Claudio Canuto, Thomas A. Zang, Alfio Quarteroni, M. Yousuff Hussaini

Spectral Methods in Fluid Dynamics

By Claudio Canuto, M. Y. Hussaini, Alfio Quarteroni et al.

• Broschiertes Buch

Produktbeschreibung

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. It provides the engineer with the tools and

guidance necessary to apply the methods successfully, and it

furnishes the mathematician with a comprehensive, rigorous

theory of 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

methods.

The book addresses graduate students and researchers in

fluid dynamics and applied mathematics as well as engineers

working on problems of practical importance.

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Dieses Buch führt in die moderne Theorie der Spektralmethoden und ihre Implementierung in die numerische Analysis der partiellen Differentialgleichungen der Hydromechanik (Turbulenz und Aerodynamik) ein. Das Buch richtet sich an fortgeschrittene Studenten, Ingenieure und angewandte Mathematiker.

Produktdetails

• Springer Series in Computational Physics
• Verlag: Springer / Springer Berlin Heidelberg / Springer, Berlin
• Artikelnr. des Verlages: 978-3-540-52205-8
• 1st ed. 1988. Corr. 2nd printing
• Seitenzahl: 584
• Erscheinungstermin: 15. März 1991
• Englisch
• Abmessung: 235mm x 155mm x 32mm
• Gewicht: 923g
• ISBN-13: 9783540522058
• ISBN-10: 3540522050
• Artikelnr.: 25648735

Inhaltsangabe

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.