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Simulation of compressible viscous flows on a variety pf MPPs : computational algorithms for unstructured dynamic meshes and performance results

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(1)Simulation of compressible viscous flows on a variety pf MPPs : computational algorithms for unstructured dynamic meshes and performance results Charbel Farhat, Stéphane Lanteri. To cite this version: Charbel Farhat, Stéphane Lanteri. Simulation of compressible viscous flows on a variety pf MPPs : computational algorithms for unstructured dynamic meshes and performance results. [Research Report] RR-2154, INRIA. 1994. �inria-00074518�. HAL Id: inria-00074518 https://hal.inria.fr/inria-00074518 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 AUTOMATIQUE. Simulation of Compressible Viscous Flows on a Variety of MPPs: Computational Algorithms for Unstructured Dynamic Meshes and Performance Results Charbel Farhat , Ste´phane Lanteri. N˚ 2154 Janvier 1994. PROGRAMME 6 Calcul scientifique, mode´lisation et logiciel nume´rique. ISSN 0249-6399. apport de recherche. 1994.

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(48) ±h— k9c9Vwxz@wquhguvu­rtjkŽze hzzvtk*˜<hgpadgÊtwƒh—y„d—ÃXzvtk*h—Ê d™<k‰zvcih—y±u ÃÄdgcvj„h—zvwxd_y„Pks{ y©k. hguv*. !. P k9zH ++ ;#"1 $ J Pd<ku8ytd_zŒ™_h—y©wqu­Àhz‰hyP® d_wxyVz!h—y Àh—yV®zew½jk<È-.ºyPzvcedVP1 r pawxytf zvtk*fgcewƒ¬™<k9o½dVpswxz‡® 5. %. + 5 -+ ; , 1 1. *. '" ( &. h—y±r u­w½ytf*Ù}PuaÈP¼¶“¿¾<Ù}§ÈV¼e”¿Xp9h—y ! Ê k@zecihy u ÃÄd_cejkŽ×wxyVzed]zetkÃÄdgoxo½d¦8wxytf]܉Å,Ù¨¼ºÜŒcvÊtwxzvcih—cv®’Å,h—fgc¾h—ytf_wqhy Ù2rtoxk cewqhyL¿2ÃÄdgcvjr©oqh—zvwxd_y?¼ºu‡k9k<ÂÃÄd_c8k9Ç©h—jto½k<! V֌dgy©kh  “ Ä¿ * + ¼ . ¿ ” 3 " :?¼ ¿ 9 3 " )­¼ 4 ¿ 5 ¼º›<¿ +-, " ( & 0 1 1 . 798 1 1 . ¦8tk9cvAk * 4*1 )v¼ . 6¿ 5 H O M ) ) ¼ ¼ . ¿ ¿ J . h—y± M ) ¼ . ¿@h—y  O ) ¼ . ¿@h—cvkze©kpadgyV™<kpszekŽpsd_yP™<kŽpszew½™<k)² r©ÇPkuf_wx™<k9y€ÊP® * M. h—y±*. Y=ZZ. <A@-@ + 0XW VU <,@R+ C [ E.@ + 0\W @. ‡¼ . ¿65TSUU ). <,@ +. . Z >. < C+ / O )¼ . ¿5TSUU <AC,<AC + @0C + UV E1C + 0X0XW W C. @ + 5 @  %^ C + 5 C  %`. Y=ZZ Z [. ¼é–V¿.

(49) =3 C"< 4'C%$  2IEC"! $ 68<8& –. !96t ! j !" (tk„Ê dgrty±th—cv®†2( ¼ , ¿*dÃ*zetk² d¦ Pdgjh—wxy¨wƒu h—cvzewxzvwxd_ytkwxyVzedh ¦Íh—oxo8Ê d_rty thce® (2¼ , ¿’hy Ëhy wxyV{ ytwxz‡®7Ê dgrty ©h—ce®\ ( ¼ , ¿* 2( ¼ , ¿5 (  ¼ , ¿ ?( ¼ , ¿¾ÈtÅLk9z

