sp]9yzq[|w])sws°bimongsswezb © htn j@])sJ qImoe[|Ãfd]²¢¨&a €¡]9jpfd]²¢¨&a€w€K ²¢¨ a € ²¢¨ a €l€ MONpPtQTSxUXWZY`MO\fPtQTW/]—^:Y`MOa. 3. . . . 8. MO\\\ Q I • k SVULW I  Y w Qx•jm SVUXWZY  S M\\a  Q I •jk SxUXW YW!]_^:Y  S  MO\ava Q I •jk SVUXWZYW/]—^ Y  MOa/ava Q I •jk W/]—^ I Y w Q

(101) •en W!]_^hY  P M\\\\ Q D •jk I SVUXW D Yw Q •jkv•jm SxUXW Y  M\\\a H Q D •jk I SxUXW I Y W/]—^hY  MO\\ava XQ D •jk I SVUXW YW/]—^ Y

(102) . ­. . .  . %8  6

(103) . H. D. I. .

(104).   %8 3   %8

(105). 3 Q  •jkv•jm •enSVUXWZYW/]—^hY%8  P MO\\a/a 3 Q  • kv•jm • nfSxUXW Y MO\ava/a Q •jk SVUXWZYW/]—^ Y

(106)  MOava/ava Q • k W!]_^ Y w Q  • kv• n  W!]_^  Y

(107)

(108)  3. wM\\ava. 3. D. ­. 8. W!]_^$Y . I. I. D. ª È _>É mte[sh © mongs u bdswswmcx)b Œžu htngsfi]$j htzfi]1hte;µ¡fd]1s]1|w|l]1e[|ls u Ÿ´mo| u |w]Œ+Æ x1]9fdfd]1s u Ÿ´mo| u |w]žˆz­¢®]1s]1|w|l]1e[|ls u Ÿ´mo| u |w]’^slmon j

(109) fdb Œ ])sÆ u ]1s u[Œ |lb ©oŒ ]1sjw|wmtbdslbdZ1\^])sx1mt|w|w])swqImon u hkn>jÆ u ]1sp]1|l|w])e[|ws u bdswqI]1|ws°b © ]1s)µIj@htn u bds ¥>e[]Ãfi])s¡])|w|l]1e[|ls u Ÿ£mo| u |w]pˆ&swmtn>j¡htslswmcx)b Œ ])s¢Æ u ])s ugŒ |lb ©oŒ ]1s¡¥ce[hkj@|°biZ)\#])s¡x)mo|w|l]1slq„mon u htn j¡Æ u ])s¬]1|w|l]1e[|ls u bdsws°biq“h»jwb © ]1s)­ {-}|. 0jI IM>IH77M 5 77yIHB)IH@A; ;yIHB:5ª?>IHGvGvIzJ. { ht|l\rbisrj@mtegj@])s#x)]1s^]1|l|w])e[|ws)µx1]1|°j hkbdn[])s#slmon j#]9yzx)fde[slb © ])\^]1n j”omoe © ]1|ln Œ ])sVq[ht| •jk  mtet•jk I ­€Ûf s1Ÿ£ht”tb¤j u ]1sp]1|l|w])e[|wsÃj@])\^q„mo|l])f¤fi])s| Œ swezfdj@htn j u Ÿ´e[n[]&bdn j Œ ”t|@hkjlbimon u ]ƒ

(110) e[n[”o]Ç&egjwj@h’.qImoe[|

(111) x1]8\^m u Z)fd] u Ÿ Œ ¥>e“hkjlbimtn u Ÿ£h ug© ])x)jlbimonžzb u bd\^]1n[s°bimtn[n[])f¤fd]t­®pmoe[sps@h © mongs u[Œ }°Æ#¥>e[]3x)]1s])|w|l]1e[|lsbdn u egbdsw])n>j swe[|e[n \^m u ] i+l2(6o u ] “moeg|lbd]1| i}Mr i¡mHlsnpo<bSVUXW¨i I*) J + meP (Tn N¡o/o9µgfd]1s

(112)

(113) ]  ]9j@spswegb © htn j@Vs K £D¼bdswqI]1|lslbdmon i™•jk  o

(114) K §f¤fi]Vh$jwmoet}~moe[|lsjw]1n u htn[x1]Æ [˜ I š !„ Ð ! Vfih © b¤j@]1slsw] u Ÿ¿h uz© ]1x9jwbdmon›htqgq“ht|w])n j@]qImoe[|&jwmoegj@])s fd]1s u bd|w])x)jwbdmon[hs Yz­Ä§f¤fi]8s)Ÿ£] ygqg|lbd\#]q“ht|Ãe[n u[Œ qgfºhkx1]1\^])n>j]9yzx1])sws°bd· u ] © hkfd]1e[x| K. * )   +. . +. iI o ™i Qx•jk/o ' ' Qi SVUXWZY:P<(W/]—^:YLo I ' k   P<(. _a`O­_=b.

(115) 

(116)     

(117)  ! "#

(118) $%. . £D¼bdsws°biq[hkjwbdmon i™•jk I o

(119) K. §f¤fi]3ht”tb¤jq“hk| “š½ÔÓ zÐÕÎ  u ]fNŸ£ht\^qgfdb¤j@e u ] È ugŒ slj@htgb¤fdbds@h»jwbdmonÄÉ u ]j@mtegj\^m u ] u ] “ moe[|°bi])| u ]8\#htngbdZ1|l]8]9yzq„mtn[]1n jwbd])f¤fd]3q“ht|Ãfd] ·Õhtx)jw]1e[|xK Vm"! igQ

(120) • k/o I ' i I*) o D ' i+ SxUXWZY:P<(W/]—^:YXo D ' k.  mkj@mon[s x)]1qI]1n u hkn>jQ¥>e[] x1]1s$]1|l|w])e[|ws u ] n“hkjwe[|w]Åq[e[|l]1\^]1n j$j@])\#qImo|l])f¤fi])sQslmon j u ] ·Õhkbdgfd]1s ]x„])jws ]1nÀx)mo\^q“ht|@h»bislmon[s u ]1sr])|w|l]1e[|ls#mtË bin j@])| © bd]1n[n[])n A jfd]1s.j@])|w\^]1s^slq“hkjwbihtezy •jm¶])j• n fimo|lsw¥>e[]n[mte[s x Y[mtbdslbdswslmon[se[nQngmo\3[|l] u ]²¢moe[|@hkn>j.- Œ ” h»fi]Æ  ­ {- 0jI IM>IH77M

(121)  5$9;>=#9G#I J {½moeg|7fi])sp])|w|l]1e[|lsÃ|w]1s°j htn jw]1s u Ÿ´mo| u |l]8ˆgµzfd] ·Õhtx9j@]1eg{| • k¡]1s°j

(122) q“ht|°·¸mtbis¢]1n[x)mo|w]8q[| Œ sw])n j™­Ämte[s

(123) hkf¤fimongs q“ht|$htge[s u ] fihtn[” hk”o]žfi]Å·Õhkbd|w] u bdswq“ht|whij@|w] u ] \#htngbdZ1|w]ÆÀq„moe © mtbd|$fd]1s$x1mt\#q[ht|w])|¯htecyD]1|w|l]1e[|ls swq[hkjwbihkfd]1s

