Numerical Computation of Internal and External Flows - Fundamentals of Computational Fluid Dynamics (2nd Edition)
This classic book delivers the most up-to-date and comprehensive text available on computational fluid dynamics for engineers and mathematicians. Already renowned for its range and authority, this new edition has been significantly developed in terms of both contents and scope. A complete, self-cont...
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| Médium: | E-kniha |
| Jazyk: | angličtina |
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Oxford
Elsevier
2007
Elsevier Science & Technology Butterworth-Heinemann |
| Vydání: | 2 |
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| ISBN: | 9780750665940, 0750665947 |
| On-line přístup: | Získat plný text |
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- Title Page Preface to the Second Edition Table of Contents I. Introduction: An Initial Guide to CFD and to This Volume Part I. The Mathematical Models for Fluid Flow Simulations at Various Levels of Approximation 1. The Basic Equations of Fluid Dynamics 2. The Dynamical Levels of Approximation 3. The Mathematical Nature of the Flow Equations and Their Boundary Conditions Part II. Basic Discretization Techniques The Structure of Part II 4. The Finite Difference Method for Structured Grids 5. Finite Volume Method and Conservative Discretization with an Introduction to Finite Element Method 6. Structured and Unstructured Grid Properties Part III. The Analysis of Numerical Schemes 7. Consistency, Stability and Error Analysis of Numerical Schemes 8. General Properties and High-Resolution Numerical Schemes Part IV. The Resolution of Numerical Schemes 9. Time Integration Methods for Space-Discretized Equations 10. Iterative Methods for the Resolution of Algebraic Systems Appendix A: Thomas Algorithm for Tridiagonal Systems Part V. Applications to Inviscid and Viscous Flows 11. Numerical Simulation of Inviscid Flows 12. Numerical Solutions of Viscous Laminar Flows Index
- 3.3 Hyperbolic and parabolic equations: characteristic surfaces and domain of dependence -- 3.4 Time-dependent and conservation form of the PDEs -- 3.5 Initial and boundary conditions -- A.3.6 Alternative definition: compatibility relations -- Conclusions and main topics to remember -- References -- Problems -- Part II: Basic Discretization Techniques -- Chapter 4 The Finite Difference Method for Structured Grids -- Objectives and guidelines -- 4.1 The basics of finite difference methods -- 4.2 Multidimensional finite difference formulas -- 4.3 Finite difference formulas on non-uniform grids -- A4.4 General method for finite difference formulas -- A4.5 Implicit finite difference formulas -- Conclusions and main topics to remember -- References -- Problems -- Chapter 5 Finite Volume Method and Conservative Discretization with an Introduction to Finite Element Method -- Objectives and guidelines -- 5.1 The conservative discretization -- 5.2 The basis of the finite volume method -- 5.3 Practical implementation of finite volume method -- A5.4 The finite element method -- Conclusions and main topics to remember -- References -- Problems -- Chapter 6 Structured and Unstructured Grid Properties -- Objectives and guidelines -- 6.1 Structured Grids -- 6.2 Unstructured grids -- 6.3 Surface and volume estimations -- 6.4 Grid quality and best practice guidelines -- Conclusions and main topics to remember -- References -- Part III: The Analysis of Numerical Schemes -- Chapter 7 Consistency, Stability and Error Analysis of Numerical Schemes -- Objectives and guidelines -- 7.1 Basic concepts and definitions -- 7.2 The Von Neumann method for stability analysis -- 7.3 New schemes for the linear convection equation -- 7.4 The spectral analysis of numerical errors -- Conclusions and main topics to remember -- References -- Problems
