Book contents
- Frontmatter
- Contents
- Foreward
- Preface
- Chapter 1 Basic Ideas of Scientific Computing
- Chapter 2 Governing Equations in Fluid Mechanics
- Chapter 3 Classification of Quasi-Linear Partial Differential Equations
- Chapter 4 Waves and Space–Time Dependence in Computing
- Chapter 5 Spatial and Temporal Discretizations of Partial Differential Equations
- Chapter 6 Solution Methods for Parabolic Partial Differential Equations
- Chapter 7 Solution Methods for Elliptic Partial Differential Equations
- Chapter 8 Solution of Hyperbolic PDEs: Signal and Error Propagation
- Chapter 9 Curvilinear Coordinate and Grid Generation
- Chapter 10 Spectral Analysis of Numerical Schemes and Aliasing Error
- Chapter 11 Higher Accuracy Methods
- Chapter 12 Introduction to Finite Volume and Finite Element Methods
- Chapter 13 Solution of Navier–Stokes Equation
- Chapter 14 Recent Developments in Discrete Finite Difference Computing
- Exercises
- References
- Index
Preface
Published online by Cambridge University Press: 05 January 2014
- Frontmatter
- Contents
- Foreward
- Preface
- Chapter 1 Basic Ideas of Scientific Computing
- Chapter 2 Governing Equations in Fluid Mechanics
- Chapter 3 Classification of Quasi-Linear Partial Differential Equations
- Chapter 4 Waves and Space–Time Dependence in Computing
- Chapter 5 Spatial and Temporal Discretizations of Partial Differential Equations
- Chapter 6 Solution Methods for Parabolic Partial Differential Equations
- Chapter 7 Solution Methods for Elliptic Partial Differential Equations
- Chapter 8 Solution of Hyperbolic PDEs: Signal and Error Propagation
- Chapter 9 Curvilinear Coordinate and Grid Generation
- Chapter 10 Spectral Analysis of Numerical Schemes and Aliasing Error
- Chapter 11 Higher Accuracy Methods
- Chapter 12 Introduction to Finite Volume and Finite Element Methods
- Chapter 13 Solution of Navier–Stokes Equation
- Chapter 14 Recent Developments in Discrete Finite Difference Computing
- Exercises
- References
- Index
Summary
Scientific theories by design, are always vulnerable to destruction just like a species, subjected to environmental pressure and is subjected to extinction … Even when scientific theories fail to survive … their evolutionary progeny carry the best “genes”— the ideas that still work — of the previous theory intact.
— Hans PagelThere are many new developments in scientific computing, in its application to fluid flows and wave phenomena, which warrant their consolidation in a single source, covering some of the key developments. I have been convinced by many students and peers that there is a definitive need for a single source book which deals with topics covered here. I would like to acknowledge their inspiration. My main motivation in writing this manuscript is to communicate something new and powerful as opposed to conventional derivatives of products churned out by existing schools of thought.
However, this book also provides general introduction to computational fluid dynamics (CFD), using well tested classical methods of solving partial differential equations (PDEs) for the sake of completeness. These are to be found in Chaps. 1 to 9 and 13, but re-interpreted using the spectral analysis method introduced in Chaps. 4, 8 and 10. This provides an unity of approach in understanding numerical methods for parabolic, elliptic and hyperbolic PDEs. The spectral analysis tool has been refined in recent years by the author's group, with which disparate methods can be easily compared.
- Type
- Chapter
- Information
- High Accuracy Computing MethodsFluid Flows and Wave Phenomena, pp. xvii - xixPublisher: Cambridge University PressPrint publication year: 2013