Ferziger / Peric Computational Methods for Fluid Dynamics

1996
ISBN: 978-3-642-97651-3
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 364 Seiten, eBook

A detailed description of the methods most often used in practice. The authors are experts in their fields and cover such advanced techniques as direct and large-eddy simulation of turbulence, multigrid methods, parallel computing, moving grids, structured, block-structured and unstructured boundary-fitted grids, and free surface flows. The book shows common roots and basic principles for many apparently different methods, while also containing a great deal of practical advice for code developers and users. All the computer codes can be accessed from the Springer server on the internet. Designed to be equally useful for beginners and experts.

Zielgruppe

Professional/practitioner

Autoren/Hrsg.

Ferziger, Joel H.

Peric, Milovan

Inhaltsverzeichnis

1. Basic Concepts of Fluid Flow.- 1.1 Introduction.- 1.2 Conservation Principles.- 1.3 Mass Conservation.- 1.4 Momentum Conservation.- 1.5 Conservation of Scalar Quantities.- 1.6 Dimensionless Form of Equations.- 1.7 Simplified Mathematical Models.- 1.7.1 Incompressible Flow.- 1.7.2 Inviscid (Euler) Flow.- 1.7.3 Potential Flow.- 1.7.4 Creeping (Stokes) Flow.- 1.7.5 Boussinesq Approximation.- 1.7.6 Boundary Layer Approximation.- 1.7.7 Modeling of Complex Flow Phenomena.- 1.8 Mathematical Classification of Flows.- 1.8.1 Hyperbolic Flows.- 1.8.2 Parabolic Flows.- 1.8.3 Elliptic Flows.- 1.8.4 Mixed Flow Types.- 1.9 Plan of This Book.- 2. Introduction to Numerical Methods.- 2.1 Approaches to Fluid Dynamical Problems.- 2.2 What is CFD?.- 2.3 Possibilities and Limitations of Numerical Methods.- 2.4 Components of a Numerical Solution Method.- 2.4.1 Mathematical Model.- 2.4.2 Discretization Method.- 2.4.3 Coordinate and Basis Vector Systems.- 2.4.4 Numerical Grid.- 2.4.5 Finite Approximations.- 2.4.6 Solution Method.- 2.4.7 Convergence Criteria.- 2.5 Properties of Numerical Solution Methods.- 2.5.1 Consistency.- 2.5.2 Stability.- 2.5.3 Convergence.- 2.5.4 Conservation.- 2.5.5 Boundedness.- 2.5.6 Realizibility.- 2.5.7 Accuracy.- 2.6 Discretization Approaches.- 2.6.1 Finite Difference Method.- 2.6.2 Finite Volume Method.- 2.6.3 Finite Element Method.- 3. Finite Difference Methods.- 3.1 Introduction.- 3.2 Basic Concept.- 3.3 Approximation of the First Derivative.- 3.3.1 Taylor Series Expansion.- 3.3.2 Polynomial Fitting.- 3.4 Approximation of the Second Derivative.- 3.5 Approximation of Mixed Derivatives.- 3.6 Approximation of Other Terms.- 3.7 Implementation of Boundary Conditions.- 3.8 An Introduction to Spectral Methods.- 3.8.1 Basic Concept.- 3.8.2 Another View of Discretization Error.- 3.9 The Algebraic Equation System.- 3.10 Discretization Errors.- 3.11 Example.- 4. Finite Volume Methods.- 4.1 Introduction.- 4.2 Approximation of Surface Integrals.- 4.3 Approximation of Volume Integrals.- 4.4 Interpolation Practices.- 4.4.1 Upwind Interpolation (UDS).- 4.4.2 Linear Interpolation (CDS).- 4.4.3 Quadratic Upwind Interpolation (QUICK).- 4.4.4 Higher-Order Schemes.- 4.4.5 Other Schemes.- 4.5 Deferred Correction.- 4.6 Implementation of Boundary Conditions.- 4.7 The Algebraic Equation System.- 4.8 Examples.- 5. Solution of Linear Equation Systems.- 5.1 Introduction.- 5.2 Direct Methods.- 5.2.1 Gauss Elimination.- 5.2.2 LU Decomposition.- 5.2.3 Tridiagonal Systems.- 5.2.4 Cyclic Reduction.- 5.3 Iterative Methods.- 5.3.1 Basic Concept.- 5.3.2 Convergence.- 5.3.3 Some Basic Methods.- 5.3.4 Incomplete LU Decomposition: Stone’s Method.- 5.3.5 ADI and Other Splitting Methods.- 5.3.6 Conjugate Gradient Methods.- 5.3.7 Biconjugate Gradients and CGSTAB.- 5.3.8 Multigrid Methods.- 5.3.9 Other Iterative Solvers.- 5.4 Coupled Equations and Their Solution.- 5.4.1 Simultaneous Solution.- 5.4.2 Sequential Solution.- 5.5 Non-Linear Equations and their Solution.