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Algorithmes et logiciels pour la simulation numérique en fluides non-Newtoniens

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(1)Algorithmes et logiciels pour la simulation numérique en fluides non-Newtoniens Pierre Saramito. To cite this version: Pierre Saramito. Algorithmes et logiciels pour la simulation numérique en fluides non-Newtoniens. Mathématiques [math]. Université Joseph-Fourier - Grenoble I, 2002. �tel-00445426�. HAL Id: tel-00445426 https://tel.archives-ouvertes.fr/tel-00445426 Submitted on 8 Jan 2010. 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..

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(382) w¡>(«6>(A Bl?@> £é 8:·« ];w\>(:C>(A Bh>(:·«§>Îpi ‹ [\A¥e> < ÛV]0D"B·[¡ 1A0?‰¤1D":·[yD

(383) Bh[¡ 1A;A;>(w\w¡>

(384) ?„ÙJ>(B(Ù nx 1«§«§>­w ‹ D£ÖD

(385) [¡B­:h>(« D"5: ÛV];>(:km 1wyD

(386) A0i ¾º®J¿™±y²ÊÁ

(387) ÂZ$± D¥’ w ‹  n(n(D1?z[¡ 1Api ‹ ];A;>9;];Ò=w¡[ynpD"Bh[\ 8AJÙ

(388) n„>(];Ë Bh:ÓD"[\BqD"AB¥Œi ‹ D"AÌD"w¡ª=?z>epi ‹ [\«™D"Y1> ‰ f >o?‚w¡ 8Y1[ynx[\>(wy??z 8AB¥i>(9;];[½?‚¢8¦1¦ ra>(ABh“[ >p’ :h>(«§>„ABZD1n(nx>

(389) ?·?z[¡Ò=w¡>

(390) ? 90D

(391) :Zw¡> :;>

(392) < ?@>

(393) D"]l[¡ABh>(:·A;>(B D‹’ “w ‹ >(A0?@>(«ÎÒ;w¡>i >‚w½D‹n„ 8«§«Î];A0D

(394) ];B=>< ?·nx[¡>pA B·Ç[ ŽŒÛV];>¥HÔ ä œ Û ‰1ՋA;>ND"9;9=w¡[ Ä n(D

(395) Bh[¡ 1+ A Da’ i >o?Ê9;:h 1Ò;“w >p’ «§>

(396) ?­pi ‹ D(¤1D"w½D"A0n g >aÔ«6 pi >(’ w¡>o?Êi >-B@ª 90>¥Y1:qD"A];w½D"[¡:·> Û >

(397) ?@BD8n„Bh];>(w\w¡>(«6>(A B D’ w ‹·>p< Bh]0i >j>Ô äó× Û ‰ B. C. |

(398) ‘

(399) ›’‡‰ˆED

(400) ˆZN‰—‡ |p”¹ˆƒ

(401) ˜™‘’‡‰ˆ. ʶ  1];:w¡>

(402) ?pÝ0];[½i >

(403) ?Z¤ [½?hnx >(< wyD1?zB·[ÛV];>

(404) ?D‹’ w¡ 1[0i >-nx 1«§90 8:hB·>(«§>(AB­i >¥B@ª9Ï>CÞjº Эµ®.ßZÐGF:H‹w½i;×8¦IÙ w¡>óBh>(A0?@>(];:-i >o?‹nx 1A B·:qD

(405) [¡ABh>

(406) ?Bh 8BÓD"w\>

(407) ?‹i> É-»­ÆoçŒâ ßKJML2NLJ>

(408) ?zB-i 8A;AN>l< 90D": ¼ JML2NL,OQPSRATVU ( ¢ W ÿX ZÔ Y Û U\[  Œ] ] ’ RQ>

(409) ?zB™w½DG9;:h>o?h?z[\ 8A g ª=i :· V?zBÓD"B·[ ÛV];>VÙ í w\>n g D"«§9 i>

(410) ? ¤[¡Bh>o?h?z>o?xÙ X Ô íZÛ O Ô ^ í U í _Û a ¢w¡>-Bh>pA0?z>(]=:¥i >

(411) ?‚BÓD"];Ë6i >li >x< £é 1:h«™D

(412) Bh[\ 8AJÙV>(bB W ÿ%c ¦s];A;>ó9;:h>(«6[ >(’ :·>¥¤ [½?hnx  ?z[¡B=> < ‰ Ñ > ^ ` Bh>pA0?z>(]=d: [i>

(413) ?anx 8ABh:ÓD"[¡ABh>o?C?z];9=9;wp>(< «6>(A BÓD"[\:h>

(414) ?-?hD

(415) Bh[y?£ÖD"[\B‰]=A;>w¡ 1[‚i>Înx 8«§90 1:hBh>p«§>(AB-i > B@ª 90>li Î[ ñó>p< :h>(ABh[\>(w ¼ eGf [ Ug[hP ( ¢ Wji X Ô íZÛ O ¦ Ôhr Û f e  Œ] ’ >

(416) ?@Bw¡>ÎBh>(«§9Ì?‰i>§:h>(w½D"Ë=D"B·[¡ 8AÙ W ilk ¦™>

(417) ?zBl];A;>’?z>onx 8A0i>§¤ [½?hnx  ?z[\B;>Î< >(B [ >o?zBs]=A;> A; 1BqD"B·[¡ 1A90 8];:-wyDi >(< :h[\¤ >(< >epi ‹KÞºЭµ.® ßZÐvi ]™Bh>(AÌ?z>(];: [Z¼ f [ í qsr [tUvu Ô í©Û [hPw[Au Ô í©Û PKx‹Ô X Ô í©Û [hUw[ X Ô í©Û·Û [ Onm U 6 mpo Œ  ] ] ’ u Ô í©Û O3Ô r§í P r§`í _Û a ¢>o?zBsw\> B·>(A0?@>(];:li >§¤V 1:hBh[½nx[¡B=>< >(>B xzy{F"Psjr |pr I>

