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Spectral Methods in Fluid Dynamics

Spectral Methods in Fluid Dynamics In certain areas of computational fluid dynamics, spectral methods have become the prevailing numerical tool for large-scale calculations. This is certainly the case for such three-dimensional applications as direct simulation of homogeneous turbulence, computation of transition in shear flows, and global weather modeling. For many other applications, such as heat transfer, boundary layers, reacting flows, compressible flows, and magnetohydrodynamics, spectral methods have proven to be a viable alternative to the traditional finite-difference and finite-element techniques. Spectral methods are characterized by the expansion of the solution in terms of global and, usually, orthogonal polynomials. Since the mid­ nineteenth century this has been a standard analytical tool for linear, separable differential equations. Nonlinearities present considerable alge­ braic difficulties, even on a modern computer. These difficulties were surmounted effectively in the early 1970s, and only then did spectral methods become competitive with alternative algorithms. By the present time, however, spectral methods have been refined and extended to the I The US Government has the right to retain a nonexclusive royalty-free license in and to any copyright concerning this paper. HUSSAINI & ZANG point where many problems in fluid mechanics are only tractable by these techniques. Numerical spectral methods for partial differential http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Annual Review of Fluid Mechanics Annual Reviews

Spectral Methods in Fluid Dynamics

Hussaini, M Y; Zang, T A
Annual Review of Fluid Mechanics , Volume 19 (1) – Jan 1, 1987
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Publisher
Annual Reviews
Copyright
Copyright 1987 Annual Reviews. All rights reserved
Subject
Review Articles
ISSN
0066-4189
eISSN
1545-4479
DOI
10.1146/annurev.fl.19.010187.002011
Publisher site
See Article on Publisher Site

Abstract

In certain areas of computational fluid dynamics, spectral methods have become the prevailing numerical tool for large-scale calculations. This is certainly the case for such three-dimensional applications as direct simulation of homogeneous turbulence, computation of transition in shear flows, and global weather modeling. For many other applications, such as heat transfer, boundary layers, reacting flows, compressible flows, and magnetohydrodynamics, spectral methods have proven to be a viable alternative to the traditional finite-difference and finite-element techniques. Spectral methods are characterized by the expansion of the solution in terms of global and, usually, orthogonal polynomials. Since the mid­ nineteenth century this has been a standard analytical tool for linear, separable differential equations. Nonlinearities present considerable alge­ braic difficulties, even on a modern computer. These difficulties were surmounted effectively in the early 1970s, and only then did spectral methods become competitive with alternative algorithms. By the present time, however, spectral methods have been refined and extended to the I The US Government has the right to retain a nonexclusive royalty-free license in and to any copyright concerning this paper. HUSSAINI & ZANG point where many problems in fluid mechanics are only tractable by these techniques. Numerical spectral methods for partial differential

Journal

Annual Review of Fluid Mechanics – Annual Reviews

Published: Jan 1, 1987

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