https://doi.org/10.1140/epjp/s13360-024-04886-w
Tutorial
An alternative numerical solution for the Orr–Sommerfeld problem
Department of Industrial Engineering, Alma Mater Studiorum Università di Bologna, Viale Risorgimento 2, 40136, Bologna, Italy
Received:
15
December
2023
Accepted:
7
January
2024
Published online:
31
January
2024
A simple tutorial for the numerical solution of the Orr–Sommerfeld problem is presented. The aim is the determination of the neutral stability threshold to the linear instability for the Poiseuille flow within a plane parallel channel. Such an instability is hydrodynamic in nature as it is driven by the advection term in the local momentum balance equation. The numerical solution is achieved by a spectral method. The basis functions are chosen as Chebyshev polynomials multiplied by a suitable overall factor meant to allow the fulfilment of the boundary conditions. The details of the numerical code implemented via the Mathematica software environment are also provided. A comparison with other numerical solutions of the same problem implemented via the tau-method is presented.
Antonio Barletta, Pedro Vayssière Brandão and Michele Celli have contributed equally to this work.
© The Author(s) 2024
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