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A Second Order Defect Correction Scheme for Unsteady Problems

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(1)A Second Order Defect Correction Scheme for Unsteady Problems Regis Martin, Hervé Guillard. To cite this version: Regis Martin, Hervé Guillard. A Second Order Defect Correction Scheme for Unsteady Problems. RR-2447, INRIA. 1994. �inria-00074228�. HAL Id: inria-00074228 https://hal.inria.fr/inria-00074228 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. A Second Order Defect Correction Scheme for Unsteady Problems Re´gis Martin, Herve´ Guillard. N˚ 2447 Novembre 1994. PROGRAMME 6 Calcul scientifique, mode´lisation et logiciel nume´rique. ISSN 0249-6399. apport de recherche. 1994.

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(38)  

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(63)  

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(77) . 2M23, . O O. j. G2. Lundi 24 Juillet 1989 10:32:31. I. O. O. i. G1. O. INRIA Sophia-Antipolis SINUS CHARGY. O. ´:hdXYeqTW^Ž ,¯aÄVYkZl\TWVzb:‘YVzbje|]+^Vz  & ' '. @BALg#@BC.

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(95)  

(96)       "!#$%& (')+*, -/. 1023$/* 1.6. q“. EXACT First Order N1I1 N2I1. 1.575 1.55 1.525 1.5 1.475 1.45 1.425 1.4 1.375 1.35 0.45 0.55 0.65 0.75 0.85 0.95. ´:hdXYeqTW^X[ ,p£„^fk|gWhxlF© ¥[f‘Y^ cˆVZkZ‘Y^fcilWhjVZka´*+¬“:Y [zk|u –“i€w“Drš[Dkqu'l\‰|^ g‚^ˆcfVZk|u2VZTWu|^fTŒgÌl\^ˆ†¶cfVYkZl\T<hd’|e8l\^l\V'[]+V8u|^fgWlhd]+†|TWV‘8]+^ˆkZl+VD  l\‰|^Hg\Vzbje#lWhjVZk³r][•hjk#bn©¬hjkTW^fu|eqcwhdk|Xl\‰q^ [z]+†8bxhnl\e|uq^Vz ‡l\‰q^VZg\cihnbxbª[LlWhdVYk+†|TW^fg\^fkZl[Ll)l\‰|^ TW^[zTŒVz l\‰|^ u|^fk|gWhxlF©'¥[f‘Y^D«š±‰8hjg msk|u8hdk|Xhdghdk XZV8V8uoes[Lbxhxly[LlWhx‘Y^>[zXZTW^ˆ^f]+^fkZl¥hxl\‰ l\‰|^ TW^ˆg‚e8bnl\gJVY’8ly[•hdk|^fu  ¡TWVZ]/l\‰|^†|TW^i‘hjVZe|gbxhdk|^[DTgÌly[D’8hxbxhnlF©·[zks[Lbx©8gWhdghjkqu8hjc[•lWhjkqX®l\‰p[Ll g\cŠ‰|^f]+^„L€i“hdgÄ]+VZTW^u8hdg\gWhd†s[•lWhn‘Z^l\‰s[•lÄg‚cy‰|^f]+^–“i€w“hdk¬l\‰|^‰8hdXZ‰® ¡TW^foe|^fk|ci©®T\[zk|XZ^D«. . . 2/29 213!  4 !$& 13</=/2 !$ . . . }^k|^y²#lÄcfVZk|gWhdu|^fTÐ[„†|TWVZ’8bj^f]. . ¥ ^wbxb|g\e8hxl\^fuŒl\V„l\‰q^e|g\^JVD phj]+†8bxhjcihxlÄg‚cy‰|^f]+^fgˆ«•±‰8hdgÐhdg)[ “i­Ì£}hdg\^fkZl\TWVY†8hdccfVY]+†|TW^fg\gÌhjVZk8­Q^y²q†s[zk|gWhdVYkVZ’8ly[•hjkq^ˆu–’Z©cˆVZ]+†|TW^fg\gWhdk|X„[X[zg:cˆVZkZly[Lhdk|^fu hdk[®cibdVYg‚^ˆu l\e|’¯^DrpcwbdVZg\^fu [•l[zk·^fk|u’Z© [+]+V‘hdk|X†8hdgWl\VYkB«q€Ìkl\‰8hdg^y²q†¯^ˆT<hd]+^fkYl„l\‰|^. gagihkj8lmm8n.

(97) Z. , "M. . 1.6. 

(98) . 2M23, . EXACT First Order N1I1 N2I1. 1.575 1.55 1.525 1.5 1.475 1.45 1.425 1.4 1.375 1.35 0.45 0.55 0.65 0.75 0.85 0.95. ´:hdXYeqTW^Œ_ ,p£„^fk|gWhxlF© ¥[f‘Y^ cˆVZkZ‘Y^fcilWhjVZka´*+. [Y. @BALg#@BC.

