CFD lecture 9 - Computational Fluid Dynamics Lecture 9 Spectral Methods The most accurate method for calculating spatial derivatives is to use Fast

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Computational Fluid Dynamics Lecture 9 Spectral Methods The most accurate method for calculating spatial derivatives is to use Fast Fourier transforms. Instead of being () () () 26 or or n x x σ ∆∆∆ x , the spectral, semi-spectral or Galerkin methods converge to the exact solution faster than any algebraic value of n < ∞ . As x decreases, the rate of convergence is exponential. That does not mean however, that for some finite value of x that the spectral method will give a perfect solution. It also fails for the 2 x wave, as did the compact schemes. i.e. The disadvantages of the spectral method are: 1. Smaller time step required for stability. fl 1 C π < 2. Slower computationally in the limit of large numbers of grid points. Computational time, using FFT’s goes as ( ) log NN compared to finite difference schemes that go as . () N In practice today, this is not a significant limitation. 3. Complex Geometries or Boundary Conditions are not as accessible as other methods.
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This note was uploaded on 06/08/2011 for the course EOC 6850 taught by Professor Slinn during the Spring '07 term at University of Florida.

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CFD lecture 9 - Computational Fluid Dynamics Lecture 9 Spectral Methods The most accurate method for calculating spatial derivatives is to use Fast

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