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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2007, Volume 47, Number 10, Pages 1672–1691
(Mi zvmmf229)
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This article is cited in 20 scientific papers (total in 20 papers)
Numerical analysis of the spectrum of the Orr–Sommerfeld problem
S. L. Skorokhodov Dorodnicyn Computing Center, Russian Academy of Sciences,
ul. Vavilova 40, Moscow, 119991, Russia
Abstract:
A high-accuracy method for computing the eigenvalues $\lambda_n$ and the eigenfunctions of the Orr–Sommerfeld operator is developed. The solution is represented as a combination of power series expansions, and the latter are then matched. The convergence rate of the expansions is analyzed by applying the theory of recurrence equations. For the Couette and Poiseuille flows in a channel, the behavior of the spectrum as the Reynolds number $\mathrm R$ increases is studied in detail. For the Couette flow, it is shown that the eigenvalues $\lambda_n$ regarded as functions of $\mathrm R$ have a countable set of branch points $\mathrm R_k>0$ at which the eigenvalues have a multiplicity of 2. The first ten of these points are presented within ten decimals.
Key words:
Orr–Sommerfeld equation, numerical analysis of the spectrum of the Orr–Sommerfeld equation, Couette flow,
Poiseuille flow, Couette–Poiseuille flow, convergence rate analysis.
Received: 29.03.2007
Citation:
S. L. Skorokhodov, “Numerical analysis of the spectrum of the Orr–Sommerfeld problem”, Zh. Vychisl. Mat. Mat. Fiz., 47:10 (2007), 1672–1691; Comput. Math. Math. Phys., 47:10 (2007), 1603–1621
Linking options:
https://www.mathnet.ru/eng/zvmmf229 https://www.mathnet.ru/eng/zvmmf/v47/i10/p1672
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Abstract page: | 636 | Full-text PDF : | 289 | References: | 70 | First page: | 4 |
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