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An Improved Petrov-Galerkin Spectral Collocation Solution for Linear Stability of Circular Jet

Xie Ming-Liang1,2, Zhou Huai-Chun1, Chan Tat-Leung3
The State Key Laboratory of Coal Combustion, Huazhong University of Science and Technology, Wuhan, 430074, China
Corresponding author. Tel.: (86) 8754 2417 8301; Email: mlxie@mail.hust.edu.cn
Department of Mechanical Engineering, Research Centre for Combustion and Pollution Control, The Hong Kong Polytechnic University, Kowloon, Hong Kong

Computer Modeling in Engineering & Sciences 2009, 46(3), 271-290. https://doi.org/10.3970/cmes.2009.046.271

Abstract

A Fourier-Chebyshev Petrov-Galerkin spectral method is described for computation of temporal linear stability in a circular jet. Basis functions presented here are exponentially mapped Chebyshev functions. They satisfy the pole condition exactly at the origin, and can be used to expand vector functions efficiently by using the solenoidal condition. The mathematical formulation is presented in detail focusing on the analyticity of solenoidal vector field used for the approximation of the flow. The scheme provides spectral accuracy in the present cases studied and the numerical results are in agreement with former works.

Keywords

hydrodynamic stability, circular jet, cylindrical system singularity, coordinate transformation, spectral-Galerkin method, projection method.

Cite This Article

Ming-Liang, X., Huai-Chun, Z., Tat-Leung, C. (2009). An Improved Petrov-Galerkin Spectral Collocation Solution for Linear Stability of Circular Jet. CMES-Computer Modeling in Engineering & Sciences, 46(3), 271–290.



This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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