- PII
- 10.31857/S2686954324050043-1
- DOI
- 10.31857/S2686954324050043
- Publication type
- Article
- Status
- Published
- Authors
- Volume/ Edition
- Volume 519 / Issue number 1
- Pages
- 18-21
- Abstract
- The problem of generating the Tollmien-Schlichting waves (leading eigenmodes) and optimal disturbances with a given accuracy using optimal blowing–suction is considered with the example of Poiseuille flow in a duct of square cross-section and streamwise-harmonic blowing-suction through the duct walls. The problem is reduced to solving optimal control problems for the linearized governing equations of viscous incompressible media. It is shown for the first time that generating the optimal disturbances using blowing–suction is much more expensive than generating the leading modes.
- Keywords
- линейная система управления течение в канале вдув–отсос ведущая мода оптимальное возмущение матричная экспонента выпуклое программирование
- Date of publication
- 15.04.2024
- Year of publication
- 2024
- Number of purchasers
- 0
- Views
- 42
References
- 1. Boiko A. V., Dovgal A. V., Grek G. R., Kozlov V. V. Physics of transitional shear flows. Springer, Berlin, 2012.
- 2. Canuto C., Hussaini M. Y., Quarteroni A., Zang T. A. Spectral methods. Fundamentals in single domains. Springer, Berlin, 2006.
- 3. Demyanko K. V., Nechepurenko Yu. M. Linear stability analysis of Poiseuille flow in a rectangular duct. Russ. J. Numer. Anal. Math. Modelling. 2013. V. 28. № 2. P. 125–148.
- 4. Nechepurenko Yu. M. On the dimension reduction of linear differential-algebraic control systems // Doklady Mathematics. 2012. V. 86. P. 457–459.
- 5. Tatsumi T., Yoshimura T. Stability of the laminar flow in a rectangular duct // J. Fluid Mech. 1990. V. 212. P. 437–449.
- 6. Boiko A. V., Nechepurenko Yu. M. Numerical spectral analysis of temporal stability of laminar duct flows with constant cross sections // J. Comput. Math. Math. Phys. 2008. V. 48. № 10. P. 1–17.
- 7. Boiko A. V., Nechepurenko Yu. M. Numerical study of stability and transient phenomena of Poiseuille flows in ducts of square cross-sections // Russ. J. Numer. Anal. Math. Modelling. 2009. V. 24. № 3. P. 193–205.
- 8. Golub G. H., Van Loan C. F. Matrix computations. Johns Hopkins University Press, Baltimore, MD, thirded., 1996 (Голуб Дж., Ван Лоун Ч. Матричные вычисления. М.: Мир, 1999).
- 9. Nechepurenko Yu. M., Sadkan M. A low-rank approximation for computing the matrix exponential norm. SIAM J. Matr. Anal. Appl. 2011. V. 32. № 2. P. 349–363.
