| Preface |
| Basic Concepts of Fluid Flow / 1.： |
| Introduction / 1.1： |
| Conservation Principles / 1.2： |
| Mass Conservation / 1.3： |
| Momentum Conservation / 1.4： |
| Conservation of Scalar Quantities / 1.5： |
| Dimensionless Form of Equations / 1.6： |
| Simplified Mathematical Models / 1.7： |
| Incompressible Flow / 1.7.1： |
| Inviscid (Euler) Flow / 1.7.2： |
| Potential Flow / 1.7.3： |
| Creeping (Stokes) Flow / 1.7.4： |
| Boussinesq Approximation / 1.7.5： |
| Boundary Layer Approximation / 1.7.6： |
| Modeling of Complex Flow Phenomena / 1.7.7： |
| Mathematical Classification of Flows / 1.8： |
| Hyperbolic Flows / 1.8.1： |
| Parabolic Flows / 1.8.2： |
| Elliptic Flows / 1.8.3： |
| Mixed Flow Types / 1.8.4： |
| Plan of This Book / 1.9： |
| Introduction to Numerical Methods / 2.： |
| Approaches to Fluid Dynamical Problems / 2.1： |
| What is CFD? / 2.2： |
| Possibilities and Limitations of Numerical Methods / 2.3： |
| Components of a Numerical Solution Method / 2.4： |
| Mathematical Model / 2.4.1： |
| Discretization Method / 2.4.2： |
| Coordinate and Basis Vector Systems / 2.4.3： |
| Numerical Grid / 2.4.4： |
| Finite Approximations / 2.4.5： |
| Solution Method / 2.4.6： |
| Convergence Criteria / 2.4.7： |
| Properties of Numerical Solution Methods / 2.5： |
| Consistency / 2.5.1： |
| Stability / 2.5.2： |
| Convergence / 2.5.3： |
| Conservation / 2.5.4： |
| Boundedness / 2.5.5： |
| Realizability / 2.5.6： |
| Accuracy / 2.5.7： |
| Discretization Approaches / 2.6： |
| Finite Difference Method / 2.6.1： |
| Finite Volume Method / 2.6.2： |
| Finite Element Method / 2.6.3： |
| Finite Difference Methods / 3.： |
| Basic Concept / 3.1： |
| Approximation of the First Derivative / 3.3： |
| Taylor Series Expansion / 3.3.1： |
| Polynomial Fitting / 3.3.2： |
| Compact Schemes / 3.3.3： |
| Non-Uniform Grids / 3.3.4： |
| Approximation of the Second Derivative / 3.4： |
| Approximation of Mixed Derivatives / 3.5： |
| Approximation of Other Terms / 3.6： |
| Implementation of Boundary Conditions / 3.7： |
| The Algebraic Equation System / 3.8： |
| Discretization Errors / 3.9： |
| An Introduction to Spectral Methods / 3.10： |
| Another View of Discretization Error / 3.10.1： |
| Example / 3.11： |
| Finite Volume Methods / 4.： |
| Approximation of Surface Integrals / 4.1： |
| Approximation of Volume Integrals / 4.3： |
| Interpolation and Differentiation Practices / 4.4： |
| Upwind Interpolation (UDS) / 4.4.1： |
| Linear Interpolation (CDS) / 4.4.2： |
| Quadratic Upwind Interpolation (QUICK) / 4.4.3： |
| Higher-Order Schemes / 4.4.4： |
| Other Schemes / 4.4.5： |
| Examples / 4.5： |
| Solution of Linear Equation Systems / 5.： |
| Direct Methods / 5.1： |
| Gauss Elimination / 5.2.1： |
| LU Decomposition / 5.2.2： |
| Tridiagonal Systems / 5.2.3： |
| Cyclic Reduction / 5.2.4： |
| Iterative Methods / 5.3： |
| Some Basic Methods / 5.3.1： |
| Incomplete LU Decomposition: Stone's Method / 5.3.4： |
| ADI and Other Splitting Methods / 5.3.5： |
| Conjugate Gradient Methods / 5.3.6： |
| Biconjugate Gradients and CGSTAB / 5.3.7： |
| Multigrid Methods / 5.3.8： |
| Other Iterative Solvers / 5.3.9： |
| Coupled Equations and Their Solution / 5.4： |
| Simultaneous Solution / 5.4.1： |
| Sequential Solution / 5.4.2： |
| Under-Relaxation / 5.4.3： |
| Non-Linear Equations and their Solution / 5.5： |
| Newton-like Techniques / 5.5.1： |
| Other Techniques / 5.5.2： |
| Deferred-Correction Approaches / 5.6： |
| Convergence Criteria and Iteration Errors / 5.7： |
| Methods for Unsteady Problems / 5.8： |
| Methods for Initial Value Problems in ODEs / 6.1： |
| Two-Level Methods / 6.2.1： |
| Predictor-Corrector and Multipoint Methods / 6.2.2： |
| Runge-Kutta Methods / 6.2.3： |
| Other Methods / 6.2.4： |
| Application to the Generic Transport Equation / 6.3： |
| Explicit Methods / 6.3.1： |
| Implicit Methods / 6.3.2： |
| Solution of the Navier-Stokes Equations / 6.3.3： |
| Special Features of the Navier-Stokes Equations / 7.1： |
| Discretization of Convective and Viscous Terms / 7.1.1： |
| Discretization of Pressure Terms and Body Forces / 7.1.2： |
