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
Foreward
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
This book aims at covering the foundations of high accuracy computing methods within the framework of Computational Fluid Dynamics (CFD) in an era of rapidly developing and evolving hardware and software.
From the hardware point of view, huge parallel machines with tens of thousands cores are installed at national facilities and research laboratories giving the practioners of scientific computing tools that they could not have dreamt of a decade ago. The advent of Graphical Processing Units (GPUs) also modifies the course of CFD as everyone tries to strain the computational tools to their last bits and extracts the highest speed-up. This is not surprising as one of the unsolved problems in classical physics is the understanding and control of turbulence in nature and technological applications.
From the software viewpoint, the advent of commercial packages including mesh generators, solvers and graphics tools, provide the numericists with appealing users interfaces and deliver numerical results for extremely different and various problems involving complicated geometries, peculiar boundary conditions and complex physics to be captured. This has had a major impact on the CFD community.
A question that is often raised consists in asking “Why should we not use the simplest schemes and run them on millions (billions) of processors?” The problem as we will discover rapidly is that simple schemes are very often too naive and lead to numerical disaster. We cannot assume that our intellectual indolence will be compensated by the computer’s power. At the end of the day, a bad method will produce inconsistent and poor results.
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- Chapter
- Information
- High Accuracy Computing MethodsFluid Flows and Wave Phenomena, pp. xiii - xviPublisher: Cambridge University PressPrint publication year: 2013