Download or read book Spectral Methods for Compressible Flow Problems written by National Aeronautics and Space Administration (NASA) and published by Createspace Independent Publishing Platform. This book was released on 2018-08-06 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent results concerning numerical simulation of shock waves using spectral methods are reviewed. Shock fitting techniques were discussed as well as shock capturing techniques with finite difference artificial viscosity. Also the notion of the information contained in the numerical results obtained by spectral methods and show how this information is recovered was discussed. Gottlieb, D. Langley Research Center NASA-CR-172395, NAS 1.26:172395, ICASE-84-29 NAS1-17070; RTOP 505-31-83

Download or read book Spectral Methods in Compressible Flow Problems written by William D. Lakin and published by . This book was released on 1981 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Spectral Methods for Compressible Flow Problems written by David Gottlieb and published by . This book was released on 1984 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Spectral Methods written by Claudio Canuto and published by Springer Science & Business Media. This book was released on 2007-06-30 with total page 616 pages. Available in PDF, EPUB and Kindle. Book excerpt: Following 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.

Download or read book Spectral Methods for Uncertainty Quantification written by Olivier Le Maitre and published by Springer Science & Business Media. This book was released on 2010-03-11 with total page 542 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with the application of spectral methods to problems of uncertainty propagation and quanti?cation in model-based computations. It speci?cally focuses on computational and algorithmic features of these methods which are most useful in dealing with models based on partial differential equations, with special att- tion to models arising in simulations of ?uid ?ows. Implementations are illustrated through applications to elementary problems, as well as more elaborate examples selected from the authors’ interests in incompressible vortex-dominated ?ows and compressible ?ows at low Mach numbers. Spectral stochastic methods are probabilistic in nature, and are consequently rooted in the rich mathematical foundation associated with probability and measure spaces. Despite the authors’ fascination with this foundation, the discussion only - ludes to those theoretical aspects needed to set the stage for subsequent applications. The book is authored by practitioners, and is primarily intended for researchers or graduate students in computational mathematics, physics, or ?uid dynamics. The book assumes familiarity with elementary methods for the numerical solution of time-dependent, partial differential equations; prior experience with spectral me- ods is naturally helpful though not essential. Full appreciation of elaborate examples in computational ?uid dynamics (CFD) would require familiarity with key, and in some cases delicate, features of the associated numerical methods. Besides these shortcomings, our aim is to treat algorithmic and computational aspects of spectral stochastic methods with details suf?cient to address and reconstruct all but those highly elaborate examples.

Download or read book Spectral Methods in Fluid Dynamics written by Claudio Canuto and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 582 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 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.

Download or read book Iterative Spectral Methods and Spectral Solutions to Compressible Flows written by M. Yousuff Hussaini and published by . This book was released on 1982 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: "A spectral multi-grid scheme is described which can solve pseudospectral discretizations of self-adjoint elliptic problems in 0(N log N) operations. An iterative technique for efficiently implementing semi-implicit time-stepping for pseudospectral discretizations of Navier-Stokes equations is discussed. This approach can handle variable coefficient terms in an effective manner. Pseudospectral solutions of compressible flow problems are presented. These include one-dimensional problems and two-dimensional Euler solutions. Results are given both for shock-capturing approaches and for shock-fitting ones" -- abstract.

Download or read book Spectral Methods for Discontinuities written by Gottlieb and published by . This book was released on 1985 with total page 4 pages. Available in PDF, EPUB and Kindle. Book excerpt: The investigators pursued research on the use of spectral methods in computational fluid dynamics. The implementation is examined for the solution of time dependent partial differential equations. Other topics pursued included the adaptation of spectral methods for compressible flow problems involving shocks, and the exploration of information content in spectral calculations. Papers produced during this effort included such titles as Spectral methods for time dependent partial differential equations, recovering pointwise values of discontinuous data within spectral accuracy, and Information content in spectral calculations.

Download or read book Spectral Methods written by Claudio Canuto and published by Springer Science & Business Media. This book was released on 2007-09-23 with total page 585 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since 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.

Download or read book Spectral Methods for Time Dependent Partial Differential Equations written by David Gottlieb and published by . This book was released on 1986 with total page 7 pages. Available in PDF, EPUB and Kindle. Book excerpt: This document discusses briefly the following research topics: 1) Spectral methods for time dependent partial differential equations; 2) Spectral methods for compressible flow problems; 3) Recovering pointwise values of discontinuous data within spectral accuracy; 4) Information content in spectral calculations; 5) Spectral methods for discontinuous problems; 6) Stability and Lyapunov stability of dynamical systems: a differential approach and a numerical method; and 7) boundary conditions for incompressible flows.

Download or read book Spectral Methods for Inviscid Compressible Flows written by M. Y. Hussaini and published by . This book was released on 1983 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book A Spectral Collocation Solution to the Compressible Stability Eigenvalue Problem written by Michele G. Macaraeg and published by . This book was released on 1988 with total page 64 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Spectral Methods and Their Applications written by Benyu Guo and published by World Scientific. This book was released on 1998 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 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.

Download or read book Spectral Methods for the Euler Equations written by and published by . This book was released on 1984 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Spectral Methods And Their Applications written by Ben-yu Guo and published by World Scientific. This book was released on 1998-05-05 with total page 359 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 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.

Download or read book Spectral Methods for Compressible and Incompressible Fluid Flows written by Patrick Hanley and published by . This book was released on 1985 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Spectral Methods for Time Dependent Problems written by Jan S. Hesthaven and published by Cambridge University Press. This book was released on 2007-01-11 with total page 4 pages. Available in PDF, EPUB and Kindle. Book excerpt: Spectral methods are well-suited to solve problems modeled by time-dependent partial differential equations: they are fast, efficient and accurate and widely used by mathematicians and practitioners. This class-tested 2007 introduction, the first on the subject, is ideal for graduate courses, or self-study. The authors describe the basic theory of spectral methods, allowing the reader to understand the techniques through numerous examples as well as more rigorous developments. They provide a detailed treatment of methods based on Fourier expansions and orthogonal polynomials (including discussions of stability, boundary conditions, filtering, and the extension from the linear to the nonlinear situation). Computational solution techniques for integration in time are dealt with by Runge-Kutta type methods. Several chapters are devoted to material not previously covered in book form, including stability theory for polynomial methods, techniques for problems with discontinuous solutions, round-off errors and the formulation of spectral methods on general grids. These will be especially helpful for practitioners.