BAIL 2006 Book of Abstracts - Institut für Numerische und ...
BAIL 2006 Book of Abstracts - Institut für Numerische und ... BAIL 2006 Book of Abstracts - Institut für Numerische und ...
ABOUTUNSTEADYBOUNDARYLAYERONADIHEDRALANGLE beingatrest.Letdenotethelinearangleof?.Itisassumed,thattheanglemovesin bythesuddenmotionofthedihedralangle?withtheconstantvelocityUintheuid KeldyshInstituteofAppliedMathematics,Miusskajasq.4,Moscow125047,Russia Theunsteadyowoftheviscousincompressibleuidisconsidered.Thisowiscaused vasiliev@keldysh.ru M.M.Vasiliev investigatedrstbyStokes[2].Steadyboundarylayerontherightdihedralanglewas consideredbyLoytsjansky[3]. theangle?.Since?isinniteinthedirectionofaxis0zandtheowiscausedonlyby thedirectionoftheedge(0z)andonlyonevelocitycomponentofuidwinthisdirection isdierentfromzero.Suchowsarecalledbylayered[1]. coordinatez.Accordingtomadeassumptions,themotionequationsreducetofollowing thewallmotion,weshallassumethatallhydrodynamicfunctionsareindependentfrom Letusintroducethecylindricalcoordinates(r;#;z).Weconnectthiscoordinateswith Theunsteadylayeredowcausedbythesuddenmotionofaninniteatplateis wheretisthetime-coordinate,s=r=p,{kinematicviscouscoecient. intersectionthewingandthefuselageofanaircraftatenoughdistancesfromtheleading andthetrailingedgesofthewing. oneequation: Inthisworkthepowergeometrymethods[4]areusedforobtainingofself-similar Theconsideredowsimulatesroughlyaboundarylayerintheneighborhoodofthe @w @t? @2w @s2+1s@w @s+1s2@2w @#2!=0: (1) solutionsofboundary-valueproblems.Thesemethodshavesimplealgorithms.They wereappliedsuccesifullebothtolinearandnonlinearproblemsinworks[5]{[9]and wasobtainedintheform wherew=U(1;2).Solutionoftheequation(2)bycorrespondingboundaryconditions others. Fortheself-similarvariables1=s=pt;2=#theequation(1)is where==andfunction1isdeterminedasaresultofthesolutionoftheboundaryvalueproblemfortheequation 12@2 @12+11+1212@1+@2 w=U1(1)cos(#); @22=0: (3) (2) TheanalyticalsolutionoftheconsideredprobleminCartesiancoordinates(x;y;z)was obtainedonlyincase==2.Thissolutionis where 12100+11+121210?21=0; w=Uerferf; (5) (4) =x 2pt;=y 2pt;erf'=2 p' Z0e?l2dl: M. VASILIEV: About unsteady Boundary Layer on a dihedral angle ✬ ✫ Speaker: VASIELIEV, M. 150 BAIL 2006 ✩ ✪
!+1. Trans.Cambr.Phil..IX,8.1851. Itischeckedthatasymptoticsofthesolutions(3)and(5)coinsidebothbyr!0and Moscow,1998(Russian).=ElsevierScience,Amsterdam,2000. [1]Schlichting,H.,Grenzschicht-Theorie.VerlagG.Braun.Karlsruhe.1951. [2]Stokes,G.G.,Ontheeectofinternalfrictionofuidonthemotionofpendumlums. [3]Loytsjansky,L.G.,LaminarBoundaryLayer.Fizmatgiz,Moscow,1962(Russian). [4]Bruno,A.D.,Powergeometryinalgebraicanddierentialequations.Fizmatlit, References bypowergeometry.Proc.oftheInternationalConferenceonBoundaryandInterior Layers(BAIL2002),Perth,WesternAustralia,2002,pp.251-256. oftheInternationalConferenceonBoundaryandInteriorLayers(BAIL2002),Perth, WesternAustralia,2002,pp.251-256. [5]Bruno,A.D.,Algorithmicanalysisofsingularperturbationsandboundarylayers [6]Vasiliev,M.M.,Asymptoticsofsomeviscous,heatconductinggasows//Proc. Toulouse,France,2004,9pp. 2003,pp.93-101. //Proc.oftheInternationalConferenceonBoundaryandInteriorLayers(BAIL2004), equationsbymethodsofpowergeometry//ProcofISAAC-2001,WorldScientic,Singapore, [8]Bruno,A.D.,Shadrina,T.V.,Theaxiallysymmetricboundarylayeronaneedle [9]Vasiliev,M.M.,Ontheself-similarsolutionofsomemagnetohydrodynamicproblems [7]Vasiliev,M.M.,Abouttheobtainingself-similarsolutionsoftheNavier-Stokes Toulouse,France,2004,6pp. //Proc.oftheInternationalConferenceonBoundaryandInteriorLayers(BAIL2004), M. VASILIEV: About unsteady Boundary Layer on a dihedral angle ✬ ✫ Speaker: VASIELIEV, M. 151 BAIL 2006 ✩ ✪