(124) bislswe[])s u e$swx Y Œ \#h u ]ƒ

(125) mz]kµ[]1n$qImos@htn Vj K •jm†bd• neb • ])h j Q

(126) •jk.b • I £Dh u bdswqI]1|ws°bimtn u Ÿ´mo| u |w]y’ K {½ht|w\rbdsfd]1s(]1|l|w])e[|ws u Ÿ´mo| u |w]¡j’ ‚ swq“hkjlbºh»fi])s ‚ѵ‘n[mte[sx1mon[s°j hkjwmon[s®fNŸ¿htgsw]1ngx1] u ] u[Œ |°b ©tŒ ]1s½x1|lmtbis Œ ])s½s°b gbd]1n¥>e;Ÿ£egn.\^m u ]¡x1mo\^qImos Œ È + (bd  coÉn;Ÿ´]1s°jq[htsqgfde[sh  ])x)j Œ ¥>e;Ÿ´e[n.\^m u ]¡s°bi\^qgfd] È + ( bc É9­ ¼€°ag{¬§/ƒaz€°ª&ag{„¨¬X7€!¨(§ ¼Ÿ«ª&ƒp¼ ƒ§¶’ z¨p²7X笂ƒ /  A   3 MO\\\ ±Q¨p² ²Ãª8Á°’ ƒ±Q¨p²7Ç ƒÃª&Ž § /   A   3 MOava/a Á°’ Ž Ÿ´]1|w|l]1e[|8slq“hkjwbihkfd]rbislswe[] u eÅswx Y Œ \#h u ]V±¯htx™²¢mo|w\#htx ³žsl]rj@|@h u egb¤j8q“ht|&e[n |w]9j ht| u hkq[q“ht|l]1n j u ]pf¾Ÿ£h ug© ]1x9jwbdmon;µgslmoe[s/bin[x9b u ]1n[x)] YzµzhteImoegj u Ÿ´e[njw]1\^q[s k µcqImoe[|/e[n-\^m u j] i+l2(6o u mon[n Œ µ u ] © hkfd]1e[|xK )  Qx•   + I Q .Y{P<( I .¨’( Y

(127) k w I    + P<( hkfdmo|ls̴ceg]fN٣])|w|l]1e[|

(128) swq[hkjwbihkfd]8bdswsle[] u eQslx Y Œ \#h u ]ƒpmc]8sw]&j@|wh u egb¤j

(129) q“ht|

(130) e[n[]h © htn[x)]LK )   Q

(131) •   + I QR .Y{P+( I .¨’ ( Y

(132) .k  + P ( ²Ÿ´]1s°j¢hV|l\^]1|bix9bÄ¥>e;Ÿ [˜  ! ! [ ˜ & !-Ô#" !

(133)

(134) !c˜ — gÐ “Ô ! &$"ÂÎ '&

(135) !&%„µo¥>e[])fd¥>e[]pswmtb¤j¬fi]

(136) \^m u ] u ] “moe[|lbd]1|x1mtn[slb u[Œ | Œ µ½¥ceg])fd¥ceg]swmtb¤j3fNŸ´bdn[x9b u ])n[x1]x Ygmtbis°bi]kµÔ ! —™Ó('–c š & !ÌÍ “Ó*)Î » š “Ó+

(137) ! Ð  '& !

(138) %-,ÛÎ.N—/½Ô՘½—›Ô#" &0 ! !cÓtиΠ21;˜ ! Ô !D—™Ó'(–cš & ! •-Î !  ! Ô#" 3! (Ó !54p¨6jwb¤j@|l] u Ÿ bdng·¸mo|w\#hkjlbimtnQ]9j u ]x)mo\^q“ht|whkbislmonÊh © ]1x J  NNµ[fd]slx Y Œ \#h u ].±¯hkx‘²¢mo|l\Vhkx ³ h#e[ng] u bdswqI]1|lslbdmon u ]n“hkj@eg|w]-slq“hkjwbihkfd]-sw])\3gfihtgfd]$Ưe[n687 swx Y Œ \Vh u ]-ƒpmc]moËd 6 b c*9²Ÿ´]1s°j#Æ u bi|l]hte/687 slx Y Œ \#hV|l])j@ht| u hkn>j

(139) fd]8qgfiegs

(140) fNŸ£h ug© ])x)jlbimon:9 ­H­¯®.°8±

(141) ²¨³´.

(142) Ž‘‰. h «p L_  

(143) . u bdswslbdq“hkjlbimtn u Ÿ´mo| u |w]ˆ>K pmoe[spq„])|wx1] © mongsbix9bfºh u bis°jwbdn[x)jlbimtnÊ]1n j@|l]fd].²¢¨ aQ€7]9jfd].²¢¨ a$€l€7q“ht|pe[nQjw]1|l\#] u ] u[Œ |°b ©tŒ ] x)|wmtbds Œ ] È n;Ÿ£h„]1x9j htn j u mon[x¢¥>e[]¡fi])s\^m u ]1sx)mo\^q„mos Œ s@ɽq„mte © htn jht”kbi|hte3sl]1n[s u ]¡fNŸ¿hkjlj Œ nce[hkjwbdmon u ]7fNŸ£ht\^qgfdb¤j@e u ]

(144) x1mo\^\^]phte^sw]1ngs u ]ÃswmonVht\^qgf¤bd¹“x1hkjwbdmon;µtslbd\#qzfi])\#])n j¢q“hk|fi]Ãs°bi”ong] u e#qg|wm u egb¤j .¨’ (TYSVUXWZYc­ ®]7·Õhkb¤j u ]

(145) x Y[mtbdslbd|fi]p²¢¨ a.€½moerfd]p²¢¨&ar€w€(q„mte[||w])sljw]1|j@moek}~moe[|wss°j htzfi]kµo|w] © bd]1n j¢Æ x1mongslb u[Œ |l]1| x)].q[|wm u egb¤j x)mo\^\^]3j@moek}~moe[|wsq„mtslb¤jwb¤·¢h © ]1x.qImoe[|x] „])j u Ÿ£hkjlj Œ n>e[])| e[nžqI]1ežqgfde[sfNŸ£ht\^qgfdb¤j@e u ] u ])s

(146) \#m u ])sx)mo\^q„mos Œ s)­ ®]·Õhkb¤j u ] x Y[mtbdslbd|7f¾Ÿ£hkf¤j@])|wn“htngx1]&]1n jw|w] fd]8²¢¨&a-€])j¢fi]²¢¨ a€w€¬q„])|w\^])jÃhkfimt|ws1µz]1n x1mtn[slb u[Œ |whtn j fd] ugŒ qgfihtx1])\^]1n jsweg|-’žbdj Œ |@h»jwbdmon[s#x1mo\^\^] Œ j htn jVe[n[]Qjw|@htngslfihkjwbdmon;µ u Ÿ bingYgbiI]1|#fi] j@])|w\^] u ] u[Œ |lb ©oŒ ]x)|wmtbds Œ ]]9j u mon[x u Ÿ£hkjwj Œ n>e[]1|pe[n qI]1e$\#mkbin[s

(147) fNŸ¿ht\^qgf¤b¤j@e u ] u ])s\^m u ]1s

(148) x)mo\^q„mos Œ s)­ ¼€°a[az€~{I¨¬X7€°ª& ag{I¨¬X7€!¨ § ¼3Ÿ¿ª&ƒ¼ ƒp§¶ˆ c¨p²7X笂ƒ ±Q¨p² ²Ãª&ƒ±Q¨p²7Ç ƒ7ª8§ ²¢¨ a €¡moeʲ¢¨ a €l€  ²¢¨&a €¡]9j²¢¨&a€w€   w / A MO\\\\ SVUXW Y I E#SxUXW Y E   w / A MO\\ava E .¨’ (TYSVUXWZY6E  c ‰ . £Dh. /. w A MOa/ava/a. I #E W!]_^{Y. W/]—^ Y. E. p e[\ Œ |lbd¥>e[]1\^])n>j1µ x)])fiÆ#sl]jw|@h u ezbdjpq“ht|Ãegn[]3h»jwj Œ n>e“hkjwbdmon u ]&f¾Ÿ£ht\^qgf¤bdjwe u ] u Ÿ´e[n¯\^m u ] i+l2( o u ] Ämte[|lbd]1| u htn[sfih u bd|w])x)jwbdmon Y hke¶„mtegj u Ÿ´e[n¶j@])\^q[sk#q“ht|fd]1sV·Õhtx)jw]1e[|ls-\3egf¤jwbdqgf¤bix1hkjwb¤·¸s slegb © htn jVK £D±$¨p² ²Ãª&ƒ±Q¨p²7ÇÁ¢²¢¨ a €7ª&‚ ²¢¨&a€w€K. Vm"! whQx• ) i + I. £D±$¨p². D. D.  +  (  #W!]_^:Y. SVUXW Y{P. ²Ãª&ƒ±Q¨p²7ÇÁ¢²¢¨ a €¢§¬X ²¢¨&a€w€K. Vm"! whQx• ) i + D. I. £. ƒ7ª8§8K. E. : "! whQx• ) i + i Vm. I. D. . 