(50) 1 ¼ , ¿@Pk9ytd_zekzvtk*dgrtz‡¦Íh—ci„rtytw½z8ytdgcvj„h—oXhz h—yV® dgw½yPz8dà 2( ¼ , ¿¾ h—y  l 1 h—y  Pk9ytd_zekzvtk*¦8hoxoL™<k oxdVpsw½z­®7hy ¬zvk9j k9c¾h—zer©cek<È 1!yzetk]¦8h—o½oLÊ dgr©y th—cv®?(2¼ , ¿iVh×ytd_´ºu‡oxw½¹padgy Pw½zew½dgy„hy h ֌w½cewqpito½k9zpsd_y Pwxzvwxd_ydgyzvtk‰zvk9j k9´ cihzertcvk’h—cek’wxj dŠu­k* =. º¼ •<¿ ڌd„Ê dgrty ©h—ce®¯psdgy Vwxzew½dgywqu*u­ kpaw|{ k¹ÃÄdgc*zvtkVk9y u­w½z‡®<È,¥Œk9y±psk< zetk7zed_zih—o@k9ytk9cvfg®À§k crtytw½z*d—à ™<dgo½rtjk]h—y „zetk*tcvkueu‡rtcek*d_y¹ze©kצÍh—o½o,h—cvkf_wx™<k9yÊV® * ” <?„ lB„ ' 5 € ¼  4  — ” ¿ <   | > E 5 <  | ¼ºl<¿ 1 W 0 “ Õtdgck9ÇVzek cey ho² d¦!uh—cvdgrty Th—w½c­ÃÄd_wxoqua2zetkÀ™Pwƒuepsd_r uksª~kpaziu7h—cekhguvu­rtjkŽ°zed ʧk?y©k9fgo½wxfgw½ÊtoxkÀhz wxyV{ ytwxz‡®<Vu‡dzv h—z]hœr©ytw|ÃÄd_cej0ÃÄcvk9k9´¶u­zecvkh—j u­z¾h—zvk™<kpszvdgc . wquwxj€§dŠu­k7dgX y ( ¼,¿* < 5. ” > l 1 5LK psu‡d<wxyu  P > W 5  ” ' ¼ _¿ ¦8tk9cvk¯wƒuzetk’hytfgo½k×dÃhzez¾hgpiÛL hy   wquzvtk‰ÃÄcek9k9´¶u­zvcekhj¸?h_p„yVrtj7ʧk c9È Õtdgcw½yPzvk9cey±h—oP² d¦!uag ( ¼ , ¿Xwqu h—cvzewxzvwxd_ytk wxyVzed*rt u‡zecekŽh—j h—y Vd—¦8y±u­zecvkh—jÊ dgrty±th—cvwxku¦8twƒp h—cvk*wxy„fgk9y©k9ciho,wxyÀpsdgyVzih_psz8¦8wxzv„zetk‰¦Íh—o½o,ʧd_rty thce® *( ¼ , N¿ 5 (  ¼ , ¿ (   $ ¼ , ¿iÈ .ºy„ze±h—z]p9hgu‡k<Pzvtk tcvk9™Pw½dgr u!Pks{±ytwxzvwxdgy„dà . wqu8wxj©ced™<k r u­w½ytfh  hcih—Ê d_oxwqp*tced{ oxk*ÃÄdgc!zetk‰ÃÄcvk9k9´¶u­zecvkh—j ™<k9o½dVpswxz‡®<È Õtdgc8k9Ç©h—j€toxk<gÃÄd_c8zetk*td_ce'w & dgyVzih—o ² d¦ Ê k9z‡¦k9k yz‡¦d toƒh—zekŽu8u­td¦8y¹w½y„Õ^w½fgrtcvk”_tdgytk’p9hyÀu­ kpsw ÃÄ® * l 1 5.¼¶‚ · >C ¼ I ¿v¿ F ¼ºµ<¿ lm  5 1 5 l1  > †. . . y. x. Õ^wxf_rtcekG”r* ¥Œd_cew'& dgyVzih—o,™<k oxdVpsw½z­® ©ced—{±oxk‰ÃÄdgc!wxyVzek9cvy h—o ² d¦!u . !#"$ " R  &%  !. (tk„² d¦ Pdgjh—wxy #‰¼ , ¿’wqu h_ueu‡rtjkzed ʧkÀh" d_ox®Vfgdgy±h—o!ʧd_rty PkŽËcek9f_wxdgy«d—Ã#. ‹'9ÈÅLk z(')¹Ê kh. ­u z¾h—y ©h—ci?zecvwqhytfgrtoƒh—zvwxdgy?dà #‰¼ , ¿¾Lhy +*¹zvtkjh—ÇVwxj„hoLoxk ytfgzv¹d—Ã@zvtkkVfgku8d—Ã,')<È~Ü%™<k9cvzek9ÇdÃÍh zecvwqhytfgo½k  wƒuŒPk ytdgzvk¬ÊV® Q  ~h—y ¹zvtk’u­k9z!d—Ã@wxz¾u)y©k9wxf_PÊ dgcvwxytf7™<k9cvzewqpakuÊP®.-¼/­¿¾ÈLÜ8z8khgpi¹™<k cezek Ç Q  ©h psk9o½o |  ¼ , ¿Xwqu8psd_y u­zvcer pazekh_uzetk]rtytwxd_yd—Ã>ze©k*u­rtÊ©zecewƒh—ytf_oxkucvku­r©oxzew½ytf×ÃÄcvdgjzetk³u­rtÊ~Pw½™Pwƒu­wxd_y ÊV®¬j€kh—y u8d—Ã@zvtk jkPwƒh—y udÃ@khgpi¹zvcewqhytfgo½k d—Ã,')zv h—z‰wƒu‰psd_ytytkpszvk¬zvd Q  ¼¶u­k9kGÕ^wxf_rtcekG“¿iÈ (tk.

