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JOURNALS // Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki // Archive

Zh. Vychisl. Mat. Mat. Fiz., 2024 Volume 64, Number 8, Pages 1476–1485 (Mi zvmmf11815)

Partial Differential Equations

Structured pseudospectra in problems of spatial stability of boundary layers

K. V. Demyankoab, G. V. Zaskoab, Yu. M. Nechepurenkoab

a Marchuk Institute of Numerical Mathematics, Russian Academy of Sciences, 119333, Moscow, Russia
b Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, 125047, Moscow, Russia

Abstract: This work is devoted to a numerical analysis of the sensitivity of the spatial stability characteristics of boundary layers to uncertainties of the main flow. It is proposed to use structured pseudospectra for this purpose. It is shown that the obtained estimates are much more accurate than estimates based on an unstructured pseudospectrum. The presentation is based on an example of the flow of a viscous incompressible fluid over a slightly concave surface with flow parameters favorable for the development of the Görtler vortices and Tollmien–Schlichting waves.

Key words: structured pseudospectra, resolvent, spatial stability, boundary layer, Görtler vortices, Tollmien–Schlichting waves.

UDC: 519.633

Received: 23.02.2024
Revised: 23.02.2024
Accepted: 02.05.2024

DOI: 10.31857/S0044466924080125


 English version:
Computational Mathematics and Mathematical Physics, 2024, 64:8, 1785–1795

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© Steklov Math. Inst. of RAS, 2025