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Numerical model for the investigation of hydrodynamic stability of shear flows in pipes of elliptic cross-section

  • Kirill V. Demyanko EMAIL logo
Published/Copyright: December 26, 2019

Abstract

A numerical model for the investigation of hydrodynamic stability of viscous incompressible shear flows in pipes of constant elliptic cross-section is proposed. The model is supplied with efficient algorithms for computing various hydrodynamic stability characteristics including the maximum possible amplification of the average kinetic energy density of disturbances and the so-called optimal disturbances. An efficient spectral reduction is also implemented, which allows one to eliminate spurious disturbances due to spatial approximation errors. The results of computing the maximum possible amplification of the average kinetic energy density of disturbances for pipes with different cross-sectional aspect ratios are presented.

MSC 2010: 76E05

Acknowledgments

The author is grateful to Prof. A. V. Boiko (ITAM SB RAS) and Prof. Yu. M. Nechepurenko (INM RAS) for discussion of the results of the paper and valuable advice, and also to A. V. Glazunov (INM RAS) and P. A. Perezhogin (INM RAS) for interest to the work and useful remarks.

  1. Funding: The work was supported by the Russian Science Foundation, project No. 17-71-20149 (development and implementation of the numerical model, numerical experiments) and by the world-class research center ‘Moscow Center for Fundamental and Applied Mathematics’ (adaptation and adjustment of known algorithms for computing the optimal disturbances and the norm of matrix exponential for the proposed model).

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Received: 2019-06-17
Accepted: 2019-10-22
Published Online: 2019-12-26
Published in Print: 2019-12-18

© 2018 Walter de Gruyter GmbH, Berlin/Boston

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