(149). SVULWzY6ExP<( D /W ]—^ YLo#k. 

(150). SxUXW Y{P<( D !W ]_^ YLo#k D.

(151) . #SVUXWpY xE P<( D E#W!]_^:Y E }o k [o. D E. §nÊmoeggfdbihtn jpfi]j@]1|l\^] u ] u[Œ |°b ©tŒ ]rx1|lmtbds Œ ]kµ„xkŸ£])slj8Æ u bd|w]3])nÊn[moegsqgfihRQ™hkn>j u htngsfihslb¤j@e“h»jwbdmon u ´Ÿ e[nÅ\^m u ].slbd\^qgfi]^moeōgbd]1n u eÅslx Y Œ \#h u ]#±¯htx^²¢mt|wn“htx ³ u htn[s fih © ])|wslbdmon+²¢¨&az€p])j8€l€

(152) ]1n hkf¤j@])|wn“hkn[x1]kµ[n[moe[sÃx)mon[s°j hkjwmon[s È u htn[s7fih.\#])swe[|l]8moË-fºh © hkfd]1eg|Ãht[slmtfieg] u Ÿ£egn[]&·¸mon[x)jlbimtn-j@|lbd”omkÁ n[mt\ Œ j@|°bi¥>e[]]1sljpj@mtet}~moe[|lspsle[q Œ |lbd]1eg|w]3mte Œ ” hkfd]3Æ^swmonQx™ht|l| Œ ÉÃ¥>e[]3Ô " gÐ1Б–;˜ zÐÕÎ ¶— gÐ  “Ô ! & ! “˜ —™Ó('–c š & ! •-Î !!c—)Ð —1˜ –  !c˜

(153) !¶ÎI˜ –  “Ô !  ˜  ! &΄˜  Ô ! zЙБ–;˜ gиΠ ՗™—™˜ ! &(˜ —™Ó'(–c š & !žÍ “Ó*)Î »š “Ó+.

(154) e“htn j

(155) hke-j@]1|l\^] u ] u[Œ |lb ©oŒ ]8x)|wmtbds Œ ]8fdmo|lsw¥>e;Ÿ bdf®])slj

(156) q[| Œ sl]1n j™µ[b¤f®ht”kbdj7htesw])n[s u ]fNŸ¿hkjlj Œ nce[hkjwbdmon \#hkbds u ]8\VhkngbiZ)|w]&j@mtet}~moe[|lspqzfie[s÷Õhkbdgfd]8q“ht|

(157) |@htqgq„mo|°j

(158) htezy-j@]1|l\^]1s u ]80\ W)\^]mo| u |w]k­ _a`O­_=b.

(159) ŽoŽ. 

(160)     

(161)  ! "#

(162) $% {-13. {IHB 5 G#I IT; $=/G#9A@ J. C 9. moegs © mtegfimtn[s.htqgq[egvo])|3n[mtsq[|lmoqImossle[|¥ceg])fd¥ceg]1sr|w])q[| Œ sw])n>j@hkjwbdmon[s3q„mtfihkbd|w])s u ]^fNŸ£])|w|w])e[| u bis~Á Iq ]1|ws°b © ]¯]9j u bislslbdq“hkjwb © ]#}~e[sw¥>e;Ÿ£Æžf¾Ÿ´mo| u |w] _])n ·¸mtn[x)jlbimon u ]fNŸ¿htng”tfi] u Ÿ bdn[x)b u ]1ngx1] u ]$fNŸ¿h ug© ])x)jwbdmon Y qImoe[|

(163) e[n$\#m u ]8slbd\^qgfd]2i I lc[o¢])jpe[nQ\^m u ]8x)mo\^q„mos Œ i#uXl¨u o ­“mte[s

(164) n[moe[spqgfihRQ1mongs u hkn[sÃfi])sx9bi|lx1mon[s~Á j hkn[x1])s u Ÿ´e[n[]pj@|@hkn[slfihkjwbdmonÆe[n[] © bdjw]1swsl] u ]p\^m u ezfi]$Q{b usle[|/e[n-\#hkb¤fdfiht”o]p| Œ ”oegf¤bi])|¢x™hk|w| Œpu ]x1mtj Œ • bdcM' c I È •jk.bdcM' c>u‘É u e[|whtn j

(165) e[n-j@])\^q[f s k.bcg­[ace[|Ãx Y“htx)e[n[] u ]1s7¹[”oe[|w])sÃn[moe[s u bislswmcx)bd]1|lmon[sÃfi])s ]1|l|w])e[|ws u ]n[hkj@e[|l]3q[eg|w]1\^])n>jj@])\#qImo|l])f¤fi])s È ƒpÇ’oÉ7x™ht|p])f¤fd]1sslmon j u Ÿ£htImo| u x1mo\^\e[n[]1s hteQslx Y Œ \#h u ]±¯htx™²¢mo|w\#htx ³]9jÆ^x)])fdegb u ]ƒpmc]tµg]1n[slegbdjw]tµÄqImoe[|Ã\^mon j@|l]1|

(166) f¾Ÿ bi\^qImo|lj@htn[x)] u ]8fd]1eg|

(167) bdng¦“eg]1n[x)]q“hk| |@hkq[q„mt|ljphtezy]1|w|l]1e[|ls u ]8n“hkj@eg|w]8qgfde[sslq“hkjlbºhkfd]1s È ag{½­¿É9­ £Dh u bdswqI]1|ws°bimtn u Ÿ´mo| u |w]y’ K pmoe[sphkf¤fimongsh  ])x)j@])|pÆ^x Y[ht¥>e[] u bd|w])x)jlbimoqn Yzµ“egnQ|wh‘vtmon u ]&j hkb¤fdfd]^Ž8¥cezb © Dh W)jw|w]8|@hkx1x1mte[|wx9b u ] fih u bis°j htn[x)].]1|l|wmon Œ ]slb(fi]swx Y Œ \#h|w]9j ht| u ]fNŸ¿h ug© ])x)jwbdmonÊmteÊhkf¤fimtn[” Œu ]fihVL\ W)\#]·ÕRh Q1mtn u hkn[s fd]8x™hts

(168) x1mtn>jw|@hkbd|w]k­Ä§nQx)mon[s Œ ¥>e[]1n[x)]tµ„e[nQslx Y Œ \#h#q“ht|l·Õh»bdj u[Œ x1|°bi|whkbdj

(169) fd]8x1]1|lx)fd] u ]|wh™vomon Žo­ REPRESENTATION POLAIRE DES DISPERSIONS O(2)-MODE(2,0) 1.5 ROE SP. RK2 1. MC SP. 1. REPRESENTATION POLAIRE DES DISPERSIONS O(2)-MODE(1,1) 1.5 ROE SP. RK2 1. MC SP. 1. 0.5. 0.5. 0 1.5. 0 1.5. 0.5. 0.5. 1. 1.  FS.V,:&B:! H&@

(170) H.$%"&($#+E!=6"-"FD):'HF+B+(>6Y4F.C26!V.$@>$@*'#" $#S N('*C2!)  r C6+EP,.'$)r+ $r @ '<' A ', + ) "$@ ,        "! # # %$ &   $ $#.C; R / / 1.5.   

