%0 Journal Article %1 orszag1971accurate %A Orszag, S. A. %D 1971 %J Journal of Fluid Mechanics %K 65l60-odes-finite-elements-rayleigh-ritz-galerkin-and-collocation-methods 76e05-parallel-shear-flows usyd %P 689--703 %R 10.1017/S0022112071002842 %T Accurate Solution of the Orr--Sommerfeld Stability Equation %U https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/accurate-solution-of-the-orrsommerfeld-stability-equation/39D4D85F9939CC4E2F4A7EF127DFB046 %V 50 %X The Orr-Sommerfeld equation is solved numerically using expansions in Chebyshev polynomials 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 suited to the solution of hydrodynamic stability problems than expansions in other, seemingly more relevant, sets of orthogonal functions.

@article{orszag1971accurate, abstract = {The Orr-Sommerfeld equation is solved numerically using expansions in Chebyshev polynomials 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 suited to the solution of hydrodynamic stability problems than expansions in other, seemingly more relevant, sets of orthogonal functions.}, added-at = {2017-06-29T07:13:07.000+0200}, author = {Orszag, S. A.}, biburl = {https://www.bibsonomy.org/bibtex/2acdae0c4907318b2aea9790809ff9ad9/gdmcbain}, citeulike-article-id = {2442230}, citeulike-attachment-1 = {orszag_71_accurate.pdf; /pdf/user/gdmcbain/article/2442230/1095329/orszag_71_accurate.pdf; fb1b69ccb69e7bf59211a2aaac5604a7c3312a34}, citeulike-linkout-0 = {http://dx.doi.org/10.1017/S0022112071002842}, doi = {10.1017/S0022112071002842}, file = {orszag_71_accurate.pdf}, interhash = {ed16ed1ce0220a111e6bca25ad0b6594}, intrahash = {acdae0c4907318b2aea9790809ff9ad9}, journal = {Journal of Fluid Mechanics}, keywords = {65l60-odes-finite-elements-rayleigh-ritz-galerkin-and-collocation-methods 76e05-parallel-shear-flows usyd}, pages = {689--703}, posted-at = {2008-02-28 10:11:03}, priority = {2}, timestamp = {2021-11-25T01:57:26.000+0100}, title = {Accurate Solution of the {O}rr--{S}ommerfeld Stability Equation}, url = {https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/accurate-solution-of-the-orrsommerfeld-stability-equation/39D4D85F9939CC4E2F4A7EF127DFB046}, volume = 50, year = 1971 }