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| Preface | |
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| Basic Concepts of Fluid Flow | |
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| Introduction | |
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| Conservation Principles | |
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| Mass Conservation | |
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| Momentum Conservation | |
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| Conservation of Scalar Quantities | |
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| Dimensionless Form of Equations | |
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| Simplified Mathematical Models | |
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| Incompressible Flow | |
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| Inviscid (Euler) Flow | |
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| Potential Flow | |
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| Creeping (Stokes) Flow | |
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| Boussinesq Approximation | |
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| Boundary Layer Approximation | |
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| Modeling of Complex Flow Phenomena | |
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| Mathematical Classification of Flows | |
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| Hyperbolic Flows | |
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| Parabolic Flows | |
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| Elliptic Flows | |
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| Mixed Flow Types | |
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| Plan of This Book | |
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| Introduction to Numerical Methods | |
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| Approaches to Fluid Dynamical Problems | |
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| What is CFD? | |
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| Possibilities and Limitations of Numerical Methods | |
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| Components of a Numerical Solution Method | |
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| Mathematical Model | |
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| Discretization Method | |
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| Coordinate and Basis Vector Systems | |
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| Numerical Grid | |
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| Finite Approximations | |
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| Solution Method | |
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| Convergence Criteria | |
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| Properties of Numerical Solution Methods | |
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| Consistency | |
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| Stability | |
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| Convergence | |
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| Conservation | |
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| Boundedness | |
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| Realizability | |
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| Accuracy | |
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| Discretization Approaches | |
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| Finite Difference Method | |
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| Finite Volume Method | |
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| Finite Element Method | |
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| Finite Difference Methods | |
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| Introduction | |
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| Basic Concept | |
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| Approximation of the First Derivative | |
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| Taylor Series Expansion | |
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| Polynomial Fitting | |
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| Compact Schemes | |
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| Non-Uniform Grids | |
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| Approximation of the Second Derivative | |
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| Approximation of Mixed Derivatives | |
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| Approximation of Other Terms | |
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| Implementation of Boundary Conditions | |
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| The Algebraic Equation System | |
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| Discretization Errors | |
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| An Introduction to Spectral Methods | |
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| Basic Concept | |
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| Another View of Discretization Error | |
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| Example | |
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| Finite Volume Methods | |
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| Introduction | |
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| Approximation of Surface Integrals | |
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| Approximation of Volume Integrals | |
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| Interpolation and Differentiation Practices | |
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| Upwind Interpolation (UDS) | |
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| Linear Interpolation (CDS) | |
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| Quadratic Upwind Interpolation (QUICK) | |
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| Higher-Order Schemes | |
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| Other Schemes | |
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| Implementation of Boundary Conditions | |
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| The Algebraic Equation System | |
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| Examples | |
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| Solution of Linear Equation Systems | |
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| Introduction | |
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| Direct Methods | |
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| Gauss Elimination | |
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| LU Decomposition | |
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| Tridiagonal Systems | |
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| Cyclic Reduction | |
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| Iterative Methods | |
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| Basic Concept | |
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| Convergence | |
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| Some Basic Methods | |
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| Incomplete LU Decomposition: Stone's Method | |
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| ADI and Other Splitting Methods | |
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| Conjugate Gradient Methods | |
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| Biconjugate Gradients and CGSTAB | |
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| Multigrid Methods | |
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| Other Iterative Solvers | |
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| Coupled Equations and Their Solution | |
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| Simultaneous Solution | |
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| Sequential Solution | |
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| Under-Relaxation | |
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| Non-Linear Equations and their Solution | |
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| Newton-like Techniques | |
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| Other Techniques | |
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| Deferred-Correction Approaches | |
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| Convergence Criteria and Iteration Errors | |
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| Examples | |
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| Methods for Unsteady Problems | |
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| Introduction | |
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| Methods for Initial Value Problems in ODEs | |
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| Two-Level Methods | |
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| Predictor-Corrector and Multipoint Methods | |
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| Runge-Kutta Methods | |
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| Other Methods | |
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| Application to the Generic Transport Equation | |
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| Explicit Methods | |
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| Implicit Methods | |
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| Other Methods | |
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| Examples | |
