A Non-Overlapping Domain Decomposition Method for Solving the Navier-Stokes Equations on Unstructured Triangular Meshes
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(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. A non-overlapping domain decomposition method for solving the Navier-Stokes equations on unstructured triangular meshes V. Dolean, S. Lanteri. N° 3977 Juin 2000. ISSN 0249-6399. ISRN INRIA/RR--3977--FR+ENG. THÈME 4. apport de recherche.
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(110) Ya. . * # & . sqx\`_r` \^djx\ dfssq`xmon u mo| u `|-itxxg^|li)kq`¨^gk-xYitn p^|w`sw`nNksqp^g^|wdjmtg^smosqxdjhfhji)kldfmon^sdfn kl\^` sqmthjgkqdjmtnkq\^`|w` mo|w``,zp|q`swsqdfn^ihfmosqs1mt _rmonmtklmonNvtª<´ xhjitswsqdfxYith ivkqmrxg^|w`*kq\^djs1p^|wmo¨^hf`_ dfsPkqm_4it«)`ixmt_4p|qmo_rdfsq`1¨3`#k ``nkq\^` ¹ |qswkBmo| u `|Bitn u kq\^` sw`xmon u mt| u `|Bswx\^`_r`s<kl\|qmog^t\ kl\`*gsq`mt±iswhjmopJ`hjdf_rdfkli)kldfmonp^|qmHx` u g^|w`o¬¯)®Zª < -Z. -Fe32 Ê 1 Ê = 36 Æ @ 2FY Ê $ > Æ . ; / 5. [ \^`xYithfxg^hji)kqdjmon mtykq\^`¤Hdfsqxmog^s'©^geze`s-xithjhfsr mo|iÄ{ ¹ ndfkq``hf`_r`nWk-itp^p^|wmYzdf_4i)kldfmon m) kl\`*xmo|q|w`swp3mon u djn4kq`|q_rs1djn°±²Rª :._4mt|q`p^|q`xdfsq`hfvtµJ¨Nvitswsqg^_rdfn^rkl\i)k kq\^`9kl\^`p^\NvHsqdfxYith ¤)it|qdjit¨^hf`s1it|w`hjdfn^`Yi)|1mtni kq|qdjitn^ohf` µmon^`mo¨ekitdfnkl\i)kO . Z i j ac[^d Z lSa [ d Z ?e W R i)|q`Yi a d i j a d Z S l a d Z e ] Z gkn Ze ] Zg n ¸. R a d \^`|q` j a d itn u lSa d it|q`xmonswki)nWk ¤o`xklmt|qsyxmo_rp^gkl` u mo n kq\^`kq|qdjitn^ohf` g^swdjn^'kl\^`*Fitxk kl\^i)k & W a d R 8h + & W a G, d Fsqdfn^x`*kq\^`xmo_rpJmon^`nNkqs mt & W it|w*` itsqswg^_r` u kqmr¨3`hfdjn^`it| mon ,ª ;m . . . ; 5 /. . 7B>'A'*1A 7A: . 5.@7A'; - -< Ê 1 Ë!^ Ç. Ì df|qdfx\^hf`k k¦vHp3` xmon u dfkqdjmtn^s it|w`yitp^phjdf` u mon LON ª y n-mtn^`\i)n u µ^ixhjitsqswdjxithTn^m¢¥¦sqhfdfp-xmon u dfkqdjmtn dfs klit«t`ndfnNklm4itxxmog^nNk1 mo|%kl\^`9¤t`hfmexdfk¦v¤t`xkqmo| O &. W R. . itn u µmonkl\^`mtkq\^`| \itn u µRitndjswmtkl\`|q_ xmon u d¯kldfmondjs xmon^sqd u `|q` u mo|%kl\`kq`_rpJ`|li¢klg^|w`O 5. \^`|q` N dfs xmo_rp^gekl` u its O. R N 5. 5. N R 5. 5. P ih ]. . +-. h PK n. ^\ `|q` P djs%kq\^`yFit|¸¥ ¹ `h u Îi)x\nWg^_¨3`|ªB[ \^`it¨Jm¤o`9xmtn u d¯kldfmon^s1it|q`yitp^p^hfdj` u dfni swkq|qmon iv O mt|iodf¤t`n§nm u ` G, %mt LON µ W a G d dfs*sq`kklmitn u a G, d klm N Lkl\` u `n^sqd¯k¦v djs «t`pk g^n^x\itno` u sqdfn^x`9kl\`*xmo|q|w`swp3mon u djn`²Wgi¢kldfmondfs \NvepJ`|w¨3mthjdfx djnmtkq\^`| mo| u sµRirnHghjh _4itsqs9©gHz»djs9df_rp3mtsq` u mon Z L2N ,ªÍLdfnithfhfvtµ;kl\^`klm)kith`n^`|qtv pJ`|9gn^dfkm)<¤tmohjg_4`4itn u kl\`*p|q`swsqg^|w`i)|q`g^p u i)kl` u i)s O Ñ ÒÓ+Ñ Ô 1. &. 5. 5. .
