Effective Diffusion in Vanishing Viscosity
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Texte intégral
(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. Effective diffusion in vanishing viscosity Fabien Campillo — Andrey Piatnitski. N° 3813 November 1999. ISSN 0249-6399. ISRN INRIA/RR--3813--FR+ENG. THÈME 4. apport de recherche.
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(151) N L vx y '.Lwvx y NEWY\YR_aNgR_ash]uvRo_ab@snW^Ri'iv_z]jsv_aWYcEB]`_ ]jsnR"]`_n_ash]jo_hR k WY_h N L vx y¡ opc k Rs _aNER]jybJjR]jihinZEQSfg_aWYb@cEiSb@c &+*S]jc k &/ l_aNgR ia]jW k cERWY@Nb@shNEb-b k i k b RXW k Rc_a\mRqXWYin_pWY WYiihQ ]j\Y\KRcEbjZE@N¡ R]jshRª@b@WYcE_abihNgbF cgbF _aN]`_Gb@Qs gi* 8 +D´F"_aNER£sa]`c k b@Q `]jsnW]`E\^Ri IPLwvx y%! 9 N ]jshRWYc k RfyRc k Rc_¡ M4b _hNEW^i0Rc k "R ob@cEihW k Rs ]`shEW_ash]jsnm¥_à"bcERW^@Nb@s0QSW^cgW^QZEQ fyb@WYc_a-i Lwvx yª]`c k Lwvx y®, 9y]jc k ] QSW^cgW^QSWY³WYcE[inR !ZERcgoRwb`9oZEsnjRui
(152) 7I 3 N $ ihZgozN _aNE]`_.
(153) I^3N-'Lwvx y§
(154) I 6JN/' Lwvx yE, 9C§
(155) R; fIPLwvx y9! 9 N]jc k *c0 ¬®|Z ¬ &I MIP±`N`N_n IPLwvx y%! 9 N¡, ;pZERB_ab[_hNER in_hshZEo_aZEsnR bjA &+*e]jc k _aNgRBozNEb@WYoR bj 8XIPL } N
(156) §X_hNERBWYc_hRsnihRo_aWYb@cdbj MI 3 N WY_hN 8pI L } N£WYicEb@c_hshWXW^]j\Gb@s]j\Y\ihZ # oWYRc_h\Ym inQ ]j\^\ -¡ #Û_"W^i]j\^inb o\YR>]`s"_aN]_
(157) b@cE\m s. ó ó × Eö Fçnö.
(158) >T. ]* G.
(159) G"
(160) . Γ1. U0(x)=U0(xs )+ β U0(x)=U0(xs ) Γ2. Γ3. 'W^jZEshRp}GuA AKh3AK> s. Γ4. L:AD4R>!wL } R4 > D2 4HVKC+'d4 w _O '\@',O O04R>@'*? mL d &+*JI LONT' & * I L mL d&+* IPLON/' &* I L } NU, c)>6 w @' 6:'*M AKh L:A:?4 w 4 AK> U A . $ . ) >6 } N $ 8 I L } N. p. ]`_O_hNERlfyb@WYc_ai\YbXo]`_aR k ]`_ ¡/;wRcEbj_aR /' 0Z O m±
(161) I ±`N_R 9$ ! ' Qm±Mj
(162) I ±`NVR 7$ pbJ b@cER o>]`c shRfE\^]joR _aNER ihR@QSRc_abi VIP±`N 3pn± n $ ]jc k VIP±`N n.± nt6 $ m _aNgRwcER/bjcERiWYcinZEozN]"]Jm _aNE]`_"_hNERwoZEsnjR M I 3 Nªb@X_z]jWYcER k W^iob@c_aWYcZEb@ZEi§Ein_hW^\Y\ yR\^b@cg@iO_ab* fIPLwvx y"! 9 N]`c k ia]`_hW^ivRie_aNERlRiv_aWYQ ]`_aR9i G &I M I ±`NcN98 IPLwvx y"! 9^Nd! Gbjs]j\^Q \ ± 8 ]jc k ±Vj MON-Zgi IPLwvx y9! 9 Nb@cE\m k RfRc k i bj?c ´&T "IPLON L R 8pI L } N $ §ª]jc k _aNER iv_z]`_hRQSRc_Sbj _aNERl\YRQSQ ]SGb@\Y\YbFi¡ : MONgR0fEshb-bj£bjª_aNER0cgRq-_ ]jihinRsv_aWYb@c¥WYi ihWYQSW^\^]jsB_hb_aN]`_Bbjª_aNER0fEsnRoR k WYcEd\^RQ Q ] ]jc k W^\Y\yR bjQ W_h_hR k ¡ Q /&/ 9IPLON
(163) r U " B Du1." H
(164) !! K= ^* 5 K £¬ W^c_aRshinRo_hi. . 8XIPL } N. .
