An efficient numerical solution for linear stability of circular jet: A combination of Petrov-Galerkin spectral method and exponential coordinate transformation based on Fornberg's treatment

This paper presents the linear stability analysis of a round jet in a radially unbounded domain using a spectral Petrov–Galerkin scheme coped with exponential coordinate transformation based on Fornberg's treatment. A Fourier–Chebyshev Petrov–Galerkin spectral method is described for the comput...

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Bibliographic Details
Published in:International journal for numerical methods in fluids 2009-11, Vol.61 (7), p.780-795
Main Authors: Xie, M. L., Lin, J. Z.
Format: Article
Language:English
Subjects:
circular jet
Computational methods in fluid dynamics
coordinate transformation
Coordinate transformations
cylindrical system singularity
Exact sciences and technology
Fluid dynamics
Focusing
Fundamental areas of phenomenology (including applications)
hydrodynamic stability
Jets
Mathematical analysis
Mathematical models
Physics
projection method
Spectral methods
spectral Petrov-Galerkin scheme
Stability
Stability analysis
Turbulent flows, convection, and heat transfer
Vectors (mathematics)
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Summary:This paper presents the linear stability analysis of a round jet in a radially unbounded domain using a spectral Petrov–Galerkin scheme coped with exponential coordinate transformation based on Fornberg's treatment. A Fourier–Chebyshev Petrov–Galerkin spectral method is described for the computation of the linear stability equations based on half a Gauss–Lobatto mesh. Complex basis functions presented here are exponentially mapped as Chebyshev functions, which 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 solenoidal vector field used for the approximation of the flow. The scheme provides spectral accuracy in the present cases and the numerical results are in agreement with former works. Copyright © 2008 John Wiley & Sons, Ltd.
ISSN:0271-2091
1097-0363
1097-0363
DOI:10.1002/fld.1975