(111) 3E.
(112) ! "$#%&'( *),+- - . . R. itn u. N. . 143 5. R a. . hd. . ; 5 5 ÈÆ -FË Ê 1 Ë!^ Ç yn LQP µ % ` i)sqsqg_4`Bkl\i¢kkq\^`<©m dfsgn^df mt|q_ kq\^djsitswsqg^_rpkqdjmondfs!¤ti)hjd u mo|$`#zHkq`|qn^ithH©^m s O W P+R a P P d dfkq\ WP R PTR h PTR h P ¸Ya h K `|q`tµtitn +3 " ©^gez u `xmo_rp3mtsqd¯kldfmondfs!g^sq` u klm xmo_rp^gkl`Pkl\`B xmo|q|w`swp3mon u djn . 0. &. . . . . .. +. .. &. . . . ¨Jmog^n u i)|wvdfnNkl`t|lith+dfn°±²Rª ¶$,ªBÎmo|w`*p|q`xdjsw`h¯voµRkl\^dfs ¨3mtg^n u it|~v-kl`|q_ dfs `¤)ithfgi)kq` u g^sqdfn^-i n^monH¥¦|q`#©`#zed¯¤o`*¤o`|wsqdfmonm)kq\^`cHkl`o`|1itn u D it|q_rdfn^r©gez u `xmo_rpJmosqd¯kldfmon+¬ ot® O .
(113) + ). W a [ d Y W R. . . . ac[. . . ;m ;. #%. T & ."A95&91*:5.@7A ´swsqg^_rdfn^ [ a e W \"d dfsBxmon^s~kitnNkBmonr`Yitx\4x`hjh dfs%itp^phjdf` u kqmkq\^`1kq`_rpJmo|lithkq`|q_ dfn-°±²Rª!$E " `²Wgi¢kldfmon^sO it|q`i a d [ \ ] a [ d [ R [ a e W \ d µ \ R
(114) Y \ itn u O \^`|q`. 1. . 1. . a [ d R !. . . a[. &!. ac[. [ P YW P d R . . [. ! . W "! d ] . . YW P d [ ] . ac[ . . Y W P d [ P ¸3E$. Fdfn4m)kl\^`| mo| u sBiy_'i)sqsPhjg_4pdjn^kl`x\^n^df²Wg^` ` mt¨kitdfn'kq\^` mthjhfm djn^sq`#k%mt+sw`_rdÃ¥ u dfsqx|q`kq`. R . J . .
(115) + ). R h. . W a [^d Y W h ] `. ¸:.. I
(116). . ¸U$. L° zphjdfxd¯k kldf_r`%dfnWkq`o|qi)kldfmonp^|qmHx` u g^|q`sL mo|!kl\^`Bkldf_r` dfnWkq`o|qi)kldfmon m)~:$¦¥ ¸U$+it|w` sqg¨e}~`x#k klmi'swki)¨^djhfd¯k¦v xmon u dfkqdjmtn `#zep^|q`sqsw` u dfnkl`|q_rs9mtBi Í ÀnWg^_¨J`|ª ynkq\^` mtkq\^`|y\^itn u µ+i)n ` 4xdj`nWkkqdj_r`i u ¤)itn^xdjn^swkl|qi)kl`tvÄxYitn ¨3`'mo¨ki)djn^` u ¨Nv@_r`itn^s mt itn§df_4phjdfxd¯khfdjn^`it|qdf³` u mo|w_g^hji)kldfmonswg^x\Äits kq\^` mon` u `sqx|wdj¨J` u dfn Í`³mog^d i)n u cHkqmog4`kY¬f3EU® itn u ¨^|qdf`©vmogkqhjdfn^` u \^`|q`tªBÍLdf|qs~kYµRitndf_rp^hjdfxd¯k1¤ti)|qdjitnNk mt±°±²Rª ~ :. |wdfkq`s1its O i)|q`Yi a d [ ac[ d R J R I
(117) ¸. 1. \ ] h . \^`|q` [ R [ [ ª[ \`n;µ$itp^phfvHdfn^i ¹ q| swk*mo| u `|9fh dfn^`Yit|wdj³i)kldfmon klm-kq\^`rn^m u ith ©gez a [ d vHdf`h u s kq\^`*· ` kqmone¥¾hjdf«t` mo|q_g^hji)kldfmon O . +. Ó!Ó=ïZè#ç [[. . . .
