Spectral Methods in Fluid Dynamics by Claudio Canuto (English) Paperback Book

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Spectral Methods in Fluid Dynamics by Claudio Canuto, M.Yousuff Hussaini, Alfio Quarteroni, Thomas A., Jr. Zang

This textbook presents the modern unified theory of spectral methods and their implementation in the numerical analysis of partial differential equations occurring in fluid dynamical problems of transition, turbulence, and aerodynamics.

FORMAT
Paperback LANGUAGE
English CONDITION
Brand New Publisher Description

This text presents the modern unified theory of spectral methods and their implementation in the numerical analysis of partial differential equations occurring in fluid dynamical problems of transition, turbulence and aerodynamics. It provides the engineer with the tools and guidance necessary to apply the methods successfully, and it furnishes the mathematician with a theoretical background to the subject. All of the essential components of spectral algorithms currently employed for large-scale computations in fluid mechanics are described in detail. Some specific applications are linear stability, boundary layer calculations, direct simulations of transition and turbulence, and compressible Euler equations. The authors also present complete algorithms for Poisson's equation, linear hyperbolic systems, the advection diffusion equation, isotropic turbulence, and boundary layer transition. Some recent developments stressed in the book are iterative techniques (including the spectral multigrid method), spectral shock-fitting algorithms, and spectral multidomain book addresses graduate students and researchers in fluid dynamics and applied mathematics as well as engineers working on problems of practical importance. For this edition the authors have added a new section on the spectral domain decomposition method, and a supplementary bibliography on recent developments.

Notes

This textbook presents the modern unified theory of spectral methods and their implementation in the numerical analysis of partial differential equations occuring in fluid dynamical problems of transition, turbulence, and aerodynamics. The book addresses graduate students and researchers in fluid dynamics and applied mathematics as well as engineers working on problems of practical importance.

Table of Contents

1. Introduction.- 1.1. Historical Background.- 1.2. Some Examples of Spectral Methods.- 1.3. The Equations of Fluid Dynamics.- 1.4. Spectral Accuracy for a Two-Dimensional Fluid Calculation.- 1.5. Three-Dimensional Applications in Fluids.- 2. Spectral Approximation.- 2.1. The Fourier System.- 2.2. Orthogonal Polynomials in ( — 1, 1).- 2.3. Legendre Polynomials.- 2.4. Chebyshev Polynomials.- 2.5. Generalizations.- 3. Fundamentals of Spectral Methods for PDEs.- 3.1. Spectral Projection of the Burgers Equation.- 3.2. Convolution Sums.- 3.3. Boundary Conditions.- 3.4. Coordinate Singularities.- 3.5. Two-Dimensional Mapping.- 4. Temporal Discretization.- 4.1. Introduction.- 4.2. The Eigenvalues of Basic Spectral Operators.- 4.3. Some Standard Schemes.- 4.4. Special Purpose Schemes.- 4.5. Conservation Forms.- 4.6. Aliasing.- 5. Solution Techniques for Implicit Spectral Equations.- 5.1. Direct Methods.- 5.2. Fundamentals of Iterative Methods.- 5.3. Conventional Iterative Methods.- 5.4. Multidimensional Preconditioning.- 5.5. Spectral Multigrid Methods.- 5.6. A Semi-Implicit Method for the Navier—Stokes Equations.- 6. Simple Incompressible Flows.- 6.1. Burgers Equation.- 6.2. Shear Flow Past a Circle.- 6.3. Boundary-Layer Flows.- 6.4. Linear Stability.- 7. Some Algorithms for Unsteady Navier—Stokes Equations.- 7.1. Introduction.- 7.2. Homogeneous Flows.- 7.3. Inhomogeneous Flows.- 7.4. Flows with Multiple Inhomogeneous Directions.- 7.5. Mixed Spectral/Finite-Difference Methods.- 8. Compressible Flow.- 8.1. Introduction.- 8.2. Boundary Conditions for Hyperbolic Problems.- 8.3. Basic Results for Scalar Nonsmooth Problems.- 8.4. Homogeneous Turbulence.- 8.5. Shock-Capturing.- 8.6. Shock-Fitting.- 8.7. Reacting Flows.- 9. Global Approximation Results.- 9.1. FourierApproximation.- 9.2. Sturm—Liouville Expansions.- 9.3. Discrete Norms.- 9.4. Legendre Approximations.- 9.5. Chebyshev Approximations.- 9.6. Other Polynomial Approximations.- 9.7. Approximation Results in Several Dimensions.- 10. Theory of Stability and Convergence for Spectral Methods.- 10.1. The Three Examples Revisited.- 10.2. Towards a General Theory.- 10.3. General Formulation of Spectral Approximations to Linear Steady Problems.- 10.4. Galerkin, Collocation and Tau Methods.- 10.5. General Formulation of Spectral Approximations to Linear Evolution Equations.- 10.6. The Error Equation.- 11. Steady, Smooth Problems.- 11.1. The Poisson Equation.- 11.2. Advection-Diffusion Equation.- 11.3. Navier—Stokes Equations.- 11.4. The Eigenvalues of Some Spectral Operators.- 12. Transient, Smooth Problems.- 12.1. Linear Hyperbolic Equations.- 12.2. Heat Equation.- 12.3. Advection-Diffusion Equation.- 13. Domain Decomposition Methods.- 13.1. Introduction.- 13.2. Patching Methods.- 13.3. Variational Methods.- 13.4. The Alternating Schwarz Method.- 13.5. Mathematical Aspects of Domain Decomposition Methods.- 13.6. Some Stability and Convergence Results.- Appendices.- A. Basic Mathematical Concepts.- B. Fast Fourier Transforms.- C. Jacobi—Gauss—Lobatto Roots.- References.

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Long Description

This is a book about spectral methods for partial differential equations: when to use them, how to implement them, and what can be learned from their of spectral methods has evolved rigorous theory. The computational side vigorously since the early 1970s, especially in computationally intensive of the more spectacular applications are applications in fluid dynamics. Some of the power of these discussed here, first in general terms as examples of the methods have been methods and later in great detail after the specifics covered. This book pays special attention to those algorithmic details which are essential to successful implementation of spectral methods. The focus is on algorithms for fluid dynamical problems in transition, turbulence, and aero

Description for Sales People

This textbook presents the modern unified theory of spectral methods and their implementation in the numerical analysis of partial differential equations occuring in fluid dynamical problems of transition, turbulence, and aerodynamics. The book addresses graduate students and researchers in fluid dynamics and applied mathematics as well as engineers working on problems of practical importance.

Details ISBN3540522050 Publisher Springer-Verlag Berlin and Heidelberg GmbH & Co. KG ISBN-10 3540522050 ISBN-13 9783540522058 Format Paperback Imprint Springer-Verlag Berlin and Heidelberg GmbH & Co. K Place of Publication Berlin Country of Publication Germany Author Thomas A., Jr. Zang Edition 1st Language English Media Book Series Scientific Computation DEWEY 530 Short Title SPECTRAL METHODS IN FLUID D-3E Pages 568 DOI Audience Postgraduate, Research & Scholarly Edition Description 1st ed. 1988. Corr. 2nd printing Year 1991 Publication Date 1991-03-15 Alternative 9783540173717 Country of Origin US Product Class Description Physics Illustrations 6 Illustrations, black and white
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