(51)  .

(52) .   .  

(53)      . •.

(54)  . Ê dgrty±th—cv®d—Ã6|  ¼ , ¿XwquVk9ytdgzvk ÊP® + |  ¼ , ¿¾Phy zvtkŒr©ytwxz@™<kpszed_cd—ÃXze©kŒd_rtz‡¦8h—c¾ytd_cej„ho§zvd + |  ¼ , ¿ ÊV® 1  ¼ , ¿ 5.¼  ^ ¼ , ¿>  ` ¼ , ¿e¿¾ÈB(tk*rtytw½dgy„d—Ã@hoxo~zetku‡k’psdgyVzecvdgo,™<dgo½rtjku@psdgy±u­zew½zertzvku8h Pwƒuepscvk9zew &h—zvwxdgy d—Ã

(55) Pdgj„hwx?y #‰¼ , ¿* . # )95  |  > *tyVrtj7Ê k9cdÃ2™<k9cvzewƒpsku2d—à ' ). . j G1. Mercredi 4 Mai. 1988 19:36:48. I. i. G2. INRIA Sophia-Antipolis SINUS STEVE. XÕ wxfgr©cek’“ *Lnd_yPzvcedgo,™<d_oxrtj€kŒw½y¹hy¹rty±u­zecvr pszvrtcekf_cewq (tk7u­±h—zewƒh—oVwquepacek9zvw'&hzewxd_y„jk9ze©dV¹hgVdgtzvk¹tk9cvk psd_jÊtw½ytkuzvtk×ÃÄd_oxoxd¦8w½ytfÃÄkhzertcvku×¼¶u­k9k  › ÃÄdgc]Pk9z¾h—w½oqu¿ *

(56) h{ ytw½zek‰™<d_oxrtjk!rtV¦8wxy „httcedÇVwxj„hzew½dgy„jk9zvtdVœÃÄdgc!ze©kpadgyV™<kpszew½™<k² rtÇVkusÈLˆŠkpsdgy±d_ciPk c u‡ h—zvwqh—o@h_p9psrtc¾hgps®Àwqu*hgpitwxk ™<kr u­w½ytfÀh—yk9ÇVzek y u­w½dgy?d—à @h—yÅLk9k9;c ýu*¸?Á׈tn@Åzvkp©ytwq}<rtk  ”s–  zvdrty±u­zecvr pszvrtcekjkŽu­tku 

(57) h7psoqh_ueu‡wqp9ho !]h—o½k9ceÛVwxy{ ytw½zek‰k oxk9jk yPzpak9yPzvk9cekŽh—t©cedÇPw½j„h—zvwxd_yÃÄdgc!zetk’Pw ª~r u­w½™<kŒ² rtÇVkusÈ ÅLk9z |  ^ & h—y  |  ( & Pk9ytd_zek7zetk7z‡¦d„cek tceku‡k9yVzih—zvwxd_y u‰d—à |  ¼ , ¿Œw½y"zvtk€psd<dgc¾Pwxy hzek„u‡®tu‡zek9ju‰Pks{ ´ ytk?ÊV® ; 1 h—y  1 ,cekŽu­ kpszv! wx™<k9o½®<È Ø®?Pka{ ytwxzvwxd_y, |  ( & wqu‰h{ ÇVk?ceksÃÄk9cvk9y psk’cek9©ceku‡k9yPz¾h—zvwxdgy?dà |  ¼ , ¿iÈ ! .ºyPzvk9fgc¾h—zvwxytf7Ù} È,¼º›Â¿d™<k9c |  ( & ®Vwxk9oƒtsu *  + ¼ . ¿  3 " 4*)‡¼ ¿ 5  ” 3 " :¼ ¿ ¼ºš<¿   . +-,.  1 0. " (&.  . 1 1 ..  1.   . 798 1 1 ..  1. !. !!wx™<k9y zv h—zze©kŒzvwxjḱPk9cew½™_h—zew½™<kwƒu2psdgj€trtzekŽ×ÃÄdgc@h*psdgy u‡zihyPz 1 h—y 7ze hz!|  ( & P d<kuytdgz@Pk §k y . dgyÀzetk’zew½jk , tzvtkj„httw½ytf Ù}§È,¼¶šÂ¿w½yPzvdg*. 1 5 1 ¼ ; 1 > , ¿@h—y±¬ze©kwqVk9yPzvwxz‡®  ; 1 5.  1. p9h—yÀÊ kr u‡k¬zvdzvcih—y±u ÃÄdgcvj.