(118) :. . i it|w`Yi a d Z a [ d [ ] Z [ n \ 1. R. +. ac[. * # & . ¸. d. . ¦½ np^|qitxkqdjx` `|q`p^hjitx`kq\^`*`#zitxkoitxmo¨d¡itnmt kq\^`sw`xmtn u mo| u `|1©gez Z Z a [ [ d ¨Nvi)n itp^p|qmYzedj_4i)kq`-oitxmo¨^djitnÄ_'i¢kl|qdÃz ac[ d sq``4kq\^`rn^`#zHksqg^¨^sw`x#kldfmon^s mt|*_rmo|w` u `klitdjhfs9itn u `mo¨ekitdfnkl\^`9 mohfhjm dfn^4hjdfn^`Yi)|1s~vHswkl`_ O ac[ d [ R i it|q`i a d ac[ d [ R ac[ d Zt.. \. 1. ]. n. . [ \^`|w`swg^hfkqdjn°±g^hj`|-df_4phjdfxd¯kkqdj_r`djnNkl`o|li¢kldfmon sqx\`_r`dfsdfn Fitx#k-iÄ_4m u d ¹ ` u · ` ¥ klmtn _r`kq\^m u ª-´sixmon^sq`²Wg^`n^x`tµ±mon`'xitn^n^mtk`nsqg^|w`'kl\^i)kkl\^dfs mo|w_g^hji)kqdjmon dfhjhPvHdj`h u i ²Wgi u |qi)kldfxYi)hjh¯vrxmonN¤t`|qtdjn^_4`#kl\^m u mo|±kldf_4`1swkq`p^sBkl`n u dfn^*kqmdfn ¹ ndfk¦vtªB[ \` _4i)kq|qdÃz a [ d dfssqp^it|qsw`-itn u \itskq\^`swg^d¯kit¨^hf`p|qmopJ`|~kldf`s u djitomoni)h u mo_rdjni)n^x`-dfn@kq\^`swxYithjit|xYitsw` i)h¯¥ hfm dfn^ kq\^`g^sq`m)9i@|w`hji¢zi)kldfmon p|qmHx` u g^|q` ¶oitxmo¨^d mo| *itgsqs~¥¸ce`d u `h rdjn mt| u `|4kqm sqmthf¤t` kl\`*hfdfn^`Yit| s~ves~kl`_ mt °±²Rª ¶t$#ªBÎmo|w`m¤o`|µJitn` 4xdj`nWk ivkqmro`k1sq`xmon u mo| u `|1itxxg^|qi)kl` swkq`Yi u vsqmohfgkqdjmons \^djhf` «t``p^dfn^kl\^` dfnNkl`|w`s~kldfn^p^|wmopJ`|wkqdj`s±mtRkl\^` ¹ |qswkPmt| u `|Boitxmo¨d¡itnr_4i¢¥ kl|wd¯zdfs klmg^sw`ykl\^`sq`xmon u mo| u `|%`hj`_r`nNkit|~vxmtnW¤t`x#kld¯¤o`©geze`s ¨i)sq` u mon-°P²Rª Z$¦¥ ¸o ¾¥ ~$ dfn@kl\`'|wdjo\Nk~¥¦\itn u sqd u `4mt °±²Rª ¶).#ª-[ \`it¨Jm¤o`'dj_rp^hfdjxdfkkldf_r`'dfnNkl`t|li)kqdjmonÄkl`x\^n^df²Hg`-djs `hfhTsqgdfkq` u klm s~kl`i u v4©m xithfxg^hji)kldfmon^s mo|<g^n^swkq`Yi u v'©m xmt_4pgki)kqdjmtn^sµkq\^dfs ¹ |qs~k%mo| u `| kldf_r`*itxxg^|li)kq`sqx\^`_4`djs o`n^`|qithfhfvg^n^itxx`pklit¨^h¯v u djswsqdfpi)kqdf¤t`tª ; ; /. +. 2 1 Æ ^2N32 Ê 1 Ê%= 6 Æ Ê 1 @ Æ t32 @ Æ Æ §. [ \^`-xmonNkl|wdj¨^gekldfmon§mt%kq\^`xmonN¤o`xkld¯¤o`kq`|q_rs*klmkq\^`oitxmo¨^djitn _4i)kq|qdÃz@djs¨itsq` u mon§i)nitpe¥ p^|wmzedf_4i)kl`'hjdfn^`Yi)|qdf³Yi)kqdjmon mt kq\^` ¹ |wswkmo| u `|*xmonN¤o`xkqdf¤t`-©gez Z.,ªÍmo|*itn ` u o` . G, G!(1Pkl\^` df_4phjdfxd¯k ¤t`|wsqdfmonmt$kl\`i)sqsqmHxdji)kq` u nHg_4`|qdfxYith+©gHzdjs mo|w_4ithjh¯v |wdfkwkl`nits O . &! R ac[. . [. !. [. . · mtkqdjn R [ µ R [ ! µ [ R [ itn u [ivHhfmo| `#zepitnsqdfmonmt$kl\`*df_rp^hfdjxdfk1©gez `*om ¨ki)djn O . . [ . W "! d R [ ! itn u g^swdjn@i ¹ |wswkrmo| u `|. &. a &. \^`|q`O. . . [ . W &! d R . a &. . a &. . W "! d ] . . W "! d R. i Z a[ Z n. &. &. a [. . !. [. +. ! . . d ] i ZZ n a . d. Ze . +. W "! d. Ñ ÒÓ+Ñ Ô.
