# Spectral methods for fluid flow

Basu, AJ (1994) Spectral methods for fluid flow. In: CFD: Advances and Applications, 1994, India.

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## Abstract

Spectral schemes are part of the Methods of Weighted Residuals (MWR), of which even the finite-difference method forms a part. The two key elements of MWR are the trial and the test functions. The trial functions are the basis for the truncated series expansion of the solution. These are infinitely differentiable global functions. The choice of trial functions differentiate spectral methods from finite-difference or finite-element methods (in the finite-difference method, for example, trial functions are local in character). The test functions are used to ensure that the differential equation is satisfied as closely as possible by the truncated series expansion. This is achieved by minimizing the residual (error between truncated series expansion solution and the exact solution). Typical basis functions used in spectral method are the Fourier, the Chebychev and the Legendre series. Of these, Fourier series can only be used in periodic geometries. Most spectral schemes use either Fourier or Chebychev basis functions because of the availability of fast transforms for these two. The choice of test functions differentiates between the three most commonly used spectral schemes, namely, the Galerkin, the Collocation and the Tau methods

Item Type: Conference or Workshop Item (Paper) Computational fluid dynamics;Finite dieference theory;Fluid flow;Fourier series;Galerkin method;Legendre functions; Spectral methods;Collocation;Finite element method;Poisson equation;Series expansion;Transformations(mathematics) ENGINEERING > Fluid Mechanics and Thermodynamics Mrs Manoranjitha M D 19 Oct 2006 24 May 2010 04:22 http://nal-ir.nal.res.in/id/eprint/3143