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| Solution of the Navier-Stokes Equations | |
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| Special Features of the Navier-Stokes Equations | |
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| Discretization of Convective and Viscous Terms | |
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| Discretization of Pressure Terms and Body Forces | |
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| Conservation Properties | |
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| Choice of Variable Arrangement on the Grid | |
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| Colocated Arrangement | |
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| Staggered Arrangements | |
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| Calculation of the Pressure | |
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| The Pressure Equation and its Solution | |
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| A Simple Explicit Time Advance Scheme | |
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| A Simple Implicit Time Advance Method | |
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| Implicit Pressure-Correction Methods | |
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| Other Methods | |
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| Fractional Step Methods | |
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| Streamfunction-Vorticity Methods | |
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| Artificial Compressibility Methods | |
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| Solution Methods for the Navier-Stokes Equations | |
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| Implicit Scheme Using Pressure-Correction and a Staggered Grid | |
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| Treatment of Pressure for Colocated Variables | |
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| SIMPLE Algorithm for a Colocated Variable Arrangement | |
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| Note on Pressure and Incompressibility | |
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| Boundary Conditions for the Navier-Stokes Equations | |
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| Examples | |
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| Complex Geometries | |
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| The Choice of Grid | |
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| Stepwise Approximation Using Regular Grids | |
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| Overlapping Grids | |
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| Boundary-Fitted Non-Orthogonal Grids | |
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| Grid Generation | |
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| The Choice of Velocity Components | |
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| Grid-Oriented Velocity Components | |
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| Cartesian Velocity Components | |
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| The Choice of Variable Arrangement | |
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| Staggered Arrangements | |
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| Colocated Arrangement | |
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| Finite Difference Methods | |
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| Methods Based on Coordinate Transformation | |
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| Method Based on Shape Functions | |
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| Finite Volume Methods | |
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| Approximation of Convective Fluxes | |
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| Approximation of Diffusive Fluxes | |
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| Approximation of Source Terms | |
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| Three-Dimensional Grids | |
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| Block-Structured Grids | |
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| Unstructured Grids | |
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| Control-Volume-Based Finite Element Methods | |
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| Pressure-Correction Equation | |
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| Axi-Symmetric Problems | |
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| Implementation of Boundary Conditions | |
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| Inlet | |
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| Outlet | |
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| Impermeable Walls | |
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| Symmetry Planes | |
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| Specified Pressure | |
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| Examples | |
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| Turbulent Flows | |
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| Introduction | |
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| Direct Numerical Simulation (DNS) | |
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| Example: Spatial Decay of Grid Turbulence | |
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| Large Eddy Simulation (LES) | |
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| Smagorinsky and Related Models | |
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| Dynamic Models | |
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| Deconvolution Models | |
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| Example: Flow Over a Wall-Mounted Cube | |
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| Example: Stratified Homogeneous Shear Flow | |
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| RANS Models | |
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| Reynolds-Averaged Navier-Stokes (RANS) Equations | |
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| Simple Turbulence Models and their Application | |
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| The v2f Model | |
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| Example: Flow Around an Engine Valve | |
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| Reynolds Stress Models | |
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| Very Large Eddy Simulation | |
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| Compressible Flow | |
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| Introduction | |
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| Pressure-Correction Methods for Arbitrary Mach Number | |
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| Pressure-Velocity-Density Coupling | |
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| Boundary Conditions | |
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| Examples | |
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| Methods Designed for Compressible Flow | |
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| An Overview of Some Specific Methods | |
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| Efficiency and Accuracy Improvement | |
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| Error Analysis and Estimation | |
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| Description of Errors | |
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| Estimation of Errors | |
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| Recommended Practice for CFD Uncertainty Analysis | |
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| Grid quality and optimization | |
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| Multigrid Methods for Flow Calculation | |
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| Adaptive Grid Methods and Local Grid Refinement | |
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| Parallel Computing in CFD | |
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| Iterative Schemes for Linear Equations | |
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| Domain Decomposition in Space | |
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| Domain Decomposition in Time | |
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| Efficiency of Parallel Computing | |
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| Special Topics | |
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| Introduction | |
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| Heat and Mass Transfer | |
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| Flows With Variable Fluid Properties | |
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| Moving Grids | |
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| Free-Surface Flows | |
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| Interface-Tracking Methods | |
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| Hybrid Methods | |
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| Meteorological and Oceanographic Applications | |
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| Multiphase flows | |
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| Combustion | |
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| Appendices | |
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| List of Computer Codes and How to Access Them | |
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| List of Frequently Used Abbreviations | |
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| References | |
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| Index | |