(119) U.
(120) ! "$#%&'( *),+- -. dfs1kq\^``,zep^hjdfxd¯ky©gHzTª °Lzep^|w`sqswdjmtn ¶e xitn¨J`sqdf_4phjd ¹ ` u dfnkq\^`*xYitsw` \^`|q`kq\^`*nHg_4`|qdfxYith ©gez- g^n^xkqdjmtnklit«t`s1kq\^`9 mo|q_ O. a &. . . a&. a[ ac[. W &! d ] a [ [ ! W &! d ac[ ! [ d W &! d [ ] a [ [ ! W &! d a [ + ! + [ d. W &! d R. . W &! d ] K a W &! d . . &. . &. . . Ímo|!djn^s~kitnx`tµ¢ mo|+kl\^`BnWg^_r`|wdjxithN©gez g^n^x#kldfmon i)sqsqmHxdji)kq` u kqm1kq\^`<itp^p^|wmzedf_4i)kl`<1df`_4itnn sqmthf¤t`|1mt mH`o¬ t¢® `\iY¤o`O. . a[ . [ . !. W &! d R. R. . kl\`|q`# mo|q` O. . a& Ka&. . W &! d R a W "! d a W "! d W &! d R a W "! d &. . . . . . &. . &. . . . . +. . ¦½ n§mtkq\^`| mt| u sµ '` mo¨klitdjn ti n§i)p^p^|qmYzedf_'i¢kl`hfdfn^`Yit|wdj³i)kldfmon ZitnÄkl\Wg^s i)n§itp^p|qmYzedj_4i)kq` oitxmo¨^djitn_4i)kq|qdÃz d¯ ` itsqswg^_r` O. Z Z. &. a&. W "! d itn u ZZ . . . . Ka. & . W &! d . · mtkq`kl\i)k mo|ykq\^`'cHkl`o`|*itn u D it|q_rdfn^¬ o)®PnWg^_r`|wdjxith±©gez gn^xkqdjmon Fsw``'°±²Jª~E$ `\iY¤t`O. . ; ; 5. . a& Ka&. W "! d R a W &! d W "! d R a W "! d &. . . . . . . 2 1 Æ ^2N32 Ê 1 Ê%= 6 Æ Ë 2 ,2A@ Æ Æ § . ´s±p|q`¤Hdfmog^swhfvtµWkq\^` df_4phjdfxd¯k±¤o`|qsqdfmon4mtRkl\^` u df3g^sqd¯¤o` ©gHz/~Y.#µo`,zep^|q`sqsqdfn^*kl\^` xmonNkl|qdf¨^gkqdjmtn mt3kl\^` kl|wd¡i)n^ohf` klmkl\` ohfmo¨i)hn^m u ith^©gez'itswsqmHxdji)kl` u kqm*kq\^` ¤o`|~kl`,z G, ¶µHdfsP mo|q_4ithfhfv |wdfkwkl`n its O . R . [ [ K [. . . . . . [ [ K [ . ^\ `|q` G ,µ G K itn u G it|w`kl\^` ¤t`|~kldfx`s*mtPkl\`r" kq|qdjitn^ohf` x`` u dfn^its mo|%kl\^`9xmonN¤o`xkld¯¤o`kl`|w_rs `mo¨ki)djn O. . ". R ]. Ó!Ó=ïZè#ç [[. . . mon^`mtB" kl\^`_ ¨J`dfn^ G, # ª{±|qm)¥. . i Z [ . [ d c a [ [. ] Z [ n K i Z [ " [ i Z [ K ] Z [ n Z [ K n K . . . . +. ". +. [ . [ ". +. ".