(165) = K .
(166) [ " = ] m IU *" !
(167) V= u5 K Gam!!. k &/ 9IPLONmk®n?gi*E!Xk &/ %IPL N. +. &/ %I L NJk®n?g Jk L. . +L. k¥!hL¡!cL. . !cL RH !. òGå óKòGô.
(168) .
(169)
(170)
(171) ! !!
(172) ". G
(173) K E @ ´&T "IPLON ~L°R W $ G*@E´&T 9I LON ~LqR W $ _
(174) G ]G
(175) u " JIKW !W NVj ( 7
(176) ^ " " ´gi*% Ogw G
(177) B G = 9 IPLwvx y%!# 9PN
(178) G ] G . k W^iv_. ó ó × Eö Fçnö. . .
(179) . ]* G.
(180) G"
(181) .
(182) ` " ©¥¡y¢ (/¡K¢B/(T;O¢{]jc k ¢[¡g¡©d¢´;O¢[¡B© ]`_aNgRQ ]`_aWYo>]`\4QSb k R\YiwW_aN R
(183) qE]`o_ shRcgb@shQ ]j\YW^³]`_aWYb@cGb@sO_aZEsnEZE\YRc_e_asa]`cEihfb@sn_¡= l_D U Kr
(184)
(185) " 5 U d "! §J}X´ GÁ}jg <- T `g§y>@4 'g¡ ©¥¡E ¢ (/¡¢w (/;O¢ ]jc k ¢[¡ g¡$©¨
(186) ¢ ´;O¢[¡ªVXZgfyRs k W9ZgihWYb@c¨WYc cER]jsh\miv_asa]_aWR k $bJi ¡ f E "!!§ W p6@} <-T Z"G @@ <g jg§J@ X¡ } ©¥¡ª¢ (T¡K¢B/ (/;¢¤]jc k ¢¡ g¡©¨
(187) ¢ ´;O¢[¡ ¢wfgfE\^WYo>]_aWYb@c bjB]jc ]`fEfEshb>qXWYQ ]_aR x <X. < _aNgRb@svm@§_ab ] QSb k R\KGb@sO_hZEshEZg\^Rc_p_ash]jcEihfb@sv_>§WY_hN R
(188) qE]`o_pshRcgb@shQ ]j\ . W^³]`_aWYb@c¡ #àc S¡Ãxl¡gV-R\Y\9R_O]j\6¡Y§-R k W_ab@s§ K5%*i u
(189)
(190) !O "G_ U "@I" " * -§FMONER #v©¨¢ jb@\^ZgQ Ri~WYc0© ]`_hNERQ ]`_hW^oi~]jc k W_ai'¢pfEfE\YW^o]`_aWYb@cEi§ f]j@Ri = <X}g@§eR £b@Us ~$§KJ@j}g¡$VXfEsnW^cg@R s ªRsn\]`E¡ T ©¥¡$¢ (T¡K¢B/ (/;¢ ]jc k ¢[¡ g¡9©d¢ ´;O¢[¡V-W^QSfE\YR[R
(191) qE]`Q fg\^RipW_aN¨GR]`_aZgshRiebj shRcgb@shQ ]j\YW^³]`_aWYb@c Gb@s[_hZEshgZE\^Rc_ _hsa]jcgihfb@sn_q¡ B K! (!! G § }jT GR '!<Dj}@}g§yJ@jTE¡ g¡ g¡ (t¢Bxl" ¡ ! "G_ k/
(192) # |U j¡ (t\^inR-W^Rs§teR$ £b@Bs ~$§ J: X¡ l¢[%¡ £Z¡ (/&£¢ ('{]jc k ]g¡Áxl% ¡ ( s (£u ; # (' ¡ ² b@QSb@@RcEW^³]`_aWYb@c bjt_hNER[iv_a:b ~`Ri R !Z]`_hW^b@cgieW_aN¨]0sa]jc k b@Qfbj_aRc_hW]`\6 ¡ ( `§ jp+T Z"GÃ} <X}@: X§9>@ ¡ l¢[¡ (ªBV oBVgVX¢B )§ g¡ ªO¡ ]# BVy§y]jc k 0¡ry¢wry¢B #T ¢ o =¡ " GI5 G "@ E7 h"= * f^ 5 §Xjb@\YZEQSR b`' f5K i
(193) *
(194) " 5 G
(195) V U 5 K¡ªeb@sn_h N < ² b@\^\^]jc k §J jX¡ x ¡á¢[¡ "¢wxw© e¢Ó]`c k t,¡ +Co¡ ² b@QSb@jRcEWY³>]`_hW^bjcGb@sB_hW^QSR k RfyRc k Rc__ !<5; W^cEob@QSfEshRihinW^E\Y#R l]jZEinihW^]jkc $bJi¡rªsnRfEsnW^c_¡ l¢[G¡ sX¢ww
(196) #à¢w
(197) ]jc k 0¡$ry¢Br¢B #T K¢ o¡ "bjcjRo_aWYb@c RcgN]jcEoR k k WyZX ihWYb@cGbjsBfyRshWYb k W^Po $bJi-¡ /.
