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Implicit Upwind Schemes for Low Mach Number Compressible Flows

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(1)Implicit Upwind Schemes for Low Mach Number Compressible Flows Cécile Viozat. To cite this version: Cécile Viozat. Implicit Upwind Schemes for Low Mach Number Compressible Flows. RR-3084, INRIA. 1997. �inria-00073607�. HAL Id: inria-00073607 https://hal.inria.fr/inria-00073607 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. Implicit Upwind Schemes for Low Mach Number Compressible Flows Ce´cile VIOZAT. N˚ 3084 Janvier 1997 THE`ME 4. ISSN 0249-6399. apport de recherche.

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(232) V\q h V¥»yPqkP a<]kV\[^Y\e 1 š ' š š    >¢. . 8. (*, "%F )- =>-/" F-F 4%F  D&. . . . . (. . -F + 7$ ,+. . ©ËLNP a¶]fLNPŠP ȟX’[^]kVW`baNe³[gqkPdNqkP l`ba h VW]_V\`baZP h [ga h [Fxc`:PXZdŸ•›VWa h ke lzLZPOQP ìÌ H HVWe³XNe_P h šÊ^[ga 1  P Pqs­  PP®­sx`oSP ï}b}  `g˜NekP q_bP h ]fLN[^]›]fLNPiaŸXNOQPq V\l[^Y1À’XonoPecOTXZe_]m˜yPiOQ` h WV ž’P h ¢ K LNP(a:XZOP q_VWl¨[^Y1À’X:nZP ec«`gq ]fLNPi`bq V\‡gVWa’[^Yʂ„¹ P ȟX’[^]kVW`baNem[gq_P. •LNP qkP.  . E

(233) É  Ä :  E ?  :  E É ?  Ä  :   ? E É

(234)  :  E É   E ? =. . . V\e›]fLZP"x`:P¬O[ ]fq_V nVWaCl `baNe_Pq_^[^]_VWgP(^[gq V½[^˜ZY\P e. X’`bq ]fLNPidNq_Pl `ba. •LNP qkP. . . ¾_‚„†<Á. ¢. h V¥]kVW`baNP h PȟX’[ ]kVW`baNe]fLNP ekP¬À’XonoPem˜yP l`bOQP. E

(235) É  Ä :  E ?  :  E É ?  Ä  Æ’É   :  ? E É

(236)  :  E É   E ? =. . . ¾_‚ bÁ. V\e›]fLZP(dZqkPl `ba h V¥]kVW`baNP qcVWal`baZekPq ^[^]kV¥bP(g[^q_V\[g˜ZYWPe¢. [ga  PP q ­ 1  P P

(237) ­¡xc`:P ï }b}

(238) ±aN`^]fP h [^Y\e_`C]kL’[^](]fLZVWe³OQ` h VWž’l[^]kVW`ba%V\e"aN`g]³aZPlP ekek[gq_j%•›VW]kL¯]fLZPÀ’Xon 8 bP l ]k`bqQekdZY¥VW]_]kVWaN‡·`g^[ga  PPqï}<Ì >¢¶K LoV\e8OQ` h VWžNl¨[^]_V\`baÃVWOQdNqk`„bP e]kLNPaŸXNOQPq V\l[^Yek`gYWXZ]_V\`bašH[^a h. ]fLZPaª]kLNPdNqkP l`ba h VW]_V\`baZP h l `bOQdNqkP eke_VW˜ZYWPŠPȟX’[ ]kVW`baNei]fPa h ]f`]fLZPdNq_Pl `ba h V¥]kVW`baNP h V\aZl`bOQdNq_Peke V\˜oY\P PȟX’[ ]kVW`baNe  }b

(239) ~ ¿¢. 8.  "%.)D+<=>F,+ +. ” Nd qk`b˜oY\P O P aNl`gXNa<]fPq_P h •›V¥]fLlPq ]z[^VWaNeHdNqkP l`ba h VW]_V\`baZPqke šZd’[^q_]kVWlXoY½[gq YWjQ]kLNPm`gaNPt`g¦K´XZqk§gP

(240) Y [ga h ]fLZP `baNP¬`^# PP q ­ 1P P

(241) ­¡xc`:PgšZVWe ]fLN[^]›]fLNP

(242) j[gq_P¬e_VWaN‡bXZY\[gq[^]e ]z[g‡baN[^]kVW`bad™`gV\a<]kem[^a h [^Y\`gaN‡8ek`baoV\l¬Y¥V\aNP e¢œu¡a `bq h Pq ]k`[¨g`gV h ]fLNP ekPie_VWaN‡bXoY½[gq VW]_V\P eš×lP q_]f[^V\aZe]kPq_OecOTXZe_]c˜yPie_O`:`g]kLNP h  }^R1`bq›˜™`bXNa h P h ek`8]fL’[ ] ]fLZP¬aN`bao­ÂaN`bqkO[^Y¥V¥]¡jŠ`g1]fLZP¬P VW‡bPa<bP l ]k`bqkem[gdNd™P¨[gq V\aZ‡Q[^]›bP q_jŠYW`„• –F[^lzLaŸXNO"˜yP q›V\e›P

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