| Conservation Properties / 7.1.3： |
| Choice of Variable Arrangement on the Grid / 7.2： |
| Colocated Arrangement / 7.2.1： |
| Staggered Arrangements / 7.2.2： |
| Calculation of the Pressure / 7.3： |
| The Pressure Equation and its Solution / 7.3.1： |
| A Simple Explicit Time Advance Scheme / 7.3.2： |
| A Simple Implicit Time Advance Method / 7.3.3： |
| Implicit Pressure-Correction Methods / 7.3.4： |
| Fractional Step Methods / 7.4： |
| Streamfunction-Vorticity Methods / 7.4.2： |
| Artificial Compressibility Methods / 7.4.3： |
| Solution Methods for the Navier-Stokes Equations / 7.5： |
| Implicit Scheme Using Pressure-Correction and a Staggered Grid / 7.5.1： |
| Treatment of Pressure for Colocated Variables / 7.5.2： |
| SIMPLE Algorithm for a Colocated Variable Arrangement / 7.5.3： |
| Note on Pressure and Incompressibility / 7.6： |
| Boundary Conditions for the Navier-Stokes Equations / 7.7： |
| Complex Geometries / 7.8： |
| The Choice of Grid / 8.1： |
| Stepwise Approximation Using Regular Grids / 8.1.1： |
| Overlapping Grids / 8.1.2： |
| Boundary-Fitted Non-Orthogonal Grids / 8.1.3： |
| Grid Generation / 8.2： |
| The Choice of Velocity Components / 8.3： |
| Grid-Oriented Velocity Components / 8.3.1： |
| Cartesian Velocity Components / 8.3.2： |
| The Choice of Variable Arrangement / 8.4： |
| Methods Based on Coordinate Transformation / 8.4.1： |
| Method Based on Shape Functions / 8.5.2： |
| Approximation of Convective Fluxes / 8.6： |
| Approximation of Diffusive Fluxes / 8.6.2： |
| Approximation of Source Terms / 8.6.3： |
| Three-Dimensional Grids / 8.6.4： |
| Block-Structured Grids / 8.6.5： |
| Unstructured Grids / 8.6.6： |
| Control-Volume-Based Finite Element Methods / 8.7： |
| Pressure-Correction Equation / 8.8： |
| Axi-Symmetric Problems / 8.9： |
| Inlet / 8.10： |
| Outlet / 8.10.2： |
| Impermeable Walls / 8.10.3： |
| Symmetry Planes / 8.10.4： |
| Specified Pressure / 8.10.5： |
| Turbulent Flows / 8.11： |
| Direct Numerical Simulation (DNS) / 9.1： |
| Example: Spatial Decay of Grid Turbulence / 9.2.1： |
| Large Eddy Simulation (LES) / 9.3： |
| Smagorinsky and Related Models / 9.3.1： |
| Dynamic Models / 9.3.2： |
| Deconvolution Models / 9.3.3： |
| Example: Flow Over a Wall-Mounted Cube / 9.3.4： |
| Example: Stratified Homogeneous Shear Flow / 9.3.5： |
| RANS Models / 9.4： |
| Reynolds-Averaged Navier-Stokes (RANS) Equations / 9.4.1： |
| Simple Turbulence Models and their Application / 9.4.2： |
| The v2f Model / 9.4.3： |
| Example: Flow Around an Engine Valve / 9.4.4： |
| Reynolds Stress Models / 9.5： |
| Very Large Eddy Simulation / 9.6： |
| Compressible Flow / 10.： |
| Pressure-Correction Methods for Arbitrary Mach Number / 10.1： |
| Pressure-Velocity-Density Coupling / 10.2.1： |
| Boundary Conditions / 10.2.2： |
| Methods Designed for Compressible Flow / 10.2.3： |
| An Overview of Some Specific Methods / 10.3.1： |
| Efficiency and Accuracy Improvement / 11.： |
| Error Analysis and Estimation / 11.1： |
| Description of Errors / 11.1.1： |
| Estimation of Errors / 11.1.2： |
| Recommended Practice for CFD Uncertainty Analysis / 11.1.3： |
| Grid quality and optimization / 11.2： |
| Multigrid Methods for Flow Calculation / 11.3： |
| Adaptive Grid Methods and Local Grid Refinement / 11.4： |
| Parallel Computing in CFD / 11.5： |
| Iterative Schemes for Linear Equations / 11.5.1： |
| Domain Decomposition in Space / 11.5.2： |
| Domain Decomposition in Time / 11.5.3： |
| Efficiency of Parallel Computing / 11.5.4： |
| Special Topics / 12.： |
| Heat and Mass Transfer / 12.1： |
| Flows With Variable Fluid Properties / 12.3： |
| Moving Grids / 12.4： |
| Free-Surface Flows / 12.5： |
| Interface-Tracking Methods / 12.5.1： |
| Hybrid Methods / 12.5.2： |
| Meteorological and Oceanographic Applications / 12.6： |
| Multiphase flows / 12.7： |
| Combustion / 12.8： |
| Appendices / A.： |
| List of Computer Codes and How to Access Them / A.1： |
| List of Frequently Used Abbreviations / A.2： |
| References |
| Index |
| Preface |
| Basic Concepts of Fluid Flow / 1.： |
| Introduction / 1.1： |
図書
