计算流体动力学：原理与应用（第三版）核心内容梳理（ComputationalFluidDynamicsPrinciplesandApplications,ThirdEdition3rdEdition）摘要：本文是JiriBlazek所著CFD经典教材第三章、第四章核心内容，系统阐述CFD控制方程数值求解框架，梳理有限差分、有限体积、有限元等主流空间离散方法，对比结构化与非结构化网格适配特性。重点详解有限体积法，划分单元中心、顶点重叠、对偶控制体积三类格式，剖析中心、矢通量分裂、Roe格式等对流离散方案，介绍显式/隐式时间推进、多重网格加速、各类湍流模型与边界条件处理思路。完整给出二维、三维结构化网格几何量计算方法，推导多种通量离散公式，兼顾理论推导与工程实现，系统讲解高精度插值、限制器、预处理等关键数值技术，是可压缩流动仿真算法的权威理论参考。ACKNOWLEDGMENTSMyfirstthanksaretoourCreator,withoutwhomnothingwouldbepossible.Furthermore,Iwishtothankmyfatherfortheinitialmotivationtostartthisproject,aswellasforhiscontinuoushelpwiththetextandinparticularwiththedrawings.IalsogratefullyacknowledgethesupportofthestaffatElsevierLtd.,foremostofC.OwenandH.Gray,duringthepreparationofthisedition.LISTOFSYMBOLSABBREVIATIONSCHAPTER1IntroductionThehistoryofthecomputationalfluiddynamics(CFD)startedintheearly1970s.Aroundthattime,itbecameanacronymforthecombinationofphysics,numericalmathematics,and,tosomeextent,computersciences—allemployedtosimulatefluidflows.ThebeginningofCFDwastriggeredbytheavailabilityofincreasinglymorepowerfulmainframes,andstilltheadvancesinCFDarecloselylinkedtotheevolutionofthecomputertechnology.AmongthefirstapplicationsoftheCFDmethodswasthesimulationoftransonicflowsbasedonthesolutionofthenon-linearpotentialequation.Withthebeginningofthe1980s,firstthesolutionsoftwo-dimensional(2-D)andlaterthree-dimensional(3-D)Eulerequationsbecamefeasible.Thankstotherapidlyincreasingspeedofsupercomputers,andduetothedevelopmentofavarietyofnumericalaccelerationtechniqueslikemultigrid,itbecamepossibletocomputeinviscidflowseitherpastcompleteaircraftconfigurationsorinsideofturbomachinery.Withthemid-1980s,thefocusstartedtoshifttothesignificantlymoredemandingsimulationsofviscousflowsgovernedbytheNavier-Stokesequations.Togetherwiththis,avarietyofturbulencemodelsevolvedwithdifferentdegreeofnumericalcomplexityandaccuracy.Theleadingedgeinturbulencemodelingisrepresentedbythedirectnumericalsimulationandthelargeeddysimulation(LES).Withtheadvancesofthenumericalmethodologies,particularlyoftheimplicitschemes,solutionofflowproblemsthatrequirerealgasmodelingalsobecamefeasiblebytheendofthe1980s.Amongthefirstlargescaleapplication,3-Dhypersonicflowpastre-entryvehicles,liketheEuropeanHERMESshuttle,wascomputedusingequilibriumandlaternon-equilibriumchemistrymodels.Manyresearchactivitieswereandstillaredevotedtothenumericalsimulationofcombustionandparticularlytoflamemodeling.Theseeffortsareveryimportantforthedevelopmentoflowemissiongasturbinesandengines.Also,themodelingofsteamandinparticularcondensationofsteambecameakeyfactorindesigningefficientsteamturbines.Duetothesteadilyincreasingdemandsonthecomplexityandthefidelityofflowsimulations,gridgenerationmethodsbecamemoreandmoresophisticated.Thedevelopmentstartedfirstwithrelativelysimplestructuredmeshes,constructedeitherbyalgebraicmethodsorbyusingpartialdifferentialequations.Butwiththeincreasinggeometricalcomplexityoftheconfigurations,thegridshadtobedividedintoanumberoftopologicallysimplerblocks(multiblockapproach).Thenextlogicalstepwastoallowfornon-matchinginterfacesbetweenthegridblocks,inordertorelievetheconstraintsimposedonthegridgenerationinasingleblock.Finally,solutionmethodologieswereintroducedthatcandealwithgridsoverlappingeachother(Chimeratechnique).Thisallowed,forexample,tosimulatetheflowpastthecompleteSpaceShuttlevehiclewiththeexternaltankandboostersattached.However,thegenerationofastructured,multiblockgridforacomplicatedgeometrymaystilltakeweekstoaccomplish.Therefore,theresearchalsofocusedonthedevelopmentofunstructuredgridgeneratorsandflowsolvers,whichpromisesignificantlyreducedsetuptimes,withonlyaminoruserintervention.Anotherveryimportantfeatureoftheunstructuredmethodologyisthepossibilityofsolution-basedgridadaptation.Thefirstunstructuredgridsconsistedexclusivelyofisotropictetrahedra,whichwasfullysufficientforinviscidflowsgovernedbytheEulerequations.However,thesolutionoftheNavier-StokesequationsathigherReynoldsnumbersrequiresgrids,whicharehighlystretchedintheshearlayers.Althoughsuchgridscanalsobeconstructedfromtetrahedralelements,itisadvisabletouseprismsorhexahedraintheviscousflowregionsandtetrahedraoutside.Thisimprovesnotonlythesolutionaccuracy,butitalsosavesthenumberofelements,faces,andedges.Thus,thememoryandrun-timerequirementsofthesimulationarereducedsignificantly.Nowadays,CFDmethodologiesareroutinelyemployedinthefieldsofaircraft,turbomachinery,car,andshipdesign.Furthermore,CFDisalsoappliedinmeteorology,oceanography,astrophysics,biology,oilrecovery,andinarchitecture.ManynumericaltechniquesdevelopedforCFDarealsoutilizedinthesolutionoftheMaxwellequationsorinaeroacoustics.Hence,CFDhasbecomeanimportantdesigntoolinengineering,andalsoanindispensableresearchtoolinvarioussciences.Duetotheadvancesinnumericalsolutionmethodsandinthecomputertechnology,geometricallyandphysicallycomplexcasescanberunevenonPCsoronPCclusters.Largescalesimulationsofviscousflowsongridsconsistingofdozensofmillionsofelementscanbeaccomplishedwithinonlyafewhoursontoday’ssupercomputers.However,itwouldbecompletelywrongtothinkthatCFDrepresentsamaturetechnologynow,like,forexample,thefinite-elementmethodsinsolidmechanics.No,therearestillmanyopenquestionsliketurbulenceandcombustionmodeling,heattransfer,efficientsolutiontechniquesforviscousflows,robustbutaccuratediscretizationmethods,automatedgridgenerators,etc.ThecouplingbetweenCFDandotherdisciplines(likethesolidmechanics)requiresfurtherresearchaswell.QuitenewopportunitiesalsoariseinthedesignoptimizationbyusingCFD.Theobjectiveofthisbookistoprovideuniversitystudentswithasolidfoundationforunderstandingthenumericalmethodsemployedintoday’sCFDandtofamiliarizethemwithmodernCFDcodesbyhands-onexperience.ThebookisalsointendedforengineersandscientistsstartingtoworkinthefieldofCFD,orwhoareapplyingCFDcodes.Themathematicsusedisalwaysconnectedtotheunderlyingphysicstofacilitatetheunderstandingofthematter.Thetextcanserveasareferencehandbooktoo.Eachchaptercontainsanextensivebibliography,whichmayformthebasisforfurtherstudies.CFDmethodsareconcernedwiththesolutionofequationsoffluidmotionaswellaswiththeinteractionofthefluidwithsolidbodies.Theequationsgoverningthemotionofaninviscidfluid(Eulerequations)andofviscousfluid(Navier-Stokesequations)arederivedinChapter2.Additionalthermodynamicrelationsforaperfectgasaswellasforarealgasarealsodiscussed.Chapter3dealswiththeprinciplesofsolutionofthegoverningequations.Themostimportantmethodologiesarebrieflydescribedandthecorrespondingreferencesareprovided.Chapter3canbeusedtogetherwithChapter2togetacquaintedwiththefundamentalprinciplesofCFD.NumerousschemesweredevelopedinthepastforthespatialdiscretizationoftheEulerandtheNavier-Stokesequations.Auniquefeatureofthepresentbookisthatitdealswithboththestructured(Chapter4)aswellaswiththeunstructuredfinite-volumeschemes(Chapter5),becauseoftheirbroadapplicationpossibilities,especiallyforthetreatmentofcomplexflowproblemsroutinelyencounteredinanindustrialenvironment.Theattentionisparticularlydevotedtothedefinitionofthevarioustypesofcontrolvolumestogetherwithspatialdiscretizationmethodologiesforconvectiveandviscousfluxes.The3-Dfinite-volumeformulationsofthemostpopularcentralandupwindschemesarepresentedindetail.Themethodologiesforthetemporaldiscretizationofthegoverningequationscanbedividedintotwomainclasses.Oneclasscomprisesexplicittime-steppingschemes(Section6.1),andtheotheroneconsistsofimplicitschemes(Section6.2).Inordertoprovideamorecompleteoverview,recentlydevelopedsolutionmethodsbasedontheNewton-iterationaswellasstandardtechniquesliketheexplicitRunge-Kuttaschemesarediscussed.Twoqualitativelydifferenttypesofviscousfluidflowsareencounteredingeneral:laminarandturbulent.ThesolutionoftheNavier-Stokesequationsdoesnotraiseanyfundamentaldifficultiesinthecaseoflaminarflows.However,thesimulationofturbulentflowscontinuestopresentasignificantchallengeasbefore.Arelativelysimplewayofmodelingtheturbulenceisofferedbytheso-calledReynolds-averagedNavier-Stokesequations.Ontheotherhand,ReynoldsstressmodelsorLESenableconsiderablymoreaccuratepredictionsofturbulentflows.InChapter7,variouswell-provenandwidelyappliedturbulencemodelsofvaryinglevelofcomplexityarepresentedindetail.Inordertoaccountforthespecificfeaturesofaparticularproblem,andtoobtainanuniquesolutionofthegoverningequations,itisnecessarytospecifyappropriateboundaryconditions.Basically,therearetwotypesofboundaryconditions:physicalandnumerical.Chapter8dealswithbothtypesindifferentsituationslikesolidwalls,inlet,outlet,injection,andfar-field.Symmetryplanes,periodicandblockboundariesaretreatedaswell.Inordertoreducethecomputertimerequiredtosolvethegoverningequationsforcomplexflowproblems,itisquiteessentialtoemploynumericalaccelerationtechniques.Chapter9dealsextensively,amongothers,withapproachesliketheimplicitresidualsmoothingandmultigrid.AnotherimportantmethodologywhichisalsodescribedinChapter9ispreconditioningofthegoverningequations.Itallowstheapplicationofasinglenumericalschemeforflows,wheretheMachnumbervariesbetweennearlyzeroandtransonicorhighervalues.Finally,Chapter9containsasectionontheparallelizationofnumericalcomputercodesbyusingdifferentapproaches.Eachdiscretizationofthegoverningequationsintroducesacertainerror—thediscretizationerror.Severalconsistencyrequirementshavetobefulfilledbythedis-cretizationscheme,inordertoensurethesolutionofthediscretizedequationscloselyapproximatesthesolutionoftheoriginalequations.ThisproblemisaddressedinthefirsttwopartsofChapter10.Beforeaparticularnumericalsolutionmethodisimplemented,itisimportanttoknow,atleastapproximately,howthemethodwillinfluencethestabilityandtheconvergencebehavioroftheCFDcode.ItwasfrequentlyconfirmedthattheVonNeumannstabilityanalysiscanprovideagoodassessmentofthepropertiesofanumericalscheme.Therefore,thethirdpartofChapter10dealswithstabilityanalysisforvariousmodelequations.OneofthechallengingtasksinCFDisthegenerationofstructuredorunstructuredbody-fittedgridsaroundcomplexgeometries.Thegridisusedtodiscretizethegoverningequationsinspace.Theaccuracyoftheflowsolutionisthereforecloselylinkedtothequalityofthegrid.InChapter11,themostimportantmethodologiesforthegenerationofstructuredaswellasunstructuredgridsarediscussedindepth.Inordertodemonstratethepracticalaspectsofdifferentnumericalsolutionmethod-ologies,varioussourcecodesareavailablefordownload.Providedarethesourcesofquasi1-DEuler,aswellasof2-DEulerandNavier-Stokesstructuredandunstructuredflowsolvers.Furthermore,sourcecodesof2-Dstructuredalgebraicandellipticgridgeneratorsareincludedtogetherwithaconverterfromstructuredtounstructuredgrids.Furthermore,twoprogramsareprovidedtoconductthelinearstabilityanalysisofexplicitandimplicittime-steppingschemes.Thesourcecodesarecompletedbyasetofworkedoutexamplesincludingthegrids,theinputfilesandtheresults.Thecodepackagealsocontainsseveralprogramsforthedemonstrationofparallelizationtechniques.Chapter12describesthecontentsofthedirectories,thecapabilitiesoftheparticularprograms,andprovidesexamplesoftheirusage.ThepresentbookisfinalizedwithanAppendixandIndex.TheAppendixcontainsthegoverningequationspresentedinadifferentialformaswellastheircharacteristicproperties.Formulationsofthegoverningequationsinrotatingframeofreferenceandformovinggridsarediscussedalongwithsomesimplifiedforms.Furthermore,Jacobianandtransformationmatricesfromconservativetocharacteristicvariablesarepresentedfortwoandthreedimensions.TheGMRESconjugategradientmethodforthesolutionoflinearequationssystemsisdescribednext.TheAppendixcloseswithabriefexplanationofthetensornotation.原资料见附件免责声明：本页面/内容部分素材来源于互联网公开信息，旨在传递更多信息，不代表本平台立场。版权归原作者或机构所有，如涉及侵权，请通过平台联系我们，我们将在核实后第一时间处理。本平台对转载内容的真实性、准确性不作任何保证，用户需自行判断并承担使用风险。
