Abstract
A new approach to formulation of asymptotic boundary conditions for eigenvalue problems arising in numerical analysis of hydrodynamic stability of such shear flows as boundary layers, separations, jets, wakes, characterized by almost constant velocity of the main flow outside the shear layer or layers is proposed and justified. This approach makes it possible to formulate and solve completely the temporal and spatial stability problems in the locally-parallel approximation, reducing them to ordinary algebraic eigenvalue problems.
Acknowledgment
The authors are grateful to A. V. Glazunov for his interest in the work and useful remarks.
Funding This work was supported by the Russian Foundation for Basic Research, project No. 16-31-60092 (adaptation of the Newton-type method for solving non-linear problems, implementation and numerical experiments), and the Presidium of the Russian Academy of Sciences, Programme No. 01, ‘Fundamental Mathematics and its Applications’, project No. PRAS-18-01 (development and justification of asymptotic boundary conditions).
References
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