(121) . . * # & . ½¦nkq\^`*it¨JmU¤t``#zep^|q`sqswdjmonTµ ac[ [ K [ d jd s od¯¤o`n¨Nv O i " j ca [ [ [ d Z a d ac[ [ [ d R t i w | Y ` i. K K Z e ] . . . . . . Zo$. . lSa [ [ K [ d Z Z g n [ \^`|w` mo|w`*kq\^`hjdfn^`it|qdf³Yi)kqdjmtnmt$kl\`¤Hdfsqxmog^s ©gezxYi)ni)hjswm'¨J` " |qd¯kqkl`ni)sO i Z [ . R i Z [ . ] Z [ n ] Z [ n ". ". . . Zt.. . [ \^` u `|qd¯¤ti¢kld¯¤o` kl`|q_rsydfn»°±²JªZt. xYitn ¨J`xmo_rp^gkl` u `#zitxkqhfv |qmo_ kq\^` `#zep^|w`swsqdfmon@m) kl\` u djswx|q`#kldf³` uu d¯Tg^swdf¤t`*©^gezxmo_rpJmon^`nWkqs m) °±²Rª ¶o$) sq``'¬¯Yat®+ mt| _4mt|q` u `#kitdfhjs#ª ; ; ;. G Æ 2Fo -P Æ Ê - +32 Ê 1. [it«Wdjn^rdfnNklmritxxmog^nNk kq\^`¤)it|qdfmog^s xmonNkl|wdj¨^gekldfmon^s mt!kl\`yp^|q`#¤Hdjmogs1swg^¨^sw`xkqdjmtn^sµkl\`ydj_rp^hfdfxd¯k dfnWkq`o|qi)kldfmonmt$kl\^`*·iY¤Hdf`|~¥¸cHklmt«t`s1`²Wgi¢kldfmon^s1p^|qmHx`` u s1djnkl\`y mohjhfm djn iYv O {±\Nveswdjxith mo| `#zep^hfdfxd¯k p^\^itsq` O$`¤)ithfgi)kldfmonrmtJkl\^` |wdjt\WkP\^itn u sqd u ` [ RmtJkl\^` hfdfn^`Yit| s~ves~kl`_ klmr¨3`swmohf¤t` u O. [ R
(122) +. + )
(123) &! ] ! . . . . ac[. . [ P W d ] 1h ` . . . . Z)a . Î i¢kl\^`_'i¢kldfxYithmo|Ldf_rp^hjdfxd¯kPp^\i)sq` O!kl\^` i) sqsq`_¨^hfdfn^mtkl\^` u df3`|w`nNkPxmtnWkq|qdf¨^gkqdjmons hf`Yi u sklm-kq\^` hfdjn^`it|ys~ves~kl`_ ac[ d [ R [ \^djx\»dfsitp^p^|wmYzdf_4i)kl`hfvsqmoh¯¤o` u ¨Nvir|q`h¡i¢zi)kqdjmtn_r`kq\^m u ªP[ \^`_4i)kq|qdÃz ac[ d djs1irn^mone¥¾swvH_r_4`#kl|wdjx*sqpi)|qsq`*_4i)kl|wd¯z3ª °Pitx\4kl`|w_mtJkl\^dfs<_4i)kq|qdÃz4djsBi u `nsq`¨hjmHx«Rª±[ \^` J ¥¾kq\'hfdjn` mtJkl\` hfdjn`Yit|PswvHs~kl`_ |wdfkq`s its O. . . . [ ]. !. . . & !. [ ! ]. [ \^` u djitomtnith;¨^hfmHx«djs od¯¤o`n¨Nv O . R
(124) . + )
(125) ½u ] . &! ] ! . . . . ac[. . . [ R [ . i Z W d ] h ` Z [ n . ZXE$ Ñ ÒÓ+Ñ Ô.
(126)
(127) ! "$#%&'( *),+- -. \^`|q`.
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Un habitat de La Tène moyenne et finale à Berry-au-Bac au lieu-dit “ Le Chemin de la Pêcherie ” (Aisne).. Jérôme Dubouloz, Michel Plateaux,
It is obvious that the steel showed the plastic strain memory effects at each test temperature, in other words, in spite of the hardness of the steel cyclic stress,
Les cités et leur territoire d'influence sont administrées par de puissantes familles, celles de l'aristocratie terrienne et marchande, qui tirent leur légitimité de
L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des
In this paper, we have defined the steady-state control problem for MDP, and shown that this question is decidable for (ergodic) MDP in polynomial time, and for labeled MDP