(99)  

(100)       "!#$%& (')+*, -/. 1023$/*. 1.6. EXACT First Order N1I1 N2I1. 1.575 1.55 1.525 1.5 1.475 1.45 1.425 1.4 1.375 1.35 0.45 0.55 0.65 0.75 0.85 0.95. ´:hdXYe|TW^¬ ,p£„^fk|gWhxlQ©¹¥[f‘Y^cfVZkZ‘Y^fcilWhjVZk aJ´*¬“YY. gagihkj8lmm8n. 4.

(101) zŽ. , "M. . 

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(103) ©  [zk|u l\‰q^TW^fu|e|cf^fu·†|TW^fg\g‚e|TW ^ - u|^imsk|^fu’Y© ,   s¢    \ ¤ s¢ s ¢  Y\ ¤ Š¤. -:¢   \¤ -:¢ Y \¤ -     -:¢   \¤ ±‰|^„cˆVZ]+†|e8ly[•lWhjVZk|g‰s[w‘Y^„’‡^f^fk u|VZk|^„VZk [Œq “i² 4 kqV8u|^„]t^fg\‰BrZ¥hxl\‰·[ cfVYk|gÌly[DkZl)lWhj]+^ gWl\^f†cfVZTWTW^ˆg‚†‡VZk|u8hdk|X+l\V>[+‘D[zT<hª[LlWhdVYk-Vz  Y#V [u|^fXYTW^fgHVD Ul\‰|^¬†s[zT\[D]+^il\^fT 4 hdk ¡VYTW]–e8bª[ ¢ 4 Y#¤\« ±‰q^Œa´ * ke|]Œ’¯^fTXZV8^ˆgÄ ¡TWVY] [ ¢)[•ll\‰|^’¯^fXDhdk|k8hdk|X¬VD (l\‰q^cˆVZ]+†|e8ly[•lWhjVZk ¤Ðl\V . *. . *. . . . *. 7. . 7. . . . .  . . . *. *. @BALg#@BC.

(104) [. 0.00000E+00. 0.20000E-04.  

(105)       "!#$%& (')+*, -/. 1023$/*. X. 8.57. Crank = -20 Degres Exact solution N2I1 scheme N1I1 scheme. 9.03. ´³hjXZe|TW^"( ,#€Ìg\^fkZl\TWVZ†8hjc–cfVY]+†|TW^fg\gWhdVZk,8†qTW^ˆg‚g\e|TW^ “  Y¢[•ll\‰q^^fk|u ¤\« !k|^k|VzlWhjcf^l\‰|^b [zTWXY^„hd]+†|TWV‘8]+^fkYl„†|TWV8u|eqcˆ^fu’Z© l\‰|^g\^fcfVZk|u8­ VZTWu|^fT®£„^La •€i“.,³±‰|^¹†|TW^fg\g\e|TW^+hdgŒcibdVYg\^fTl\Vl\‰|^ [zks[•bn©lWhdc[Lbg\Vzbje#lWhjVZk'¥hnl\‰¦„L€i“ l\‰s[zk}¥hxl\‰§Œ“i€i“Z«š±‰8hjg–hd]t†qTWV‘8]t^fkZl+hjg¬^f]+†|‰s[zgWh f^fu}’Y©¦cfVYkqgWhjuq^ˆT<hdk|Xl\‰|^ u|^fk|gWhxlQ© cfe|T<‘Z^ˆg)¥H‰|^fTW^l\‰|^g\Vzbje8lWhdVZk|g¼VZ’8ly[•hjkq^ˆu¬¥hnl\‰ „•€w“g\cŠ‰|^f]+^hdgJ[•bd]tVZgWlšl\‰|^gy[z]+^l\‰s[zk l\‰|^^y²p[zcwlVZk|^D«  ^[Lbdg\V–k|VDl\^VZkl\‰|^fg\^„u|^fk|gÌhnlF© cfe|T<‘Y^fgl\‰p[Ll„•€w“„g\cŠ‰|^f]t^„TW^fu|e|cf^fg u|T\[z]lWhdc[Lbxbx© l\‰|^VZg\cihnbxbª[LlWhdVYkqgVD {l\‰|^u|^fk|gWhxlF©>†|TW^fg\^fkZlk|^[zTl\‰|^†#hjgWl\VZk³« .  . !,+ ! 4 % . !„eqT)l\‰8hjTWu. k e|]+^ˆT<hdc[Lb¯l\^fgWlhdgcˆVZ]+†‡VZg\^fuVz ³l\‰q^cibª[Dg‚gWhjc[•b³V8ug\‰qV8cZ¬l\e|’¯^†qTWVY’8bd^f]>« hdgk|Vzl¼¥^ibxb‡g\e8hxl\^fu¬ ¡VYTUhd]t†#bnhx­ cihxl¼g\cŠ‰|^f]t^fg)[Ll{b [zTWXY^aJ´* ke|]Œ’¯^fTwr[DkquŒl\‰s[•lÐl\‰q^V‘Y^fT\[•bnb|†¯^fT< ¡VYTW]k|cf^fgÐVz |hj]+†8bxhdcwhxl g\cŠ‰|^f]+^ˆgUVZkŒl\‰8hdgU†|TWVY’#bj^f] [zTW^†¯V8VYTw«•±‰|^cfVY]+†|e#ly[LlWhdVYkqg¼‰s[w‘Y^’¯^f^fk®†¯^fT< ¡VYTW]+^fuŒhdk+[ g\oes[zTW^„VD U“fcˆ]@bd^fk|XDl\‰VZk [“ Yq“i² 4 k|V8uq^]+^fg\‰¥hnl\‰>[¬a+´ *-k#eq]Œ’¯^ˆTJVDa  [8«±‰q^‘D[zk. }^^f]+†|‰s[zgWhf^Jl\‰s[Ll)l\‰8hdg)gWl\TWVZk|XDbx©+e|k|gWl\^[zu8©®†|TWVZ’8bd^f]. gagihkj8lmm8n.

