The results obtained by this method were more economical than the modified Chebyshev collocation if the comparison could be done in the same accuracy, the same collocation points to find the most unstable eigenvalue. | Calculation of the Orr-Sommerfeld stability equation for the plane Poiseuille flow 122 SCIENCE & TECHNOLOGY DEVELOPMENT JOURNAL: NATURAL SCIENCES, VOL 2, ISSUE 5, 2018 Calculation of the Orr-Sommerfeld stability equation for the plane Poiseuille flow Trinh Anh Ngoc, Tran Vuong Lap Dong Abstract—The stability of plane Poiseuille flow implement in the efficient approach by using depends on eigenvalues and solutions which are Chebyshev collocation method [6]. We obtained generated by solving Orr-Sommerfeld equation with results require considerably less computer time, input parameters including real wavenumber and computational expense and storage to achieve the Reynolds number . In the reseach of this paper, the same accuracy, about finding an eigenvalue which Orr-Sommerfeld equation for the plane Poiseuille had the largest imaginary part, than were required flow was solved numerically by improving the by the modified Chebyshev collocation method Chebyshev collocation method so that the solution of the Orr-Sommerfeld equation could be [3]. approximated even and odd polynomial by relying About the plane Poiseuille flow we wished to on results of proposition that is proved in detail study numerically the stream flow of an in section 2. The results obtained by this method incompressible viscous fluid through a chanel and were more economical than the modified Chebyshev driven by a pressure gradient in the - direction. collocation if the comparison could be done in the We used uints of the half-width of the channel and same accuracy, the same collocation points to find units of the undisturbed stream velocity at the the most unstable eigenvalue. Specifically, the centre of the channel to measure all lengths and present method needs 49 nodes and only takes to create eigenvalue velocities. In the Poiseuille case, the undisturbed while primary flow was only depended the modified Chebyshev collocation also .
