Computational Fluid Mechanics and Heat Transfer

Thoroughly updated to include the latest developments in the field, this classic text on finite-difference and finite-volume computational methods maintains the fundamental concepts covered in the first edition. As an introductory text for advanced undergraduates and first-year graduate students, Computational Fluid Mechanics and Heat Transfer, Third Edition provides the background necessary for solving complex problems in fluid mechanics and heat transfer. Divided into two parts, the book first lays the groundwork for the essential concepts preceding the fluids equations in the second part. It includes expanded coverage of turbulence and large-eddy simulation (LES) and additional material included on detached-eddy simulation (DES) and direct numerical simulation (DNS). Designed as a valuable resource for practitioners and students, new homework problems have been added to further enhance the student’s understanding of the fundamentals and applications.

Part I: FundamentalsIntroductionGeneral RemarksComparison of Experimental, Theoretical, and Computational ApproachesHistorical PerspectivePartial Differential EquationsIntroductionPhysical ClassificationMathematical ClassificationWell-Posed ProblemSystems of Partial Differential EquationsOther PDEs of InterestProblemsBasics of Discretization MethodsIntroductionFinite DifferencesDifference Representation of Partial Differential EquationsFurther Examples of Methods for Obtaining Finite-Difference EquationsFinite-Volume MethodIntroduction to the Use of Irregular MeshesStability ConsiderationsProblemsApplication of Numerical Methods to Selected Model EquationsWave EquationHeat EquationLaplace’s EquationBurgers’ Equation (Inviscid)Burgers’ Equation (Viscous)Concluding RemarksProblemsPart II: Application of Numerical Methods to the Equations of Fluid Mechanics and Heat Transfer Governing Equations of Fluid Mechanics and Heat TransferFundamental EquationsAveraged Equations for Turbulent FlowsBoundary-Layer EquationsIntroduction to Turbulence ModelingEuler EquationsNumerical Methods for Inviscid Flow EquationsIntroductionMethod of CharacteristicsClassical Shock-Capturing MethodsFlux Splitting SchemesFlux-Difference Splitting SchemesMultidimensional Case in a General Coordinate SystemBoundary Conditions for the Euler EquationsMethods for Solving the Potential EquationTransonic Small-Disturbance EquationsMethods for Solving Laplace’s EquationProblemsNumerical Methods for Boundary-Layer-Type EquationsIntroductionBrief Comparison of Prediction MethodsFinite-Difference Methods for Two-Dimensional or Axisymmetric Steady External FlowsInverse Methods, Separated Flows, and Viscous–Inviscid InteractionMethods for Internal FlowsApplication to Free-Shear FlowsThree-Dimensional Boundary LayersUnsteady Boundary LayersProblemsNumerical Methods for the "Parabolized" Navier–Stokes EquationsIntroductionThin-Layer Navier–Stokes Equations"Parabolized" Navier–Stokes EquationsParabolized and Partially Parabolized Navier–Stokes Procedures for Subsonic FlowsViscous Shock-Layer Equations"Conical" Navier–Stokes EquationsProblemsNumerical Methods for the Navier–Stokes EquationsIntroductionCompressible Navier–Stokes EquationsIncompressible Navier–Stokes EquationsGrid GenerationIntroductionAlgebraic MethodsDifferential Equation MethodsVariational MethodsUnstructured Grid SchemesOther ApproachesAdaptive GridsProblemsAppendix A: Subroutine for Solving a Tridiagonal System of EquationsAppendix B: Subroutines for Solving Block Tridiagonal Systems of EquationsAppendix C: Modified Strongly Implicit ProcedureNomenclatureReferencesIndex