- Page 122 and 123: A. KAUSHIK, K.K. SHARMA: A Robust N
- Page 124 and 125: P. KNOBLOCH: On methods diminishing
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- Page 142 and 143: K. MORINISHI: Rarefied Gas Boundary
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- Page 152 and 153: N. PARUMASUR, J. BANASIAK, J.M. KOZ
- Page 154 and 155: B. RASUO: On Boundary Layer Control
- Page 156 and 157: H.-G. ROOS: A Comparison of Stabili
- Page 158 and 159: B. SCHEICHL, A. KLUWICK: On Turbule
- Page 160 and 161: O. SHISHKINA, C. WAGNER: Boundary a
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- Page 186 and 187: Authors Alizard, F., 67 Alrutz, Th,
ABOUTUNSTEADYBOUNDARYLAYERONADIHEDRALANGLE<br />
beingatrest.Letdenotethelinearangle<strong>of</strong>?.Itisassumed,thattheanglemovesin bythesuddenmotion<strong>of</strong>thedihedralangle?withtheconstantvelocityUintheuid Keldysh<strong>Institut</strong>e<strong>of</strong>AppliedMathematics,Miusskajasq.4,Moscow125047,Russia Theunsteadyow<strong>of</strong>theviscousincompressibleuidisconsidered.Thisowiscaused vasiliev@keldysh.ru M.M.Vasiliev<br />
investigatedrstbyStokes[2].Steadybo<strong>und</strong>arylayerontherightdihedralanglewas consideredbyLoytsjansky[3]. theangle?.Since?isinniteinthedirection<strong>of</strong>axis0zandtheowiscausedonlyby thedirection<strong>of</strong>theedge(0z)andonlyonevelocitycomponent<strong>of</strong>uidwinthisdirection isdierentfromzero.Suchowsarecalledbylayered[1].<br />
coordinatez.Accordingtomadeassumptions,themotionequationsreducet<strong>of</strong>ollowing thewallmotion,weshallassumethatallhydrodynamicfunctionsareindependentfrom Letusintroducethecylindricalcoordinates(r;#;z).Weconnectthiscoordinateswith Theunsteadylayeredowcausedbythesuddenmotion<strong>of</strong>aninniteatplateis<br />
wheretisthetime-coordinate,s=r=p,{kinematicviscouscoecient. intersectionthewingandthefuselage<strong>of</strong>anaircraftatenoughdistancesfromtheleading andthetrailingedges<strong>of</strong>thewing. oneequation:<br />
Inthisworkthepowergeometrymethods[4]areusedforobtaining<strong>of</strong>self-similar Theconsideredowsimulatesroughlyabo<strong>und</strong>arylayerintheneighborhood<strong>of</strong>the @w @t? @2w @s2+1s@w @s+1s2@2w @#2!=0: (1)<br />
solutions<strong>of</strong>bo<strong>und</strong>ary-valueproblems.Thesemethodshavesimplealgorithms.They wereappliedsuccesifullebothtolinearandnonlinearproblemsinworks[5]{[9]and<br />
wasobtainedintheform wherew=U(1;2).Solution<strong>of</strong>theequation(2)bycorrespondingbo<strong>und</strong>aryconditions others. Fortheself-similarvariables1=s=pt;2=#theequation(1)is<br />
where==andfunction1isdeterminedasaresult<strong>of</strong>thesolution<strong>of</strong>thebo<strong>und</strong>aryvalueproblemfortheequation 12@2 @12+11+1212@1+@2 w=U1(1)cos(#); @22=0: (3) (2)<br />
Theanalyticalsolution<strong>of</strong>theconsideredprobleminCartesiancoordinates(x;y;z)was obtainedonlyincase==2.Thissolutionis where 12100+11+121210?21=0; w=Uerferf; (5) (4)<br />
=x 2pt;=y 2pt;erf'=2 p' Z0e?l2dl:<br />
M. VASILIEV: About unsteady Bo<strong>und</strong>ary Layer on a dihedral angle<br />
✬<br />
✫<br />
Speaker: VASIELIEV, M. 150 <strong>BAIL</strong> <strong>2006</strong><br />
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