Spectral Methods for Incompressible Viscous Flow

Inbunden, Engelska, 2002

Av Roger Peyret

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This well-written book explains the theory of spectral methods and their application to the computation of viscous incompressible fluid flow in clear and elementary terms. It begins with an introduction to the fundamentals of spectral methods and then moves on to cover, in particular, the Fourier and Chebyshev methods. Examples are included. Chapters 6 and 7 handle streamfunction-vorticity and velocity-pressure formulations of the Navier-Stokes equations. Chapters 8 and 9 address special topics, such as self-adaptive coordinate transform, treatment of singularities, and domain decomposition. The work will be useful to those teaching in the field at the graduate level, as well as to researchers working in the area.

Produktinformation

Utgivningsdatum2002-03-28
Mått155 x 235 x 26 mm
Vikt757 g
FormatInbunden
SpråkEngelska
SerieApplied Mathematical Sciences
Antal sidor434
Upplaga2002
FörlagSpringer-Verlag New York Inc.
ISBN9780387952215

Tillhör följande kategorier

I Basic spectral methods.- 1 Fundamentals of spectral methods.- 2 Fourier Method.- 3 Chebyshev method.- 4 Time-dependent equations.- II. Navier-Stokes equations.- 5 Navier-Stokes equations for incompressible fluids.- 6 Vorticity-Streamfunction Equations.- 7 Velocity-Pressure Equations.- III Special topics.- 8 Stiff and singular problems.- 9 Domain Decomposition Method.- Appendix A Formulas on Chebyshev polynomials.- A.1 Definition and general properties.- A.2 Differentiation.- A.3 Collocation points.- A.4 Truncated series expansion.- A.5 Lagrange interpolation polynomial.- A.6 Derivatives at Gauss-Lobatto points.- A.7 Integration.- A.8 Numerical integration based on Gauss-Lobatto points.- Appendix B Solution of a quasi-tridiagonal system.- Appendix C Theorems on the zeros of a polynomial.- References.

From the reviews: "Spectral Methods for Incompressible Viscous Flow is a clear, thorough, and authoritative book ... . The author, throughout the book, frequently points out topics that are beyond the scope of this book and gives references to where such information is found. This makes the book an excellent resource for the entire field. ... this is an excellent book, which can serve both as a textbook for those who want to learn about spectral methods, as well as a reference for practitioners solving the Navier-Stokes equations." (Sigal Gottlieb and David Gottlieb, SIAM Review, Vol. 45 (2), 2003) "The importance of spectral methods in obtaining the solutions of boundary value problems in a variety of situations of physical and engineering interest is well-known. ... This book gives a good understanding of spectral methods which deal with the flows of incompressible viscous fluid governed by Navier-Stokes equations. ... On the whole, this book is an excellent text for graduate students or researchers interested in learning spectral methods and in their application to incompressible fluid flows, and is a good addition to any library." (Adabala Ramachandra Rao, Zentralblatt MATH, Vol. 1005, 2003) "The author sets out 'to provide a comprehensive discussion of Fourier and Chebyshev spectral methods for the computation of incompressible viscous flows, based on the Navier-Stokes equations.' He has succeeded admirably. The book ... provides a clear exposition of the associated computational techniques, and gives information on the implementation of these techniques. ... It will appeal to applied mathematicians and CFD-oriented engineers at the post-graduate level and to anyone teaching or undertaking research on problems described by the Navier-Stokes equations. This book is highly recommended." (G de Vahl Davis, Applied Mechanics Reviews, Vol. 56 (1), 2003)