(58) =3 C"< 4'C%$  2IEC"! $ 68<8& l  . ,. . . .  ;1 0.     $. 391 " 41 )e¼ ..      $. ¿  ;1. 5 .     $. Õ^wxy±h—oxo½®<Pw½yPzvk9fgc¾h—zvwxytf7Ù} ÈL¼e” ·Â¿@ÊP®€ h—cvziu8oxkh_tuzed *     ; ,   . 1   $. 4*1 )e¼ .. . 0.  . 0. .    h .   h   $ . 0. . .   h   ” $.  . ¿ "

(59) 1  ¼ , ¿ . . “ . ›. .

(60). ¿ "

(61) 1  ¼ , ¿ . ¼e”_”—¿. .

(62). ¿ " 3 1 F  ;1 – F  F F ^ ^ ^ ¦8tk9cvk + |  & ¼ , ¿5 + |  & ¼ , ¿ + | & ¼ , ¿¾,h—y±  F 5  F ¼ ; > I ¿@wqu!zetk€b8”u‡ h— k ÃÄrty pszvwxd_yPks{ ytkŽ"hz ze©kי<k cezek Ç Q  hy ¹h_ueu­dVpawqh—zvk¬¦8w½ze„ze©k×zvcewƒh—ytf_oxk ×È Ü { ciu‡zŒd_ciPk9c{±ytwxzvkי<d_oxrtj€k‰Pwƒuepscvk9zew &h—zvwxd_yd—à ” f_d<ku‰hguÃÄdgo½oxd¦!su * ” 5   .      .   0 , a¼ .   > .  > 1  ¿ ¼e” “¿ 5. . .  78.   :?¼. ¼e” ·Â¿. ”.

(63). 41)¼.. $ . ¿"1¼,¿. 4*1 )e¼ .. $. ” 93 " :?¼ ¿ 798 1 1 .  ; 1. . $. . 1 .. .  . . . . . . . . . !. #".  . . . $%'&. . )(. . ¦8tk9cvk  Pk9ytd_zeku‰ze©k7h—cekŽhdÃ@zetk7psd_yPzvced_o2™<dgo½rtjk jkŽhgu­r©cekÀh—z*zew½jk , V 1  ¼ , ¿!Pk ytdgzvku*h u­±h—zewƒh—otj€kh—y’™ghoxrtk@d—Ã~ze©k8ytdgcvj„h—oVzed + |  ^ & ¼ , ¿¾—zvtk8zew½oqPk@u‡rt k9ciuvpscew½tzPku‡wxf_y h—zvku2hŒzvk9j dgc¾h—oVjkh—y ™_h—o½rtkŒÊ k9z‡¦@k9k9y , ³h—y  ,  9Phy  Pk9y©dgzekŽuh‰yPr©jk9cewƒp9h—o<² rtÇ ÃÄrty pazewxd_yzv h—zÍh—t©cedÇPw½j„h—zvku^zvtk ÃÄdgo½oxd¦8wxy©f7}Âr hyPzvwxz‡® * | ^&. *. . . . ". +$%'&. i¼ .  > .. ,$. % &. . >)(   1. ¿. -,. . . $.0/1 $.   h   $. 41)¼.. ¿"1¼,¿. ¼e” ›Â¿.

