The Mathematical Institute, University of Oxford, Eprints Archive

A spectral Petrov-Galerkin formulation for pipe flow I: Linear stability and transient growth

Meseguer, A. and Trefethen, Lloyd N. (2000) A spectral Petrov-Galerkin formulation for pipe flow I: Linear stability and transient growth. Technical Report. Unspecified. (Submitted)

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Abstract

A spectral Petrov-Galerkin scheme for the numerical approximation of flow in a circular pipe is presented. The mathematical formulation is presented in detail focusing on the analyticity of solenoidal vector fields used for the approximation of the flow. A comprehensive study of linear stability is reported for axisymmetric, non-axisymmetric, streamwise dependent and streamwise independent perturbations . The scheme provides spectral accuracy in all cases studied and the numerical results are in agreement with former works. A parametric exploration of pseudospectra and transient growth has been carried out for the aforementioned cases.

This research was supported by UK Engineering and Physical Sciences Research Council Grant GR/M30890.

Item Type:Technical Report (Technical Report)
Subjects:H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:1255
Deposited By:Lotti Ekert
Deposited On:21 May 2011 17:06
Last Modified:21 May 2011 17:06

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