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Employing The Spectral Collocation Method In The Modeling Of Laminar Tube Flow Dynamics, Corey Michael Thibeault

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The spectral collocation method is a numerical approximation technique that seeks the solution of a differential equation using a finite series of infinitely differentiable basis functions. This inherently global technique enjoys an exponential rate of convergence and has proven to be extremely effective in computational fluid dynamics. This paper presents a basic review of the spectral collocation method. The derivation is driven with an example of the approximation to the solution of a 1D Helmholtz equation. A Matlab code modeling two fluid dynamics problems is then given. First, the classic two-dimensional Graetz problem is simulated and compared to an analytical …