A Fourrier Petrov Galerkin spectral method is described for high accuracy computation of linearized dynamics for flow in a circular pipe. The code used here is based on solenoidal velocity variables. It is written in FORTRAN. Systematic studies are presented on the dependence of eigenvalues and other quantities on the axial and azimuthal wave number; the reynolds’ number Re and a new none-dimensional number Ne. The flow will be considered stable if all the real parts of the eigenvalues are negative and unstable if only one of them is positive.
References
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Kakeshita, T., et al. (1985) Composition Dependence of Magnetic Field-Induced Martensitic Transformations in Fe-Ni Alloys. Acta Metallurgica, 33, 1381-1389. https://doi.org/10.1016/0001-6160(85)90039-2
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Aogaki, R., Fueki, K. and Mukaibo, T. (1975) Application of Magnetohydrodynamic Effect to the Analysis of Electrochemical Reactions. 2. Diffusion Process in MHD Forced Flow of Electrolyte Solution. Denki Kagaku, 43, 509-514. https://doi.org/10.5796/kogyobutsurikagaku.43.509
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Torbet, J., Freyssinet, J.-M. and Hudry-Clergeon, G. (1981) Oriented Fibrin Gels Formed by Polymerization in Strong Magnetic Fields. Nature, 289, 91. https://doi.org/10.1038/289091a0
[5]
Meseguer, A. and Trefethen, L.N. (2003) Linearized Pipe Flow to Reynolds Number 107. Journal of Computational Physics, 186, 178-197. https://doi.org/10.1016/S0021-9991(03)00029-9
[6]
Zikanov, O.Yu. (1996) On the Instability of Pipe Poiseuille Flow. Physics of Fluids, 8, 2923. https://doi.org/10.1063/1.869071
[7]
Bergstrom, L. (1997) Optimal Growth of Small Disturbances in Pipe Poiseuille Flow. Physics of Fluids, 9, 1043.
[8]
Leonard, A. and Wray, A. (1982) A New Numerical Method for the Simulation of Three-Dimensional Flow in a Pipe. In: Krause, E., Ed., Proceedings of the 8th International Conference on Numerical Methods in Fluid Dynamics on Numerical Methods in Fluid Dynamics, Springer, Berlin, 335-342. https://doi.org/10.1007/3-540-11948-5_40
[9]
Schmid, P.J. and Henningson, D.S. (1994) Optimal Energy Grothin Hagen-Poiseuille Flow. Journal of Fluid Mechanics, 277, 197. https://doi.org/10.1017/S0022112094002739
[10]
Trefethen, A.E., Trefethen, L.N. and Schmid, P.J. (1999) Spectra and Pseudospectra for Pipe Poiseuille Flow. Computer Methods in Applied Mechanics and Engineering, 175, 413-420. https://doi.org/10.1016/S0045-7825(98)00364-8
[11]
Matsuzaki, A. and Nagakura, S. (1976) Magnetic Quenching of Fluorescence Observed with Carbon Disulfide and Glyoxal. Journal of Luminescence, 12-13, 787-791. https://doi.org/10.1016/0022-2313(76)90177-0
[12]
Kakeshita, T., et al. (1985) Composition Dependence of Magnetic Field-Induced Martensitic Transformations in Fe-Ni Alloys. Acta Metallurgica, 33, 1381-1389. https://doi.org/10.1016/0001-6160(85)90039-2
[13]
Aogaki, R., Fueki, K. and Mukaibo, T. (1975) Application of Magnetohydrodynamic Effect to the Analysis of Electrochemical Reactions. 2. Diffusion Process in MHD Forced Flow of Electrolyte Solution. Denki Kagaku, 43, 509-514. https://doi.org/10.5796/kogyobutsurikagaku.43.509
[14]
Torbet, J., Freyssinet, J.-M. and Hudry-Clergeon, G. (1981) Oriented Fibrin Gels Formed by Polymerization in Strong Magnetic Fields. Nature, 289, 91. https://doi.org/10.1038/289091a0
[15]
Meseguer, A. and Trefethen, L.N. (2003) Linearized Pipe Flow to Reynolds Number 107. Journal of Computational Physics, 186, 178-197. https://doi.org/10.1016/S0021-9991(03)00029-9
[16]
Zikanov, O.Yu. (1996) On the Instability of Pipe Poiseuille Flow. Physics of Fluids, 8, 2923. https://doi.org/10.1063/1.869071
[17]
Bergstrom, L. (1997) Optimal Growth of Small Disturbances in Pipe Poiseuille Flow. Physics of Fluids, 9, 1043.
[18]
Leonard, A. and Wray, A. (1982) A New Numerical Method for the Simulation of Three-Dimensional Flow in a Pipe. In: Krause, E., Ed., Proceedings of the 8th International Conference on Numerical Methods in Fluid Dynamics on Numerical Methods in Fluid Dynamics, Springer, Berlin, 335-342. https://doi.org/10.1007/3-540-11948-5_40
[19]
Schmid, P.J. and Henningson, D.S. (1994) Optimal Energy Grothin Hagen-Poiseuille Flow. Journal of Fluid Mechanics, 277, 197. https://doi.org/10.1017/S0022112094002739
[20]
Trefethen, A.E., Trefethen, L.N. and Schmid, P.J. (1999) Spectra and Pseudospectra for Pipe Poiseuille Flow. Computer Methods in Applied Mechanics and Engineering, 175, 413-420. https://doi.org/10.1016/S0045-7825(98)00364-8
