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Titlebook: Spectral Methods in Fluid Dynamics; Claudio Canuto,M. Yousuff Hussaini,Thomas A. Zang Textbook 1988 Springer-Verlag Berlin Heidelberg 1988

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书目名称Spectral Methods in Fluid Dynamics
编辑Claudio Canuto,M. Yousuff Hussaini,Thomas A. Zang
视频video
丛书名称Scientific Computation
图书封面Titlebook: Spectral Methods in Fluid Dynamics;  Claudio Canuto,M. Yousuff Hussaini,Thomas A. Zang Textbook 1988 Springer-Verlag Berlin Heidelberg 1988
描述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 dynamics. This book does not address specific applications in meteorology, partly because of the lack of experience of the authors in this field and partly because of the coverage provided by Haltiner and Williams (1980). The success of spectral methods in practical computations has led to an increasing interest in their theoretical aspects, especially since the mid-1970s. Although the theory does not yet cover the complete spectrum of
出版日期Textbook 1988
关键词Aerodynamics; Aerodynamik; Hydromechanik; Numerical Analysis; Numerische Analysis; Partial Differential E
版次1
doihttps://doi.org/10.1007/978-3-642-84108-8
isbn_softcover978-3-540-52205-8
isbn_ebook978-3-642-84108-8Series ISSN 1434-8322 Series E-ISSN 2198-2589
issn_series 1434-8322
copyrightSpringer-Verlag Berlin Heidelberg 1988
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Introduction,thod of weighted residuals (MWR) (Finlayson and Scriven (1966)). The key elements of the MWR are the trial functions (also called the expansion or approximating functions) and the test functions (also known as weight functions). The trial functions are used as the basis functions for a truncated ser
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Temporal Discretization, conventional finite-differences. The typical evolution equation can be written.where the (generally) non-linear operator . contains the spatial part of the PDE. (The dependence of . upon . will not be indicated explicitly hereafter except when it is essential.) Following the general formulation of
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Theory of Stability and Convergence for Spectral Methods,blems. Analysis of several non-linear problems is presented in Chaps. 11 and 12. For time-dependent problems, only the discretizations in space are considered. Stability for fully discretized time-dependent problems is discussed in Chap. 4 by a classical eigenvalue analysis, and in Chap. 12 by varia
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Introduction,on instead of the exact solution, with respect to a suitable norm. An equivalent requirement is that the residual satisfy a suitable orthogonality condition with respect to each of the test functions.
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