A Spectral Method with Staggered Grid for Incompressible Navier-stokes Equations
Author: F. Montigny-Rannou
Publisher:
Published: 1987
Total Pages: 15
ISBN-13:
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Author: F. Montigny-Rannou
Publisher:
Published: 1987
Total Pages: 15
ISBN-13:
DOWNLOAD EBOOKAuthor: Institute for Computer Applications in Science and Engineering
Publisher:
Published: 1985
Total Pages: 32
ISBN-13:
DOWNLOAD EBOOKAuthor: M. R. Malik
Publisher:
Published: 1984
Total Pages: 56
ISBN-13:
DOWNLOAD EBOOKAuthor: Claudio Canuto
Publisher: Springer Science & Business Media
Published: 2007-06-30
Total Pages: 616
ISBN-13: 3540307281
DOWNLOAD EBOOKFollowing up the seminal Spectral Methods in Fluid Dynamics, Spectral Methods: Evolution to Complex Geometries and Applications to Fluid Dynamics contains an extensive survey of the essential algorithmic and theoretical aspects of spectral methods for complex geometries. These types of spectral methods were only just emerging at the time the earlier book was published. The discussion of spectral algorithms for linear and nonlinear fluid dynamics stability analyses is greatly expanded. The chapter on spectral algorithms for incompressible flow focuses on algorithms that have proven most useful in practice, has much greater coverage of algorithms for two or more non-periodic directions, and shows how to treat outflow boundaries. Material on spectral methods for compressible flow emphasizes boundary conditions for hyperbolic systems, algorithms for simulation of homogeneous turbulence, and improved methods for shock fitting. This book is a companion to Spectral Methods: Fundamentals in Single Domains.
Author: Bhekumuzi J. Gwamanda
Publisher:
Published: 2004
Total Pages: 130
ISBN-13:
DOWNLOAD EBOOK"We examine the history and performance of the sequential spectral method. We find that the sequential spectral method is related to Waveform Relaxation methods and to iterative schemes that precede its inception by a century." --
Author: Roger Peyret
Publisher: Springer Science & Business Media
Published: 2013-03-09
Total Pages: 438
ISBN-13: 1475765576
DOWNLOAD EBOOKThis 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. With many examples throughout, the work will be useful to those teaching at the graduate level, as well as to researchers working in the area.
Author: Claudio Canuto
Publisher: Springer Science & Business Media
Published: 2007-09-23
Total Pages: 585
ISBN-13: 3540307265
DOWNLOAD EBOOKSince the publication of "Spectral Methods in Fluid Dynamics" 1988, spectral methods have become firmly established as a mainstream tool for scientific and engineering computation. The authors of that book have incorporated into this new edition the many improvements in the algorithms and the theory of spectral methods that have been made since then. This latest book retains the tight integration between the theoretical and practical aspects of spectral methods, and the chapters are enhanced with material on the Galerkin with numerical integration version of spectral methods. The discussion of direct and iterative solution methods is also greatly expanded.
Author: Ben-yu Guo
Publisher: World Scientific
Published: 1998-05-05
Total Pages: 359
ISBN-13: 9814496642
DOWNLOAD EBOOKThis book presents the basic algorithms, the main theoretical results, and some applications of spectral methods. Particular attention is paid to the applications of spectral methods to nonlinear problems arising in fluid dynamics, quantum mechanics, weather prediction, heat conduction and other fields.The book consists of three parts. The first part deals with orthogonal approximations in Sobolev spaces and the stability and convergence of approximations for nonlinear problems, as the mathematical foundation of spectral methods. In the second part, various spectral methods are described, with some applications. It includes Fourier spectral method, Legendre spectral method, Chebyshev spectral method, spectral penalty method, spectral vanishing viscosity method, spectral approximation of isolated solutions, multi-dimensional spectral method, spectral method for high-order equations, spectral-domain decomposition method and spectral multigrid method. The third part is devoted to some recent developments of spectral methods, such as mixed spectral methods, combined spectral methods and spectral methods on the surface.
Author: Claudio Canuto
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 582
ISBN-13: 3642841082
DOWNLOAD EBOOKThis 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 applications, the analytical techniques which have been developed in recent years have facilitated the examination of an increasing number of problems of practical interest. In this book we present a unified theory of the mathematical analysis of spectral methods and apply it to many of the algorithms in current use.
Author: Daniele Funaro
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 222
ISBN-13: 364259185X
DOWNLOAD EBOOKIn the last few years there has been a growing interest in the development of numerical techniques appropriate for the approximation of differential model problems presenting multiscale solutions. This is the case, for instance, with functions displaying a smooth behavior, except in certain regions where sudden and sharp variations are localized. Typical examples are internal or boundary layers. When the number of degrees of freedom in the discretization process is not sufficient to ensure a fine resolution of the layers, some stabilization procedures are needed to avoid unpleasant oscillatory effects, without adding too much artificial viscosity to the scheme. In the field of finite elements, the streamline diffusion method, the Galerkin least-squares method, the bub ble function approach, and other recent similar techniques provide excellent treatments of transport equations of elliptic type with small diffusive terms, referred to in fluid dynamics as advection-diffusion (or convection-diffusion) equations. Goals This book is an attempt to guide the reader in the construction of a computa tional code based on the spectral collocation method, using algebraic polyno mials. The main topic is the approximation of elliptic type boundary-value par tial differential equations in 2-D, with special attention to transport-diffusion equations, where the second-order diffusive terms are strongly dominated by the first-order advective terms. Applications will be considered especially in the case where nonlinear systems of partial differential equations can be re duced to a sequence of transport-diffusion equations.