(418) ?zBl];A90D(Ä :qD

(419) + « >(’ B·:h>li >wyD6i‚>(< :h[\¤ >p< >sŒi ‹KÞºÐʵ ® ß1Ð ‰ Ñ D w\ 8[i>nx 1«§90 8:hB·>(«§>(ABCÔ·r Û >

(420) ?@Banx 8]=9;wp>(< >jD"];Ë e> < ÛV]0D"B·[¡ 1A0?¥i >lnx 8AÌ?z>(:·¤8D

(421) Bh[\ 8Ai>‰w½D Ûè]ÌD"ABh[¡B=>l< i >a«§ 8];¤V>p«§>xABZ>(B-i>‰w½Ds«™D8?·?z?> ¼ í 6í qsr§í € îÊá ‚ }~ m U P [>PKW Ô¢ Û ÿ ‚ í Uv^ƒR O ¦ mpo i [¡¤ í O ¦ ÔØ Û.

(422) }£. Ü6Ý Þß0à

(423) á â

(424) ã­ä å çaåVâÎÝß;ÞáéêVáåÝçlå ë ìZí­áéîÊåç ë­ß0ëÀïÓëÊåVðâ

(425) ß0ë­áåëÊç.  Œ]d’ }C>o?zBJwyD i >(A0?@[¡B=>V< Ù(?@];9;90 V?>(< >¥nx 1A0?zBÓD"ABh>-Ô1>o< nx 8];w\>(«§>(AB;[\A0nx 8«69;:h>

(426) ?·?z[\Ò;w¡> Û ‰ Ñ >

(427) ?ó>e< ÛV]0D

(428) Bh[¡ 1A0? Ôhr Û ÄÓÔØ Û >(< BÓD"ABs90 V?>(< >

(429) ?si=D"A0?s];A i  8«™D

(430) [¡A;> „ i>‡†tˆ Ù‰ O¢Š|qØ Ù­w¡>Î9;:h 1Ò;w“>(’ «6>ÎD"];Ëv[¡A Ä nx 1A;A ]=>

(431) ?ZÔ [‹| í |ZR Û >

(432) ?zBjnx 8«§9=w(>(< B=>‰< 9ÌD":i>

(433) ?anx 8A0i[¡Bh[\ 8A0?aD

(434) ];ËGw\[¡«§[\Bh>

(435) ?¥?@];: í Ù­?@];:sw\>ÒÏ 1:qi >(ABh:ÓD"AB90 1];5: [Ù D"[¡AÌ?zŒ[ Ûè]=>Ci >o?n„ 8A0i [\Bh[\ 8A0?Z[¡A=[¡Bh[½D"w\>

(436) ?Ê90 8];: í >(%B [p‰ Ñ  1:q;? ÛV];>Cw½D‹£é:h 8ABh“[ >(’ :h> i ]Îi  1«™D"[\A;>‚>o?zBZ:=>(< Y8];w\“[ >(’ :·>‚>(Bw¡>

(437) ?Zi 8A;AN>p< >

(438) ?ZD8?·?zg> Ú¥90>(B·[¡B·>

(439) ?xÙ f  1w¡w\>(BhB·>C¾Æ­±yº ®¯Ï¯ ´sŒ >(B à >

(440) D"A Ä f wyD

(441) ]0i >ÎÅ;»­ÆJ¼ 8AB‹«§ 1A B·:=Ž> < F d 8` »•IJw ‹ >pË [½?zBh>pA0nx>-Y8w¡ 1Ò0D"w\>li >l?z 8w\];Bh[\ 8A0a? ‰ e e Ñ >ón(D8?Zw¡[\«§[¡B·> O ¦sn„ 8:h:·>

(442) ?z90 1A0+ i DC’ ];A Ý0];[yi>‹A;Ñ> Ü¥Bh 8A=[¡>(.A ‰ ¶Ê 8];: c ¦ Ùnx>¥«§ Œi >p’ w¡>¥90>(:zÄ «§>(B i >li >o< nx:h[\:h>ai >o?¥?z 8w\];Bh[\ 8A0?-i >a90 8w\ª ] « >p’ :h>ói;D"A0?¥];A’?z 1w¡¤1D"AB-A;g> Ü¥Bh 1A;[¡>pA– 1]™Ò;[¡>(A’i >o? « >(< w½D"A;Y1>

(443) ?‚i>‰90 1w¡ª+ « >(’ :h>o/? ‰ f >(BhB·>aw¡ 8[J90>(]=BCa? ‹h>(< B·>(A0i :·O> D ’ Œi ‹ D"]=Bh:h>o?‚«§ pi >(’ w\>

(444) ?‚i Î[ ñó>(< :h>(ABh[\>(wy?„Ù Bh>pwyE? ÛV];>sw\>‰«6 pi >(’ w¡>ei > á3âÀ»²ÏÏÄ ãCâ­±y´Ï²v>(DB ãó»Z²­²­´Ïw µ F ?¶ ëE넕•IÙ0i> ¾j±y´ÏÁ

(445) ´0ÂZÆ­lÁ F d [\e> »8¢ I‰ ¶ZD

(446) :sD

(447) [¡w\w¡>(];:Ó?Cnx>

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