Chebyshev tau-QZ algorithm methods for calculating spectra of hydrodynamic stability problems. (English) Zbl 0867.76025

Orr-Sommerfeld type differential equations governing the hydrodynamic stability of shear and related flows (applications in weather studies, aeroplane wing dynamics, electrohydrodynamics) are considered. The authors study the implementation of a Chebyshev tau-QZ algorithm for finding all the eigenvalues and eigenfunctions in these equations, for the treatment of multilayer flows, for the removing of spurious eigenvalues, and for finding the eigenvalues at high Reynolds numbers. Three versions of the Chebyshev tau method referred to as \(D^4\) (\(D^4\) is the fourth derivative operator), \(D^2\), and \(D\) methods, are discussed and compared (the underlying physical problems include Poiseuille flow, Couette flow, and pressure gradient circular pipe flow). The Orr-Sommerfeld like flows for two immiscible fluids are also dealt with, and some spectra of the flows are shown.
Reviewer: V.Burjan (Praha)


76E05 Parallel shear flows in hydrodynamic stability
65L15 Numerical solution of eigenvalue problems involving ordinary differential equations


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