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Numerical methods for Orr–Sommerfeld problems
Author(s) -
Gersting John M.,
Jankowski Daniel F.
Publication year - 1972
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620040206
Subject(s) - hagen–poiseuille equation , numerical analysis , algebraic number , class (philosophy) , numerical integration , mathematics , flow (mathematics) , differential (mechanical device) , computer science , plane (geometry) , finite difference method , calculus (dental) , mathematical optimization , mathematical analysis , geometry , aerospace engineering , engineering , artificial intelligence , medicine , dentistry
Five previously employed numerical methods for the solution of Orr–Sommerfeld problems have been compared to each other and to a new method, the differential method of near ‐orthonormalized integration. Brief summaries of each method are included. The comparison, based on seven factors, reflects the results of an implementation of a computer program for each method for the classic Orr–Sommerfeld problem of plane Poiseuille flow. This comparison shows that the new method and the algebraic finite difference method are currently the best available numerical solution methods for the problems in this class, with the new method being less problem dependent.