fundamentals of computational fluid dynamics - lomax, pulliam

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1、FundamentalsofComputationalFluidDynamicsHarvardLomaxandThomasH.PulliamNASAAmesResearchCenterDavidW.ZinggUniversityofTorontoInstituteforAerospaceStudiesAugust26,1999Contents1INTRODUCTION11.1Motivation.................................11.2Background..............................

2、..21.2.1ProblemSpecicationandGeometryPreparation.......21.2.2SelectionofGoverningEquationsandBoundaryConditions.31.2.3SelectionofGriddingStrategyandNumericalMethod....31.2.4AssessmentandInterpretationofResults............41.3Overview..................................41.4Nota

3、tion..................................52CONSERVATIONLAWSANDTHEMODELEQUATIONS72.1ConservationLaws............................72.2TheNavier-StokesandEulerEquations.................82.3TheLinearConvectionEquation....................122.3.1DierentialForm.........................

4、122.3.2SolutioninWaveSpace......................132.4TheDiusionEquation..........................142.4.1DierentialForm.........................142.4.2SolutioninWaveSpace......................152.5LinearHyperbolicSystems........................162.6Problems..................

5、................173FINITE-DIFFERENCEAPPROXIMATIONS213.1MeshesandFinite-DierenceNotation.................213.2SpaceDerivativeAproximations....................243.3Finite-DierenceOperators.......................253.3.1PointDierenceOperators....................253.3.2MatrixDi

6、erenceOperators...................253.3.3PeriodicMatrices.........................293.3.4CirculantMatrices........................30iii3.4ConstructingDierencingSchemesofAnyOrder............313.4.1TaylorTables...........................313.4.2GeneralizationofDierenceFormula

7、s..............343.4.3LagrangeandHermiteInterpolationPolynomials.......353.4.4PracticalApplicationofPadeFormulas.............373.4.5OtherHigher-OrderSchemes...................383.5FourierErrorAnalysis..........................393.5.1ApplicationtoaSpatialOperator.............

8、...393.6DierenceOperatorsatBoundaries...................433.6.1TheL