CFD lecture 10 - Computational Fluid Dynamics Lecture 10 In...

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Computational Fluid Dynamics Lecture 10 In general, spectral methods belong to a class of methods called Weighted Residual Methods (Chapter 5 in Fletcher), where a continuous function ()( ) ( 1 ,,, ,, N kk k ) xyzt a t xyz φφ = = is represented in a series of basis functions. When the basis functions () sin k x kx φ π = then the method is the spectral method. Another alternative is to use algebraic functions or polynomials 1 k k x = . The other, most common method is to use simple basis functions leading to the Finite Element Method. The chief disadvantage with the Finite Element Method is that it requires solution of a set of implicit equations, which can be expensive for 2 & 3 D flows. The large advantage is the ability to use variable grids that focus grid nodes where complex geometry exists. Suppose F is an operator involving spatial derivatives of ψ . 2 2 e.g. ..... C xx ψψ γ  ∂∂ −+   0 F t += is the PDE to be solved with specified B.C.’s and initial conditions.
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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 10 - Computational Fluid Dynamics Lecture 10 In...

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