- Cover -- Copyright Page -- Contents -- Preface to the Second Edition -- Nomenclature -- Introduction: An Initial Guide to CFD and to this Volume -- I.1 The position of CFD in the world of virtual prototyping -- I.1.1 The Definition Phase -- I.1.2 The Simulation and Analysis Phase -- I.1.3 The Manufacturing Cycle Phase -- I.2 The components of a CFD simulation system -- I.2.1 Step 1: Defining the Mathematical Model -- I.2.2 Step 2: Defining the Discretization Process -- I.2.3 Step 3: Performing the Analysis Phase -- I.2.4 Step 4: Defining the Resolution Phase -- I.3 The structure of this volume -- References -- Part I: The Mathematical Models for Fluid Flow Simulations at Various Levels of Approximation -- Chapter 1 The Basic Equations of Fluid Dynamics -- Objectives and guidelines -- 1.1 General form of a conservation law -- 1.2 The mass conservation equation -- 1.3 The momentum conservation law or equation of motion -- 1.4 The energy conservation equation -- A1.5 Rotating frame of reference -- A1.6 Advanced applications of control volume formulations -- Summary of the basic flow equations -- Conclusions and main topics to remember -- References -- Problems -- Chapter 2 The Dynamical Levels of Approximation -- Objectives and guidelines -- 2.1 The Navier-Stokes equations -- 2.2 Approximations of turbulent flows -- 2.3 Thin shear layer approximation (TSL) -- 2.4 Parabolized Navier-Stokes equations -- 2.5 Boundary layer approximation -- 2.6 The distributed loss model -- 2.7 Inviscid flow model: Euler equations -- 2.8 Potential flow model -- 2.9 Summary -- References -- Problems -- Chapter 3 The Mathematical Nature of the Flow Equations and Their Boundary Conditions -- Objectives and guidelines -- 3.1 Simplified models of a convection-diffusion equation -- 3.2 Definition of the mathematical properties of a system of PDEs
- Chapter 8 General Properties and High-Resolution Numerical Schemes -- Objectives and guidelines -- 8.1 General formulation of numerical schemes -- 8.2 The generation of new schemes with prescribed order of accuracy -- 8.3 Monotonicity of numerical schemes -- 8.4 Finite volume formulation of schemes and limiters -- Conclusions and main topics to remember -- References -- Problems -- Part IV: The Resolution of Numerical Schemes -- Chapter 9 Time Integration Methods for Space-discretized Equations -- Objectives and guidelines -- 9.1 Analysis of the space-discretized systems -- 9.2 Analysis of time integration schemes -- 9.3 A selection of time integration methods -- A9.4 Implicit schemes for multidimensional problems: approximate factorization methods -- Conclusions and main topics to remember -- References -- Problems -- Chapter 10 Iterative Methods for the Resolution of Algebraic Systems -- Objectives and guidelines -- 10.1 Basic iterative methods -- 10.2 Overrelaxation methods -- 10.3 Preconditioning techniques -- 10.4 Nonlinear problems -- 10.5 The multigrid method -- Conclusions and main topics to remember -- References -- Problems -- Appendix A: Thomas Algorithm for Tridiagonal Systems -- Part V: Applications to Inviscid and Viscous Flows -- Chapter 11 Numerical Simulation of Inviscid Flows -- Objectives and guidelines -- 11.1 The inviscid Euler equations -- 11.2 The potential flow model -- 11.3 Numerical solutions for the potential equation -- 11.4 Finite volume discretization of the Euler equations -- 11.5 Numerical solutions for the Euler equations -- Conclusions and main topics to remember -- References -- Chapter 12 Numerical Solutions of Viscous Laminar Flows -- Objectives and guidelines -- 12.1 Navier-Stokes equations for laminar flows -- 12.2 Density-based methods for viscous flows -- 12.3 Numerical solutions with the density-based method
- 12.4 Pressure correction method -- 12.5 Numerical solutions with the pressure correction method -- 12.6 Best practice advice -- Conclusions and main topics to remember -- References -- Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- J -- K -- L -- M -- N -- O -- P -- Q -- R -- S -- T -- U -- V -- W -- Z -- Colour Plates