(171)    (  & ? A' );5  78  ( :;& $   ( 

(172) ! ?<. 1.5. )  780). B =B . . . . 7B.  mte[s ©tŒ |lb¤¹“mongs-gbd]1n¶¥>e;Ÿ´e[n[]¯bdn j Œ ”o|@hkjlbimtn u ]¯ƒpe[ng”o]ÊÇ&egjlj h ’Å]1n[”t]1n u |l]¯e[ng]¯]1|l|w])e[| u bdswqI]1|lslb © ] hte[”t\#])n j htn j

(173) fºh © b¤j@]1slsw] u Ÿ£h ug© ])x)jlbimon$\#hkbds

(174) jwmoet}~moeg|ws u ]&\#htngbdZ1|l]&bing· Œ |lbd]1e[|pÆ3fNŸ£])|w|l]1e[|

(175) swq[hkjwbihkfd] u bis~Á qI]1|ws°b © ] u e slx Y Œ \#h u ] ƒ

(176) mz]k­mte[s^x1mon[s°j hkjwmon[s Œ ” hkfd]1\^]1n j#¥>e[]f¾Ÿ´]1|l|w]1eg|rswq“hkjlbºh»fi] u bdswqI]1|lslb © ] u e swx Y Œ \#h u ]±¯htx‘²¢mt|w\#htx ³|w]9j ht| u ] fih © b¤j@])swsl] u Ÿ£h ug© ]1x9jwbdmonQ]9j

(177) x1]kµI’·¸mtbisÃqzfie[sÃ¥>e[]&fNŸ£])|w|l]1e[|Ãslq“hkjwbihkfd] u e$swx Y Œ \#h u ]ƒ

(178) mz]&n[]&fNŸ¿h © htn[x)]t­ £Dh u bdswslbdq“hkjlbimtn u Ÿ´mo| u |w]>ˆ K pmoe[shkf¤fdmon[s-h  ])x)j@])|Æ+x Y“hk¥ceg] u bi|l]1x9jwbdmon Yzµ/e[n |@h™vtmon |w])q[| Œ sw]1n j@htn jfi]ÊqImoe[|lx1])n>j@ht”o] u ] fNŸ¿hk\#qzfdb¤j@e u ]#¥>e;Ÿ b¤f¬q[| Œ sw]1| © ]VhteÅ\^m u ] u ] Ämte[|lbd]1|&x)mon[slb u[Œ | Œ ­(§nÅx1mongs Œ ¥>e[])n[x1]kµ½egn slx Y Œ \#h q“hk|l·Õhkb¤j u[Œ x)|lbd|@hkb¤j

(179) fi]8x)]1|wx9fi] u ]8|@h™vtmonŽ™‰o„‰ i.-eo9­ ­H­¯®.°8±

(180) ²¨³´. .

(181) ŽÑ’. h «p L_  

(182)  REPRESENTATION POLAIRE DES DISSIPATIONS O(3)-MODE(2,0) 150 RK2 100% MC SP. ROE SP. 100. REPRESENTATION POLAIRE DES DISSIPATIONS O(3)-MODE(1,1) 150 RK2 100% MC CASI ET II SP. MC CASI OU II SP. ROE SP. 100. 50. 50. 0. 0. 150. 150. 50. 50. 100. 100.  FS. ,:&(HH&B.$%"&@  Q.$%" &E$#+( "="!D\:'#!+A+(N6Y4!HF.C26! .$@V$@:'#" $#S]C2 C6+(K,.K$ @'  N(' ) r  '  r+ $%r " "FS<$%" &E'<    $#D):+A& *C2$%"&(' R        "! "# # %$ & '/ A / ',+ ) 150. 150. . . . . . . .   

(183)    (  & ? A' ),5  7 8 . (:& $  (=

(184) ! ?<. )  7 8). B =B . . . . 7B.  mte[s ©oŒ |lb¤¹“mon[s¥ceg]¯f¾Ÿ´e[swht”o] u Ÿ´e[n[]Qbin j Œ ”o|@h»jwbdmon u ]ʃ

(185) e[n[”t]žÇ&egjwj@h ’mcx1x1htslbdmon[n[]¯e[n ]x„])j-htn jwbÂÁ u bdsws°biq“h»jwb¤·~­Ÿ´]1|w|l]1e[|swq[hkjwbihkfd] u bdsws°biq[hkjwb © ] u e+swx Y Œ \#h u ]Vƒpmc]^]1slj3x1monz·¸mo|w\^]VÆ$n[mkj@|w]#q[| Œ1u bdx)jlbimonTK q[|l]1n[mongs1µ>q“ht|] yg])\^qgfi]kµ>Yªbdczµtf¾Ÿ´]1|l|w])e[|¡slq“hkjlbºhkfd] u bdswslbdq“hkjlb © ] u e#swx Y Œ \#h u ]±¯htx™²¢mo|w\#htx ³^h»jwj Œ n>e[] fNŸ¿ht\^qgf¤b¤j@e u ] u Ÿ£])n © bd|wmt(n t‰ -­„‚n[] u moe[zfi]rh»jwj Œ n>e“hkjwbdmon u ]3x)])jwjw]3n“h»j@e[|l].hkjlj Œ n>e[])|@hkb¤jfNŸ£ht\^qgfdb¤j@e u ] u Ÿ´]1n © bi|lmon^’ mo|x1])x)bz]1sljI}~e[s°j@]1\^])n>j½f¾Ÿ£hkjlj Œ n>e“h»jwbdmon u eg]¢ÆÃf¾Ÿ´]1|l|w])e[|slq“hkjwbihkfd] u bislslbdq“hkjwb © ] u eslx Y Œ \#h u ]8ƒ

(186) mz]k­“{hk|

(187) hkbdf¤fd]1e[|ls1µ“n[moegspqImoe © mon[s

(188) n[mtjw]1|Ã¥>e[]&fd]1s

(189) x] „])jws u bislslbdq“hkjwb¤·¸s u ]1s © ]1|ws°bimtn[sqg| Œ sl]1n j Œ ]1s u e swx Y Œ \#h u ]±¯hkx‘²¢mo|l\Vhkx ³swe[|

(190) fi]&\^m u ]8x1mo\^qImos Œ swmtn>j u b #x)b¤fi])\^]1n j u bdsljlbing”oe“htgfd]1s)­ €ÛfÄ]1s°j¬x)fihkbd|/]9j¬q„mte[|·Õhkbd|w]Ãfi]Ízbdfihtn;µ ¥>e[]Ãfd]1s¬q[Y Œ n[mo\^Z1n[])s u bdswqI]1|lslb¤·¸s u Ÿ£mo| u |w]p’ ]9j u bislslbdq“hkjwb¤·¸s u Ÿ£mt| u |l] ˆ#htswslmzx9b Œ sÆ^x Y“ht¥>e[]swx Y Œ \VhVsw]1|wh^fih^swmo\^\^] u ]1s u bislq„])|wslbdmon[sp])j u bdsws°biq“h»jwbdmon[sjw]1\^qImo|w]9fdfd]1s È x)mo\.Á \3egn[]1s3htezyÅslx Y Œ \#hts@É])jswq[hkjwbihkfd]1shtswslmzx9b Œ ]1s.Æ x Y“htx)e[n u ]Vx)]1sswx Y Œ \Vhks1­½moe[sq[|lmoq„mtswmon[s u mongx u ]q[| Œ sw]1n jw]1|&sweg|fd]1sL\ W)\#])s ]9yz])\#qzfi])s fi])s ]1|l|w]1eg|wsjwmtj hkfd]1s u bdswqI]1|lslb © ]1s u Ÿ´mo| u |w].’#])j u bdswslbdq“hkjlb © ]1s u Ÿ´mo| u |w]1spˆ#h © ]1x8fd]1s

