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Titlebook: Spectral Methods for Incompressible Viscous Flow; Roger Peyret Textbook 2002 Springer Science+Business Media New York 2002 Navier-Stokes e

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书目名称Spectral Methods for Incompressible Viscous Flow
编辑Roger Peyret
视频video
概述Includes supplementary material:
丛书名称Applied Mathematical Sciences
图书封面Titlebook: Spectral Methods for Incompressible Viscous Flow;  Roger Peyret Textbook 2002 Springer Science+Business Media New York 2002 Navier-Stokes e
描述The objective of this book is to provide a comprehensive discussion of Fourier and Chebyshev spectral methods for the computation of incom­ pressible viscous flows, based on the Navier-Stokes equations. and confidence in the numerical results, the re­ For reasons of efficiency searchers and practitioners involved in computational fluid dynamics must be able to master the numerical methods they use. Therefore, in writing this book, beyond the description of the algorithms, I have also tried to provide information on the mathematical and computational, as well as implementational characteristics of the methods. The book contains three parts. The first is intended to present the fun­ damentals of the Fourier and Chebyshev methods for the solution of differ­ ential problems. The second part is entirely devoted to the solution of the N avier-Stokes equations, considered in vorticity-streamfunction and velocity-pressure formulations. The third part is concerned with the so­ lution of stiff and singular problems, and with the domain decomposition method. In writing this book, lowe a great debt to the joint contribution of several people to whom I wish to express my deep gratitude. First,
出版日期Textbook 2002
关键词Navier-Stokes equation; Numerical integration; Spectral methods; computational fluid dynamics; fluid dyn
版次1
doihttps://doi.org/10.1007/978-1-4757-6557-1
isbn_softcover978-1-4419-2913-6
isbn_ebook978-1-4757-6557-1Series ISSN 0066-5452 Series E-ISSN 2196-968X
issn_series 0066-5452
copyrightSpringer Science+Business Media New York 2002
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Introductiontion as a truncated series expansion, the unknowns being the expansion coefficients. The Fourier basis is appropriate for periodic problems. For nonperiodic problems, the Chebyshev or Legendre polynomial bases are commonly used, but other basis functions could be considered according to the problem
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Fundamentals of spectral methodson. By using the notion of residual, it will be shown how spectral approximation can be defined for the representation of a given function as well as for the solution of a differential problem. These questions will be addressed in detail in the following two chapters devoted, respectively, to Fourie
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Chebyshev methodt the boundaries. In the case of nonperiodic problems, it is advisable to have recourse to better-suited basis functions. Orthogonal polynomials, like Chebyshev polynomials, constitute a proper alternative to the Fourier basis. The Chebyshev series expansion may be seen as a cosine Fourier series, s
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Time-dependent equationsons, their analysis is developed in the linear case and, more especially, for the advection-diffusion equation. First, we address the stability of the spectral approximation, namely, the existence of a bounded solution of the differential equations in time resulting from the spectral approximation.
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Vorticity-Streamfunction Equationsnected domains. These advantages are well known: (1) the velocity field is automatically divergence-free, (2) the mathematical properties of the equations permit the construction of simple and robust solution methods, (3) computing time is saved because of the smaller number of equations. In the pre
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Velocity-Pressure Equationstion than the vorticity-streamfunction equations which are restricted to two-dimensional flows. First, the Fourier method for computing fully periodic flows is discussed. Then the major part of the chapter is devoted to the case of one or more nonperiodic directions. In such a situation, the classic
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