EIGENVALUES CALCULATION OF ORR-SOMMERFELD SPECTRAL PROBLEM
نویسندگان
چکیده
منابع مشابه
Eigenvalues of the Orr - Sommerfeld Equation
A very simple proof is presented of the fact that the Orr-Sommerfeld equation for flows that approach exponentially to a constant at infinity has at most finitely many eigenvalues. A completely elementary argument shows that the Orr-Sommerfeld equation for such flows has no eigenvalues when the product of the Reynolds number and the wave number is small enough.
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The most eeective and widely used methods for integrating the Orr-Sommerfeld equation by shooting are the continuous orthogonalization method and the compound matrix method. In this paper, we consider this problem from a diierential-geometric point of view. A new deenition of orthogonalization is presented: restriction of the Orr-Sommerfeld to a complex Stiefel manifold, and this deenition lead...
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Article history: Received 19 February 2008 Received in revised form 6 October 2008 Accepted 14 October 2008 Available online 1 November 2008 PACS: 65L15 65L60 76E05 76E17 76E25
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The Orr-Sommerfeld equation is solved numerically using expansions in Chebyshevpolynomials and the QR matrix eigenvalue algorithm. It is shown that results of great accuracy are obtained very economically. The method is applied to the stability of plane Poiseuille flow; it is found that the critical Reynolds number is 5772.22. It is explained why expansions in Chebyshev polynomials are better s...
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ژورنال
عنوان ژورنال: Современные наукоемкие технологии (Modern High Technologies)
سال: 2018
ISSN: 1812-7320
DOI: 10.17513/snt.37125