(191) L\ W1\^]1spx1mongx1]1qzj@s u ]8|w]1qg| Œ sl]1n j h»jwbdmon;­ £Dh u bdswqI]1|ws°bimtnQj@mkj hkfd] u Ÿ´mo| u |l]y’ K  fimt“hkfd]1\^]1n j™µ¡q“ht|fd]ʍgbihkbds u ]¯fih u bdswqI]1|lslbdmon u ]Ên“hkjwe[|w]Qj@]1\^qImo|w]9fdfd]tµ¡fi]Êslx Y Œ \#h u ]žƒ

(192) mc] hteg”o\^]1n j@]Ãfih © b¤j@]1slsw] u Ÿ¿h ug© ])x)jwbdmonhtegj hkn>j © mtbd|w]pe[nVqI]1e#qgfde[s¬q„mte[|fi])s¡\^m u ]1s¬x)mo\^q„mos Œ s/¥>e[] fd]8swx Y Œ \Vh u ]±¯htx™²¢mo|w\#htx ³n[]&fih u bi\rbdnceg] È © mtbd|ù“”oe[|l]1s

(193) x)b;ÁÛx1mon j@|l]‘É ­ £Dh u bdswslbdq“hkjlbimtnQj@mkj hkfd] u Ÿ´mo| u |l]>ˆ K  fimt“hkfd]1\^]1n j™µ fd]1s¡swx Y Œ \Vhks¢]1n © bds@ht” Œ s7mon j/e[n[] u bislslbdq“hkjlbimonV\^mtbings/bd\^q„mo|°j htn jw]¥>e[]pfi])e[| u bis~Á swhtq“hkjlbimon8slq“hkjwbihkfd]¬|w]1slq„])x)jlb © ]t­Ñ€Ûfis Œ n Œ ¹“x)bd]1n j u ex™ht|whtx)jwZ1|w]/htn jlb¤Á u bislslbdq“hkjlbd· u Ÿ£egn[]bin j Œ ”o|@h»jwbdmon ƒ

(194) e[n[”o]Ç&egjlj h#’ È © mkbi|ù“”oeg|w]1s

(195) x9b¤ÁÛx1mon j@|l]‘É ­ _a`O­_=b. .

(196) Ž‘ˆ. 

(197)     

(198)  ! "#

(199) $% REPRESENTATION POLAIRE DE LA DISPERSION-MODE(2,0) 1.5 SCH. ROE 1. SCH. MC. REPRESENTATION POLAIRE DE LA DISPERSION-MODE(1,1) 1.5 SCH. ROE 1. SCH. MC. 1. 1. 0.5. 0.5. 0. 0. 1.5. 1.5. 0.5. 0.5. 1. 1. 1.5. 1.5. REPRESENTATION POLAIRE DE LA DISSIPATION-MODE(2,0) 100 100% SCH. MC 80 SCH. ROE. REPRESENTATION POLAIRE DE LA DISSIPATION-MODE(1,1) 100 100% SCH. MC CASI ET II 80 SCH. MC CASI OU II SCH. ROE. 60. 60. 40. 40. 20. 20. 0. 0. 100. 100 20. 20. 40. 40. 60. 60. 80. 80.  FS. ,:&(H:.& #  F[W<$#S<" 6"N,:&(HH&B.$%"&@  N ' ) Fr ]?.$@',. Q+ r ,. N'C2W<A !D)'$@Q+ ) <SDP2& <S<! S.V+(DP'.,.V&BD\:+E 

(200)  @$#S.C2W< 6"=C2'D)*'#     K,'&("  KR RA7 * / */ R 100. 100. . . . <. . . . . . . . . 4 ^\( 4 \(? A Y A *  B C \OD* B Y ¼ htn[s¡fi])s7htq[qzfdbdx™hkjlbimtn[s7¥>egb © mon jÃslegb © |l]tµgngmoe[s¢|l]1s°j@]1|lmon[sÃh © ]1x e[ng] © bdjw]1swsl]"Q8b uswe[|¡e[n[] ”o|°bdf¤fd] u ] zŽ8qImtbin jwspsle[| zŽh © ]1x • bdcM' c I µ - b c/' .]9j u ]1s

(201) x1mon u bdjlbimtn[s u ]Imo| u sÃq Œ |lbdm u bi¥>e[])s1­.

(202) . ­H­¯®.°8±

(203) ²¨³´.

(204) Ž™_. h «p L_  

(205)  X@7[;>9$=/Gv=};y3 E 7 M;:3HB)9'E$Id~9 ; ?pB)9; J. 3:-/,. (—™Ô zÐÕÎ  &½˜ š›Î & !

(206) 3— !cԸΠ Y b w D K ®]\^m u ] u ] Ämte[|lbd]1| È Žtµ¿‰ Éx Y[mkbis°b„n Ÿ£])slj7])n|°bi])ne[n[]pY“htezj@]÷¸| Œ ¥ceg]1n[x)] ])j/qImoe[|lj@htn j/n[moe[s/\^mon j@|wmtn[s fih u[Œ ” Œ n Œ | Œ x1])n[x1]Æfdmon[”Qjw]1|l\#] È ’»_ ‰o‰-bdj Œ |whkjwbdmon[s@É u ]^x)]V\^m u ] u htn[s8fºh slb¤j@e“h»jwbdmon u ]#x™h»fix)egf u e ²¢¨&a€ È bingslj hkgfi]™É7q“ht|

(207) |@htqgq„mo|°jphteQ²¢¨&a€w€ È slj@htgfd]‘É7qImoe[|Ãx1]9jwjw]bdn[x)b u ])n[x1]k­  

(208) . ADVECTION EN TRANSLATION-THETA=-PI/4-MODE(1,0). ADVECTION EN TRANSLATION-THETA=-PI/4-MODE(1,0) CAS I. U(X,Y,10). CAS II. U(X,Y,10). 4 3.5 3 2.5 2 1.5 1 0.5 0. 4 3.5 3 2.5 2 1.5 1 0.5 0 1. 0. 1. 0. 0.5. 0.5. Y. 0.5. Y. 0.5. X 1. X. 0. 1. ADVECTION EN TRANSLATION-THETA=-PI/4-MODE(1,0). 0. ADVECTION EN TRANSLATION-THETA=-PI/4-MODE(1,0) CAS I. U(X,Y,11). CAS II. U(X,Y,11). 4 3.5 3 2.5 2 1.5 1 0.5 0. 4 3.5 3 2.5 2 1.5 1 0.5 0 1. 0. 1. 0. 0.5. 0.5. Y. 0.5. Y. 0.5. X 1. X. 0. 1. ADVECTION EN TRANSLATION-THETA=-PI/4-MODE(1,0). 0. ADVECTION EN TRANSLATION-THETA=-PI/4-MODE(1,0) CAS I. U(X,Y,12). CAS II. U(X,Y,12). 4 3.5 3 2.5 2 1.5 1 0.5 0. 4 3.5 3 2.5 2 1.5 1 0.5 0 1. 0. 1. 0. 0.5. 0.5. Y. 0.5. Y. 0.5. X. X. 0. 0.  @'+AS<"&('P$#S\C;'S. ,:S "FD),.KW<$#S<"Q! '?.$@Q,:S]JLNMPO #$#S.C W< 6"=,:S JLNM\OO K,'&("  $#.H+($%"&('P,:S DP'<,.  

(209) 3 U  JLNM\OQ&A. "$@?:+( QJ LVMPOO  "H$@?:+E 1. 1. . < . . . . . . _a`O­_=b.

(210) Ž. 