(64). ÁŒV¦8wxy Pw½ytf!wqu,wxyVzecedVVr psk‰ÊV®×k ÇPzvk9y Pw½ytf!‹)d<k ýu2httcedÇVwxj„hzek‹8wxk j„h—yty’u‡dgox™<k c |”9“ <zvd*P®Vy h—j€wqp jku‡tku@h—y Àpsdgj©rtzew½ytf h_u

(65) ÃÄdgoxo½d¦!us* i¼ .  > . > 1  ¿25 4*1 )e¼ .  ¿ 0 “ 41 )e¼ . ¿ " 1  ¼e”a–P¿ ¼  ¿  ¼ .  > . > 1  t¿ 4¼ % 1 " 1  ¿ " . “ .  " ¦8tk9cvk wqu@‹)d<"k üu

(66) jkŽh—y7™ghoxrtk]d—ÃXze©kŒ² rtǀ˜<hgpsd_Êtwqhy„j„h—zvcewxÇ + M + 1 ¼ . ¿  wqu2zvtk‰wqVk9yPzvwxz‡®jh—zecvwxÇ~ h—y±zvtk’Pdgz8©cedVPr paz % 1 " 1  wƒupsd_jtrtzvkhgu8u‡rtfgf_ku­zvk¬cvkpsk9yVzeo½® ÊP. ®€Ú ü»³d_ytf<h hy  !!rtwxo½oqh—c¾ |”g” =* .. $% &. $. % &. . )(. . . 354. . )(. . 2(. . (. 2(. . . 76. 86. 3. 4. 9(. :(. .

(67)  .

(68) .   .  

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(70)  . Sj Si. P2ij. Õ^w½fgrtcvk’› *Lndgj€trtzihzew½dgy„d—à % 1 " 1  (tk’psdgyVzecvdgo,™<d_oxrtjk]h—cvkh   wƒurt~th—zvk¹r u­w½ytf ze©k³ÃÄd_oxo½d—¦8w½ytf{ ytw½zek*™<dgo½rtjk]uepitk9jk * . *. .   5. .  0. !". ,.  . ¼e” l¿. ":(   1  1 %(. . tÕ dgoxo½d¦8wxytf‰zvtk8¸?Á*ˆtn@Åzekpitytwƒ}ÂrtkŠu­kpsd_y dgc¾Pk9ch_p9psrtc¾hgps®’wquXhgpitwxk ™<k×w½yk9ÇVtcekŽueu­w½dgy„¼v”9›Â¿ ™Pwƒh htwxkŽpsk9¦8wqu‡k*oxwxy©kh—c‰w½yPzvk9ce d_oqh—zvwxd_y?d—Ã@zetk7u‡zihzeku .  hy  .  h—z‰zvtk wxyVzek9c‡Ã¶hgpsk’Ê k9z‡¦k9k9ypsk9o½oqu|  h—y±D | È (©wqu

(71) cvk}<rtwxcvku^ze©kŒk9™_hoxr hzewxd_yd—à zetk!fgc¾hgPw½k9yVzd—à zetk]u­d_oxrtzvwxd_y„h—z@khgpi™<k cezek Ç hgu2ÃÄdgo½oxd¦!us* ” ¼ 3 ¿  " Q Q  5   .  .  0 “ 1 .   1 ¼e” g¿ ”  .  5 .  “ ¼ 3 1 . ¿  " Q  1 Q ¦8tk9cvk . 5.ƒ¼ < >@ >C?> W ¿ F m w½y×d_zetk c^¦@dgci©us9ze©k

(72) w½yPzvk9ce d_oqh—zvwxd_ywquL k9c‡ÃÄdgcvjkŒd_yze©k

(73) ©P®©u­wƒp9h—o ™_h—cvwqh—Ê©oxku^w½y u­zvkhg d—Ã~zvtk‰padgy u‡k9ce™_h—zvwx™<k@™ghcewƒh—Êto½kusÈ (©k!h—ttcvdÇPw½j„h—zvkytdVthoLf_cihgVwxk9yVziu¼ 3 1 . ¿  h—cvk dgÊ©zih—w½ytk„r u­w½ytf7 h ,´¶psdgjÊ©wxy hzewxd_ydÃ@psk9yVzek cekhy ÃÄr©oxox®7rtV¦8wxy f_cihgVwxk9yVzivu * ¼ 3 1 . ¿  5.¼e” 

(74) 2¿i¼ 3 1 . ¿   $ 0

(75) ¼ 3 1 . ¿  ~  ¼e” µÂ¿ (tk  ho|ÃÄ´ÄrtP¦8w½y ?uepitk9j€k¼ 5 “” ¿8wƒu‰u­w½jtox®€dgÊtz¾h—wxy©k¹ÊP®Àjkhy u)dÃÍho½wxytkŽh—c!wxyVzek9cv§d_oqhzewxd_y d—ÃÌzetk !]h—o½k9ceÛVwxyf_cih_Pwxk9yVziu8padgjtr©zekd_y¹kh_p„zvcewqhytfgo½k*d—à |  * . . . . . . . . . . .

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