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Numerical methods for eigensystems: the Orr–Sommerfeld problem

✍ Scribed by John M. Gerstring Jr.

Publisher
Elsevier Science
Year
1977
Tongue
English
Weight
484 KB
Volume
3
Category
Article
ISSN
0898-1221

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✦ Synopsis

A test problem which may be set up as an initial value, boundary value or eigenvalue problem with adjustable stiffness is presented. It is used to compare five methods (RKI, ORTNRM, SUPORT, GEAR and finite difference) of analysing stiff eigensystems in order to select methods powerful enough to be used effectively on the Orr-Sommerfeld equation. Results are then obtained for plane Poiseuille flow employing the methods found acceptable using the test problem. The plane Poiseuille Row results are then used to further evaluate the methods. Finite difference remains the best algebraic method tested with SUPORT being the best differential method and the least problem dependent.

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We study the inverse problem of recovering differential operators of the Orr -Sommerfeld type from the Weyl matrix. Properties of the Weyl matrix are investigated, and an uniqueness theorem for the solution of the inverse problem is proved.