(106) Z_. , "M. 

(107) . 2M23, . -0.80000E-02. 0.20000E-04. . 8.57. X Crank = -20 Degres Exact solution N2I1 scheme N1I1 scheme. 9.03. ´:hdXZe|TW^Œ” ,8€<g\^fkZl\TWVY†#hjccfVZ]+†|TW^fg\gWhdVYk ,pu|^fk|gWhxlQ©. @BALg#@BC.

(108) . 0.00000E+00. 0.10000E+01.  

(109)       "!#$%& (')+*, -/. 1023$/*. X. 0.00. time = 0.1600 Exact solution N2I1 scheme N1I1 scheme. 1.00. ´³hjXZe|TW^“Y ,¯V8u-‰|V8c Z±Ðe|’¯^ ,q†|TW^fg\g\e|TW^ /Hbd’s[Dup[‘D[zk-*³^ˆ^fTbxhd]®hxl\^fTWg‰s[w‘Y^’¯^ˆ^fk e|g\^fu³rq’|e8l¥^u|V+k|VDl^ˆ]+†8bdV©>[zkZ© \^fkZl\TWVY†Z©. mq² |«¯´:hdXYeqTW^ˆg¢‚“:Y8rn“Y“Drd“¤Uu8hjg‚†8b [w©>TW^fg\†‡^fcilWhx‘Y^ibn©¹l\‰|^†|TW^fg\g\eqTW^Zrpuq^ˆkqgWhnlF©·[zk|u ‘Z^ibjV8cihxlQ© [•llWhj]+^ @Y#Vn“•_8«±‰|^„]tVZgWlTW^f]TZL[z’8bd^„ ¡^[Ll\e|TW^Vz Bl\‰|^„L€i“„g\cy‰|^f]+^HhjgÄl\‰|^„b [zTWXZ^ VZg\cihnbxbª[LlWhdVYk†qTW^ˆg‚^ˆkZl[•ll\‰|^TW^[zTVD Bl\‰|^T\[zTW^i Ê[DcilWhdVYk¥[w‘Y^D«8±‰8hdgVYg‚cwhxbxb [•lWhjVZk+hdg]Œe|cŠ‰ ]+VZTW^g\]bxbj^fT„¥hnl\‰¦–“w€i“tg‚cy‰|^f]+^D« !kl\‰8hdgŒVzl\‰|^fT‰s[zk|u³r³l\‰|^ „L€i“+g\cy‰|^f]+^]+VYTW^  Ê[•hnl\‰# ¡e8bnbx©TW^fg\†‡^fcil\gl\‰|^„cfVZkYly[zcilu8hdg\cfVYkZlWhdk#e#hnlF© ¢‚“Y“L¤š¥‰#hjcŠ‰hjgJ’s[DTW^ibx©+‘#hdgWhd’8bd^VZkl\‰|^ TW^fg\e8bxl\gHVY’8ly[•hdk|^fu ¥hxl\‰ l\‰|^Œ–“w€i“g\cy‰q^ˆ]+^D«  1. L * 02: 'L" '&¼ˆ *t1¦"  1¦ * ¶ L&() .   • }^2^fk|u l\‰8hdg†s[z†‡^fT’Y©ºl\‰|^}gWl\e|u8© Vz ®l\‰|^¶¸sV¥ hjk l\‰|^¶hdkYly[ ZD^}†|‰s[zg\^¶VD [§’8hx­ u8hd]+^fk|gWhdVYks[•b8†8bª[Dks[zT(]+V8u|^ib8VD s[H†8hdgWl\VZkŒ^fk|Xzhjkq^Z«•±‰|^XY^fVZ]+^wl\T<©eqk|u|^fT(hdkZ‘Y^fgWlWhdX#[•lWhjVZk. gagihkj8lmm8n.

(110) .(. , "M. 

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