(211)     

(212)  ! "#

(213) $%. ®]1s]1|w|l]1e[|ls u Ÿ£htq[q[|lm™yzbd\#hkjwbdmon[sn>e[\ Œ |lbd¥>e[]1s u ]#Y“htezj@]1s·¸| Œ ¥>e[])n[x1])s3¹“ngbdswsl]1n j u mongxVj@mtet}~moe[|lsq“hk| htq[q[ht|@hij@|l]&]1n j@|whtn[slfihkjlbimon$q“ht|7fd]Ã}~]1e u ]1sp]1|l|w])e[|ws u Ÿ£ht|w|lmon u bN­  •-Γ Ð gÐ ÕÎ  &$"¤˜  !žÓ ԸήÓ' !"& ! “˜(—™—tœ mte[s8n[moe[sq[|wmtq„moslmon[s8\#hkbdn>jw]1n“hkn>j u ]^q[|l]1n u |l]Vegn[]^x)fdmzx Y[] u ]hke[sws8])j u ]rfdegb·Õhkbd|w]^q“ht|lx1moeg|lbd| e[nžfiht|w”o]rx)]1|lx)fd] u ]rq Œ |lbd\#Z9j@|l] k‰ È t‰o‰t‰bdj Œ |@h»jwbdmon[s É ­®mte[s&moqgjwmon[s&qImoe[| u ])ezyžj!vcqI]1s u ]^x™hkfdx1ezfisxK fNŸ£e[n$|w])q„mts@htn jp]9yzx)fde[s°b © ]1\^]1n j8sweg|

(214) fd]²¢¨&a€ È u mon[n[htn jegnQL\ W1\^]| Œ swegf¤j hkjp¥>e[]&fNŸ¿hkf¤j@])|wn“hkn[x1]]1n j@|l] ²¢¨&a€¢]9j²¢¨&a€w€/e[n[]8·¸mtbisÃsle[| u ]1ecy“ÉÃ])j

(215) fNŸ¿hkegj@|l]&x Y[mtbdslbdsws@hkn>jfi]²¢¨ a €¡moefi]²¢¨&a€w€¡]1n ·¸mon[x9jwbdmon u ]-fNŸ´bdn[x9b u ])n[x1q] Y u ]\#htngbdZ1|l]$ÆÊ|w]1s°j@])|^jwmoet}~moeg|wsrslj@htgfd]t­¨e[q“ht|wh © hkn>j1µn[moegs#qImoe © mon[srx)mon[slj@hkj@])| ¥>e;Ÿ´e[n[]3jw])f¤fi].x)mon u b¤jwbdmonÊbdngb¤jwbihkfi]kµ„|°bix Yg].]1nž\^m u ]1s u ] “moe[|°bi])|1µIh ug© ]1x)j Œ ]r])nÊj@|@hkn[slfihkjwbdmon u htn[segn[] x1mtng¹“”oe[|whkjwbdmon u[Œ ¹“nzbi]Vx1mo\^\^] Œ j htn jbingslj hkgfi]kµ ugŒ ” Œ n[Z1|l]Vj@|lZ1s|@htqzb u ])\^]1n j™­

(216) e[]Vsl]q“hkswsw] ÁÛj°ÁÛb¤f¬]1n |wmkj hkjlbimon ROTATION SUR 5000 ITERATIONS. TRANSLATION A THETA=-PI/4 EN 283 ITERATIONS SOLUTION EXACTE. U(X,Y,50). CAS I. U(X,Y,2.83) 3.5. 3. 3 2.5. 2.5 2. 2 1.5 1. 1. 1.5 0. 0.5. 0. 0.5. Y. 0.5. Y. 0.5. X. X. 0. 1. 1. ROTATION SUR 5000 ITERATIONS. 0. ROTATION SUR 5000 ITERATIONS CAS I. U(X,Y,50). CAS I OU II. U(X,Y,50). 3. 3. 2.5. 2.5. 2. 2 1. 1.5. 1 1.5. 0. 0.5. 0. 0.5. Y. 0.5. Y. 0.5. X. 0. X. 0. QJ +('<C2W<>,. $#S. ,. @$#S.C2W< ,'&("V6"=,.KW<$#S<"Q! ?.$@. 7 Z"$%"  <$#+U6X<$@C2"   H$#.+E$%" &E'<KF &E" S<$%"&(' ,UTE&B."$@?:&A+B&("  JLNM)O *3 ' U    = '@"$%" &E'<KF &E" S<$%"&('P,UTE&B."$@?:&A+B&("  JLNMPOQ6X.C6+AS.H&(Y ='@"H$%"&('G! H&("S<$%"&('),. "$@?:&A+B&("  JLNMPOQ'SPOHO= !+(' 3 1. . 1. . §n.|wmkj hkjlbimon µ™f¾Ÿ bingslj hkgbdf¤b¤j Œ n>e[\ Œ |°bi¥>e[]¢sw]1\gfd]7n[]¢q[hts½| Œ e[slslbd|Æ

(217) s1Ÿ Œ j hkgfdbd|1­t²¢])fiÆq[|lm © bd]1n jswhtn[s u moegjw] u eÊ·Õhkb¤j&¥>e[].fd]1s ¥>e[]9fi¥>e[])s\^m u ]1sbin[s°j htzfi])sslmon j j@|lZ1s&\^moe © htn jws8h © ]1xeY]9j&¥>e[].fd]r” hkbdnʍgbd]1nÅ¥>e[] swegq Œ |lbd]1e[|ÃÆVŽ n[]qg|w]1n u q“hts¢egn[] © hkfd]1e[| u[Œ \^]1sle[| Œ ]t­[¨ x1]9j Œ ” hk| u µc|@htqgq„]9fimongs¢n[moegs1µgq[ht|¢] yg])\^qgfi]kµ ­H­¯®.°8±

(218) ²¨³´.

(219) Ž‘‹. h «p L_  

(220) . >¥ e[]8fi] u[Œ q“htslsw]1\^])n>j ]1sljp])n - D b AA  q„moeg|{Y b w D ­ ¨bdn[s°b¾µI]1nÊ|lmtj h»jwbdmon;µ“bdf(])slj ngmtj htzfi]3htegj hkn>j¥>e[].sle[|wq[|l]1n“hkn>j u Ÿ´mogj@])ngbd|e[n[]swmtfdegjlbimonQj@|wZ)sx)mo|w|l]1x)jw] u htngse[n[]/slb¤j@e[hkjwbdmon3bdn[slj@htgfd]tµ © mtbd|w]¡\LW1\^]tµkq[|w])sw¥>e[]7\^])b¤f¤fi])e[|w]¡x™ht|(sw])n[slbdgfd]1\^]1n j/\^mtbings u bdsws°biq“h»jwb © ] È u ]8fNŸ´mo| u |l] u —Ÿ u -#É 9.  ~ 4  IT; C J moegs © moegfdmon[s(swmoezfdbd”on[])|(bdx)b fd]1s(htslq„])x)j@s u bdswqI]1|lslb¤·¸s])j u bdsws°biq[hkjwb¤·¸s½swhtn[s®j@|lmon[x1hkj@e[|l] u eslx Y Œ \#h u ] ±¯htx™²¢mo|w\#htx ³#q“ht|/|@hkq[q„mt|lj¡hteslx Y Œ \#h u ] ƒ

(221) mz]ph © ])x q„mte[|¡x)] u ]1|wnzbi])|¢e[n[]pbin j Œ ”o|whkjwbdmonVjw]1\^qImo|w]9fdfd] u ]ƒ