(198) Wi=G S V U " § `TGÁ}@}j@} < 3T '@g§>@jTE¡ 'l¢[ ¡ s-¢Bp
(199) #à¢B0 ]jc k S¡pry¢wry¢B #T ¢ o ¡ ;pWYyZEihWYb@c WYc _aZEsnEZE\YRcEoRj¡ V *
(200) " ( ="n G1 " `Ul " §9 ' 5GYj j@ <X}@}`TE§9Jj ¡ òGå óKòGô.
(201) F .
(202)
(203)
(204) ! !!
(205) ". @ g¡fs~x # (/;[¡M G
(206) `"C D ¡)(t\^inR-WYRs§$¢pQ iv_aRs k ]jQ§J X¡ @ ¡[¡ # §Vy¡$©¥¡ [§]jc k ¡g¢¡ ( #´ #S¡ B D ! | ! " 5 +"B I G#.I5 ´B OuDu G R¡ªVXfEsnW^cg@R s ªRsn\]`E§KJ@jTg¡ J } ² ¡ (£VXM (ª ¡ " ( ="27
(207) " 5 K§@bj\^ZEQSR bj V B ´
(208) *
(209) 5"¡ "WYUs ~ N jZgihRs§ "b@in_hb@c§KJj X¡ > T Vy ¡ [¡ Rb@QSR_hshWYo[]`ihfRo_hiwbj'NEb@QSb@@RcEWY³>]`_hW^b@c90¡
(210) " < U ,f5= "!§ET@fT p5:Z"GÃg <T@TE§J@@g¡ Vy¡¹©
(211) ¡ ]`c k ¢[¡ t¡9r £¢tM #àMe V r##z ¡B¢ jRsh]j@WYcE b@c ] ]jo ~@shbjZEc k bj j]`cEW^inNEWYcE -WYihobjihW_àm@¡
(212) / O = [§$ 'Wpv@ Z¥GY`Tg <K j§yJjg@¡ l¢[¡ ¡ t¡r £¢tMi #àMe V 0û]`c k V¡¹©¥¡ ¡ ² b@QSb@@RcgW^³]`_aWYb@c¥]jc k `]jcgW^inNX W^cE¥XWYihob@ihW_àm@¡ #àc w¡ shWY@R\^WYb@cEWYi§OR k WY_hb@s§ *
(213) " ( =" G 5 U 'f 5 !!!T = ]
(214) H 77" u j§4fE]j@Ri}@4} '!<X}@}@g¡ lVg r @©¨ b ~-in\]`i§ J@4 'g¡ . . . ! $. ó ó × Eö Fçnö. $.
(215) Unité de recherche INRIA Sophia Antipolis 2004, route des Lucioles - B.P. 93 - 06902 Sophia Antipolis Cedex (France) Unité de recherche INRIA Lorraine : Technopôle de Nancy-Brabois - Campus scientifique 615, rue du Jardin Botanique - B.P. 101 - 54602 Villers lès Nancy Cedex (France) Unité de recherche INRIA Rennes : IRISA, Campus universitaire de Beaulieu - 35042 Rennes Cedex (France) Unité de recherche INRIA Rhône-Alpes : 655, avenue de l’Europe - 38330 Montbonnot St Martin (France) Unité de recherche INRIA Rocquencourt : Domaine de Voluceau - Rocquencourt - B.P. 105 - 78153 Le Chesnay Cedex (France). Éditeur INRIA - Domaine de Voluceau - Rocquencourt, B.P. 105 - 78153 Le Chesnay Cedex (France).
(216). . ISSN 0249-6399.
(217)
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