- 5.5.1 Newton-like Techniques.- 5.5.2 Other Techniques.- 5.6 Convergence Criteria.- 5.7 Examples.- 6. Methods for Unsteady Problems.- 6.1 Introduction.- 6.2 Methods for Initial Value Problems in ODEs.- 6.2.1 Two-Level Methods.- 6.2.2 Predictor-Corrector and Multipoint Methods.- 6.2.3 Runge-Kutta Methods.- 6.2.4 Other Methods.- 6.3 Application to the Generic Transport Equation.- 6.3.1 Explicit Methods.- 6.3.2 Implicit Methods.- 6.3.3 Other Methods.- 6.4 Examples.- 7. Solution of the Navier-Stokes Equations.- 7.1 Special Features of the Navier-Stokes Equations.- 7.1.1 Discretization of Convective and Viscous Terms.- 7.1.2 Discretization of Pressure Terms and Body Forces.- 7.1.3 Conservation Properties.- 7.2 Choice of Variable Arrangement on the Grid.- 7.2.1 Colocated Arrangement.- 7.2.2 Staggered Arrangements.- 7.3 Calculation of the Pressure.- 7.3.1 The Pressure Equation and its Solution.- 7.3.2 A Simple Explicit Time Advance Scheme.- 7.3.3 A Simple Implicit Time Advance Method.- 7.3.4 Implicit Pressure-Correction Methods.- 7.4 Other Methods.- 7.4.1 Fractional Step Methods.- 7.4.2 Streamfunction-Vorticity Methods.- 7.4.3 Artificial Compressibility Methods.- 7.5 Solution Methods for the Navier-Stokes Equations.- 7.5.1 Implicit Scheme Using Pressure-Correction and a Staggered Grid.- 7.5.2 Treatment of Pressure for Colocated Variables.- 7.5.3 SIMPLE Algorithm for a Colocated Variable Arrangement.- 7.6 Note on Pressure and Incompressibility.- 7.7 Boundary Conditions for the Navier-Stokes Equations.- 7.8 Examples.- 8. Complex Geometries.- 8.1 The Choice of Grid.- 8.1.1 Stepwise Approximation Using Regular Grids.- 8.1.2 Overlapping Grids.- 8.1.3 Boundary-Fitted Non-Orthogonal Grids.- 8.2 Grid Generation.- 8.3 The Choice of Velocity Components.- 8.3.1 Grid-Oriented Velocity Components.- 8.3.2 Cartesian Velocity Components.- 8.4 The Choice of Variable Arrangement.- 8.4.1 Staggered Arrangements.- 8.4.2 Colocated Arrangement.- 8.5 Finite Difference Methods.- 8.6 Finite Volume Methods.- 8.6.1 Approximation of Convective Fluxes.- 8.6.2 Approximation of Diffusive Fluxes.- 8.6.3 Approximation of Source Terms.- 8.6.4 Three-Dimensional Grids.- 8.6.5 Block-Structured Grids.- 8.6.6 Unstructured Grids.- 8.7 Control-Volume-Based Finite Element Methods.- 8.8 Pressure-Correction Equation.- 8.9 Axisymmetric Problems.- 8.10 Implementation of Boundary Conditions.- 8.10.1 Inlet.- 8.10.2 Outlet.- 8.10.3 Impermeable Walls.- 8.10.4 Symmetry Planes.- 8.10.5 Specified Pressure.- 8.11 Examples.- 9. Turbulent Flows.- 9.1 Introduction.- 9.2 Direct Numerical Simulation (DNS).- 9.2.1 Example: Spatial Decay of Grid Turbulence.- 9.3 Large Eddy Simulation (LES).- 9.3.1 Smagorinsky and Related Models.- 9.3.2 Dynamic Models.- 9.3.3 Example: Flow Over a Wall-Mounted Cube.- 9.4 RANS Models.- 9.4.1 Reynolds Averaged Navier-Stokes (RANS) Equations.- 9.4.2 Simple Turbulence Models and their Application.- 9.4.3 Example: Flow Around a Valve.- 9.5 Reynolds Stress Models.- 10. Compressible Flow.- 10.1 Introduction.- 10.2 Pressure-Correction Methods for Arbitrary Mach Number.- 10.2.1 Pressure-Velocity-Density Coupling.- 10.2.2 Boundary Conditions.- 10.2.3 Examples.- 10.3 Methods Designed for Compressible Flow.- 10.3.1 An Overview of Some Specific Methods.- 11. Efficiency and Accuracy Improvement.- 11.1 Multigrid Methods for Flow Calculation.- 11.2 Adaptive Grid Methods and Local Grid Refinement.- 11.3 Parallel Computing in CFD.- 11.3.1 Iterative Schemes for Linear Equations.- 11.3.2 Domain Decomposition in Space.- 11.3.3 Domain Decomposition in Time.- 11.3.4 Efficiency of Parallel Computing.- 12. Special Topics.- 12.1 Moving Grids.- 12.2 Free Surface Flows.- 12.3 Heat Transfer.- 12.4 Flow With Variable Fluid Properties.- 12.5 Meteorological and Oceanographic Applications.- 12.6 Combustion.- A. Appendeces.- A.1 List of Computer Codes and How to Access Them.- A.2 List of Frequently Used Abbreviations.