(222) e[n[”o]Ç&egjwj@h#’z­  

(223) (—™Ô gиΠ &½˜ š›Î & ! %   3— !cԸΠ Yªb cgœ mte[s © bdswe“h»fdbdswmongs½fd]1s(| Œ slegf¤j hkjws u hkn[se[n3qgfihtnq„])|wqI]1n u bix)egfºh»bi|l]7hteqgfihtn u Ÿ£])swq“htx)]¢]9j½mt|lbd]1n j Œ swegb © htn j fih u bd|w]1x9jwbdmon u ]fih¯n[mo|l\#hkfi]-htezybislm © hkfd]1eg|ws u ]-x)]-\^m u ]-slbd\^qgfi]xkŸ£])slj#Æ u bi|l]-swegb © htn jrf¾Ÿ£h»yz] u ])s m­ÄXmoet}~moe[|ls u htn[sÃfd]1s

(224) \LW1\^]1sx1mon u bdjlbimongs1µ“n[moegs

(225) b¤j Œ |wmongs ’ k‰o‰3·¸mtbds1­Ä¼ htngs

(226) fihr¹“”oe[|l]x9b¤Á u ]1slswmoegs1µ“fi])s f Œ ”o])n u ]1spswmtn>jpq“hk|pmt| u |l] u[Œ x)|wmtbdswswhtn j u Ÿ£ht\^qgf¤bdjwe u ]t­ 3:-}|.  ?AB:5h9>9A=?A@)EhI M;:3HB)9 ~. 4 . . TRANSLATION THETA=0 - 2500 ITERATIONS - MODE (2,0). U(X,Y,25). SOL. EXACTE M.C. ROE. 3 2.5 2 1.5 1. UHC W<FDP$-,.='-$$#.C;V$#S<"H$#@". .SX<>+(>C2W<!D)$-,. $@CVJ '#2DP$@C

(227) 6"H$@ ,.@R UHC W<FDP$-,.='>,:&B&(* KY4'&B :+BS. .S<>+(>C2W<!D)$-,. $@CJ '#2DP$@C

(228) :R. u bdswqI]1|ws°bimtn K ¼ hkn[s7e[n[]slb¤j@e“h»jwbdmon u ] u bislq„])|wslbdmon \#h»ycbi\#hkfd]tµzslb„fi]swx Y Œ \Vh u ] ±¯htx™²¢mo|w\#htx ³V|w])j@ht| u ]fNŸ¿h u Á © ]1x)jlbimtn;µofi]Ãslx Y Œ \#h u ]

(229) ƒ

(230) mz]7fNŸ¿h © htn[x)] u Ÿ£htegj hkn>j1­>²¢]1x9bÄx1monz·¸mo|ljw]7f¾Ÿ Œ jwe u ] u ])s u bislq„])|wslbdmon[s¬·Õhkb¤j@])s ÆQfNŸ´mo| u |l]’ u htn[sfd]-q“hk|@ht”o|whtq[Y[]Vq[| Œ x Œ)u ]1n j™­²¢]1s.slx Y Œ \#htsrmon j u mon[x u ]1s.x)mo\^q„mo|°j@])\#])n j@s u bdswqI]1|lslb¤·¸s u bºht\ Œ j@|@h»fi])\#])n jmoqgq„mos Œ s)­ £Dh u bdswslbdq“hkjlbimtn K ¼ hkn[se[n[]

(231) slb¤j@e[hkjwbdmon u ] u bdsws°biq“h»jwbdmonV\#h»ycbd\#hkfi]kµofi]Ãslx Y Œ \#h u ]

(232) ƒpmc]7mcx1x1htslbdmon[n[]

(233) gbd]1n^e[ng] u bis~Á s°biq“h»jwbdmon u moe[zfi] q[ht|¢|whtq[qImo|lj7Æfºh u bislslbdq“hkjwbdmon u eslx Y Œ \#h u ]8±Qhtx‘²¢mo|l\#htx ³Ä­Ä²¢]1x9b®x1monz·¸mo|ljw] fNŸ Œ j@e u ] u ]1s u bdswslbdq“hkjlbimtn[s ·Õhkb¤j@]1sÆVfNŸ£mo| u |w]3ˆ u hkn[sfd].q“ht|wht”o|whtq[Y[]q[| Œ x Œ)u ]1n j™­;]swx Y Œ \#h u ] ±¯hkx‘²¢mo|l\Vhkx ³]1slj u mtn[x8n[])jlj@]1\^])n>j\^mtbings u bislslbdq“hkjwb¤·¥>e[]8fd]slx Y Œ \#h u ]ƒpmc]t­ £Dh. _a`O­_=b.

(234) ŽÑŠ. 

(235)     

(236)  ! "#

(237) $%. -• ΓРgиΠ &$"d˜ !ÅÓ ÔÕήÓ' !"& ! [˜½—™—kœ mte[sV|l] © ]1n[mongssweg|Vx)])jwjw]¯s°bdjwe“hkjwbdmonÀ·Õhkbds@htn jhkbingslbhtq[qI])fƞfºh u b © ]1|lslb¤j ŒÊu ]1s#\#m u ])s u ] “moe[|°bi])| x1mtn>jw]1n>e[s-q[ht|e[ng]Qj@]9fdfd]Qbdngb¤jwbihkf¤biswhkjwbdmon hkbdn[s°b¥>e[]$fºh q[|lbdsw]Ê])nÌx)mo\^qgj@] u ]$jwmoegj@])sVfd]1s u bi|l]1x)jlbimtn[s u Ÿ£h ug© ]1x)jlbimtn[js Y]1n u[Œ x1|lb © htn j3egn jwmoe[|8x1mo\^qgfd])j]) n t‰o‰t‰bdj Œ |@h»jwbdmon[s1­€Ûf¬])sljx)fihkbd|¥>e[]#n[moegsn Ÿ£mocÁ sw])| © ]1|wmtn[sq[htsÃfi]&q[Y Œ n[mo\^Z)n[] u bislq„])|wslb¤·x1ht|Ãx1])s])|w|l]1e[|lsps)Ÿ¿hkn[n>egfdfd]1n jhtq[|lZ1sph © mtbd|Ã¥>e[]&fi]8slbd”on“h»fhkb¤j u[Œ x1|lb¤j/]1n jwbdZ1|l]1\^]1n j¡fi]Ãx)]1|wx9fi]k­c{ht|x)mon j@|w]

(238) sle[|fi]

(239) qgfihtn u ]Ãfºh u bdsws°biq[hkjwbdmon;µofd]

(240) x1mon[s°j hkj u Ÿ£e[ng]p\^mtbdn u |l] © bislx1mos°bdj Œ ht|ljlbd¹“x9bi]9fdfd] u ežslx Y Œ \#h u ]^±¯hkx‘²¢mo|l\Vhkx ³ È L\ W)\#]rs°j htzfi]k­d­¤­«Épq“ht| |whtq[qImo|lj hteÊswx Y Œ \#h u ] ƒ

(241) mz]&])slj

(242) ¦Äht”o|whtn j™­ . ROTATION SUR 5000 ITERATIONS CAS I OU II. U(X,Y,50) 3. 2.5. 2 1 1.5 0. 0.5. Y. 0.5 X 1. 0. ROTATION SUR 5000 ITERATIONS ROE. U(X,Y,50) 3. 2.5. 2 1 1.5 0. . 0.5. Y. 0.5. '@"$%" &E'  S<C6+('<C2W<>,.$#S.HQ "DP'<&B. $%"H"FS<-.$@+(>C2W<!D)$-,. $@CJ '#2DP$@C

(243) 8 &BC6& JLNMPO'S J LNM\OO DP$#&B <$#& ! @!<!$#+ <S<.$@+(>C2W<!D)$-,.'#R © h»fi])e[|\#h»ycbi\#hkfd]mtgj@])nceg] q[ht|-fi]Åslx Y Œ \#h u ]+±Qhtx‘²¢mo|l\#htx ³ ]1s°j u Ÿ£])n © bd|wmon u ] I l  q„moeg| X. 1. 0. .  h sw])egfd]1\^]1n j I l I qImoe[| fd]#slx Y Œ \#h u ]#ƒpmc]rswmtb¤j - u Ÿ Œ x™ht|°j™­mte[s&q„mte © mongs ©tŒ |lb¤¹“])|3htegswslb¬¥>e[]rfih u bdsws°biq“h»jwbdmon u ]ƒ

(244) mz]&|l] © bd]1n j Ære[ng] u bislslbdq“hkjwbdmon u moe[gfd] u ]8x1]9fdfd] u ]3±Qhtx‘²¢mo|l\#htx ³ZK  I '  I '   . ­H­¯®.°8±

(245) ²¨³´. . I ' I.

