Key Features
• New approach takes readers seamlessly from first principles to more advanced and applied topics
• Presents the essential components of a simulation system at a level suitable for those coming into contact with CFD for the first time, and is ideal for those who need a comprehensive refresher on the fundamentals of CFD
• Enhanced pedagogy features chapter objectives, hands-on practice examples and end of chapter exercises
• Extended coverage of finite difference, finite
volume and finite element methods
• New chapters include an introduction to grid
properties and the use of grids in practice
• Includes material on 2-D inviscid, potential
and Euler flows, 2-D viscous flows, Navier-
Stokes flows to enable the reader to develop basic CFD simulations
• Includes Best-Practice guidelines for applying existing commercial or shareware CFD tools
Description
The second edition of 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 contained text, it will form the basis of study for many leading CFD courses at senior undergraduate and graduate level: a truly formidable resource covering the fundamentals of CFD.
Readership
Senior undergraduate and graduate level courses as a basic introduction to the fundamentals and first applications of CFD. Its high didactic approach will guide the student through the various steps in setting up and/or analyzing CFD methods.
It will also be beneficial for graduate and professional mechanical engineering disciplines, such as aeronautical, automotive, thermal, combustion, pipeline, chemical, civil, industrial and manufacturing engineering; as well as Applied mathematics and numerical methods, biomechanics, ocean-sciences and hydrological sciences, and meteorology.
Numerical Computation of Internal and External Flows: The Fundamentals of Computational Fluid Dynamics, 2nd Edition
Introduction: An Initial Guide to CFD and to this Volume 1
Part I The Mathematical Models for Fluid Flow Simulations at Various Levels of Approximation
1 The Basic Equations of Fluid Dynamics
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
Conclusions and main topics to remember
2 The Dynamical Levels of Approximation
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
3 The Mathematical Nature of the Flow Equations and Their Boundary Conditions
3.1 Simplified models of a convection–diffusion equation
3.2 Definition of the mathematical properties of a system of PDEs
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
Part II Basic Discretization Techniques
4 The Finite Difference Method for Structured Grids
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
5 Finite Volume Method and Conservative Discretization with an Introduction to Finite Element Method
5.1 The conservative discretization
5.2 The basis of the finite volume method
5.3 Practical implementation of finite volume method
A.5.4 The finite element method
A5.4.1 Finite Element Definition of Interpolation Functions
A5.4.2 Finite Element Definition of the Equation Discretization: Integral Formulation
A5.4.3 The Method of Weighted Residuals or Weak Formulation
A5.4.4 The Galerkin Method
A5.4.5 Finite Element Galerkin Method for a Conservation Law
A5.4.6 Subdomain Collocation: Finite Volume Method
Conclusions and main topics to remember
6 Structured and Unstructured Grid Properties
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
Part III The Analysis of Numerical Schemes
7 Consistency, Stability and Error Analysis of Numerical Schemes
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
8 General Properties and High-Resolution Numerical Schemes
8.1 General formulation of numerical schemes
A8.1.5 An Addition to the Stability Analysis
A8.1.6 An Advanced Addition to the Accuracy Barrier
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
Part IV The Resolution of Numerical Schemes
9 Time Integration Methods for Space-discretized Equations
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
A9.4.1 Two-Dimensional Diffusion Equation
A9.4.2 ADI Method for the Convection Equation
Conclusions and main topics to remember
10 Iterative Methods for the Resolution of Algebraic Systems
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
Appendix A: Thomas Algorithm for Tridiagonal Systems
A.1. Scalar Tridiagonal Systems
A.2. Periodic Tridiagonal Systems
PartV Applications to Inviscid andViscous Flows
11 Numerical Simulation of Inviscid Flows
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
12 Numerical Solutions of Viscous Laminar Flows
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
