Hjem

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 Realizability. -
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.
3.
3 Compact Schemes. -
3.
3.
4 Non-Uniform Grids. -
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 The Algebraic Equation System. -
3.
9 Discretization Errors. -
3.
10 An Introduction to Spectral Methods. -
3.
10.
1 Basic Concept. -
3.
10.
2 Another View of Discretization Error. -
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 and Differentiation 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 Implementation of Boundary Conditions. -
4.
6 The Algebraic Equation System. -
4.
7 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.
4.
3 Under-Relaxation. -
5.
5 Non-Linear Equations and their Solution. -
5.
5.
1 Newton-like Techniques. -
5.
5.
2 Other Techniques. -
5.
6 Deferred-Correction Approaches. -
5.
7 Convergence Criteria and Iteration Errors. -
5.
8 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 GridGri. -
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.
5.
1 Methods Based on Coordinate Transform ation. -
8.
5.
2 Method Based on Shape Functions. -
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 Axi-Symmetric 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 Deconvolution Models. -
9.
3.
4 Example: Flow Over a Wall-Mounted Cube. -
9.
3.
5 Example: Stratified Homogeneous Shear Flow. -
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 The v2f Model. -
9.
4.
4 Example: Flow Around an Engine Valve. -
9.
5 Reynolds Stress Models. -
9.
6 Very Large Eddy Simulation. -
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 Error Analysis and Estimation. -
11.
1.
1 Description of Errors. -
11.
1.
2 Estimation of Errors. -
11.
1.
3 Recommended Practice for CFD Uncertainty Analysis. -
11.
2 Grid quality and optimization. -
11.
3 Multigrid Methods for Flow Calculation. -
11.
4 Adaptive Grid Methods and Local Grid Refinement. -
11.
5 Parallel Computing in CFD. -
11.
5.
1 Iterative Schemes for Linear Equations. -
11.
5.
2 Domain Decomposition in Space. -
11.
5.
3 Domain Decomposition in Time. -
11.
5.
4 Efficiency of Parallel Comput ing. -
12. Special Topics. -
12.
1 Introduction
-
12.
2 Heat and Mass Transfer. -
12.
3 Flows With Variable Fluid Properties. -
12.
4 Moving Grids. -
12.
5 Free-Surface Flows. -
12.
5.
1 Interface-Tracking Methods. -
12.
5.
2 Hybrid Methods. -
12.
6 Meteorological and Oceanographic Applications. -
12.
7 Multiphase flows. -
12.
8 Combustion. - A. Appendices. - A. l List of Computer Codes and How to Access Them. - A.
2 List of Frequently Used Abbreviations. - References.