(246) Ž. h «p L_  

(247) . BDC[Y. B . \. B Y. 57>?5ª?  EhI G#9 `;y9 =vGv=};y3.J. -/,. 4. ® ]Ãswx Y Œ \Vh u ]p±¯htx™²¢mo|w\#htx ³3]1slj/])n#\^])swe[|l] u ]p\^mon jw|w]1|sle[|fNŸ Œ ¥ce[hkjwbdmon u Ÿ¿h ug© ])x)jwbdmon#gb u bi\^])nzÁ slbdmon[ng])f¤fi]

(248) e[n[]Ãbdn[slj@htgb¤fdb¤j Œ ])n © ]1|ls u ]1s¬\^m u ])s u ] “moe[|°bi])| u ]ÃY“htegjw]1s·¸| Œ ¥>e[]1ngx1]1s/sw]9fimtn#fNŸ´bdn[x9b u ])n[x1]hYz­ ²¢])jlj@]bin[s°j htzbdf¤bdj Œ ])slj slmoe[|ln[mtbdsw]3x1ht|p])f¤fi]q„])egjq[htswsl]1| x)mo\^qgfiZ9j@])\#])n j bin[htq„])| Q)e[]t­„{ht|x Y“htn[x)]tµÄfi])s u _b  Œ |w])n>jw]1s¬htqgq[|wmcx Y[]1s u e.swx Y Œ \#h u ]

(249) ±¯hkx‘²¢mo|l\Vhkx ³ u hkn[s½fih·ÕRh Q)mon u ]¡x™hkfdx1egfd]1|½fi]/¦“ezy„µtqI]1|l\#]9jwjw]1n j u Ÿ´mogjw]1ngbd| u ])ezy © ]1|lslbdmon[s jwmoet}~moe[|lss°j htzfi])s u ].x)]3swx Y Œ \#h-q„mte[|jwmoegj@])sfd]1s u bi|l]1x9jwbdmon[s YVh © ]1x.egn[] x1mtn u b¤jwbdmonQsle[|Ãfi]8n[mt\3[|l] u ]²¢moeg|@htn .j - ng] u ] © htn jpq“hts W)jw|w]8swe[q Œ |°bi])e[|Æ - / K £ ²¢¨ a €7ª8‚ €l€¢])n$·¸mongx)jwbdmon u ª ] Y^h © ]1,x - / b   ­ £ ²¢¨ a €¢§/XD€w€¡]1nQhkfdjw]1|ln“htn[x)]egn[]&bdj Œ |@h»jwbdmonQsle[| u ]1ecyQh © ]1, x - / b A ­ ®]rx1m u ]Vaz€~§¬ƒƒ

(250) ¨ u ].fNŸ«ª&§/ƒ

(251) ¨ s1Ÿ bin j Œ |w])swswhtn jrhtezy Œ ¥>e“hkjlbimtn[s u ]rfºh\ Œ x1htngbd¥ceg] u ])s&¦“egb u ]1s8n;Ÿ£h q“hts.jwmoegjw]-fºhÊslmoe[qgfd]1slsw]$q„moeg|.| Œ hkfdbdsw])|rfi])s u b © ]1|wsl]1sVhtq[q[|lmzx Yg]1s u ] x1mtng¹“”oe[|whkjwbdmon u eÀslx Y Œ \#h u ] ±¯htx™²¢mo|w\#htx ³]9jpq„])egj u mon[x © |@hkbdsw])\3gfihtgfd]1\^])n>j sw]&j@|lmoe © ])|

(252) ]1n$slb¤j@e“hkjlbimtn u Ÿ bdn[slj@htgb¤fdb¤j Œ ­ ¼])s u[Œ)© ])fdmoq[qI]1\^]1n j@s u e›x1m u ] ac€~§/ƒpƒ

(253) ¨mon j Œ j Œ | Œ h»fdbds Œ s u ]\#htngbdZ1|w] ÆÊqImoe © mtbd|3bin jw|wm u egbd|w]-fd] ²¢¨&a€w€¡])jp kjlbi|7fd]1s u ])ezy © ])|ws°bimongs u e swx Y Œ \#hswezb © htn j@])Vs K £ ²¢¨ a €7ª8‚ €l€¢])n$·¸mongx)jwbdmon u ]&fih © b¤j@]1slsw ] i}Ml  o

(254) hkswswmcx)b Œ Æ#x Y[ht¥>e[]x)])f¤fiezfi] K M 

(255) c £ -}|. š ‡ ƒZltM  c. š ‡ ƒ`ƒ. ²¢¨ a €¢§/XD€w€¡]1nQhkfdjw]1|ln“htn[x)]egn[]&bdj Œ |@h»jwbdmonQsle[| u ]1ecy ­ 4. 57>?5ª?  EhI I/yIH77/t@f7hB)3p=#587:ITJ. ®]#slx Y Œ \#h u ]±Qhtx‘²¢mo|l\#htx ³Äµ½x)mo\^q“ht|@h»jwb © ]1\^])n>j3hte swx Y Œ \#h u ]#ƒpmc]rqImoe[|&f¾Ÿ Œ ¥>e“h»jwbdmon u Ÿ¿h u Á © ])x)jlbimon$gb u bd\#])n[slbdmon[ng])f¤fi]kµ„sl]| Œ)© Z)fd]GW9j@|l]ng])jwjw]1\^]1n jp\^mtbdn[s u bislslbdq“hkjlbd·~­Ä¼]&qzfie[s)µ[bdf;]1n[”o])n u |l]egn[] ]1|l|w])e[| u bislq„])|wslb © ] © biswhtn j7Æ8|w]9j ht| u ]1|fNŸ¿h uz© ]1x9jwbdmonx)]¥>egbI])slj/q“ht|°·Õhkbdjw]1\^]1n j¡x1mon jw|@hkbd|w]pÆ&fºh&j@])n u htn[x)] u e$swx Y Œ \#h u ]ƒ

Références

Documents relatifs

Chez l’Homme, les segments de gène V H ont été classés en sept familles (la famille 7 n’est pas représentée ici car aucun segment fonctionnel n’y a été décrit) qui ont

Le Négus consacra une énergie considérable en vue de gagner cet appui international, mais, malgré la force de son discours prononcé en juin 1936 devant ses pairs à la tribune de la

In this paper, we propose a novel approach based on the barycentric coordinates of automatically tracked 2D facial landmarks from videos to objectively evaluate the facial

Dirk Obbink (dir.), Doctrine and Doxography. Studies on Heraclitus and Pythagoras, Berlin / Boston, De Gruyter, 2013, p.. et le logos auquel les hommes devraient accorder

Les exorcismes ne sont pas publics, les sœurs noires elles-mêmes sont tenues le plus possible à l’écart, et c’est chaque fois Jeanne qui force les choses pour que, finalement,

Toute- fois, d’autres marqueurs des cellules POMC tels que NeuroD1 n’ont pas été induits dans cette expérience, ce qui indique que Tpit suffit in vivo pour provoquer la

Mais elle y occupait une place modeste : il faudra la liberté et le goût de la transgression du roman en langue vulgaire pour que la situation soit renversée :

Les thèmes majeurs (tab.5.4) abordés par les îliens interrogés sont, pour la grande majorité, les mêmes sur toutes les îles : ils concernent les usages anciens