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.

An alternative numerical solution for the Orr–Sommerfeld problem / Barletta A.; Brandão Pedro.; Celli M.. - In: THE EUROPEAN PHYSICAL JOURNAL PLUS. - ISSN 2190-5444. - ELETTRONICO. - 139:(2024), pp. 102.1-102.9. [10.1140/epjp/s13360-024-04886-w]

An alternative numerical solution for the Orr–Sommerfeld problem

Barletta A.
;
Brandão Pedro.;Celli M.
2024

Abstract

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.
2024
An alternative numerical solution for the Orr–Sommerfeld problem / Barletta A.; Brandão Pedro.; Celli M.. - In: THE EUROPEAN PHYSICAL JOURNAL PLUS. - ISSN 2190-5444. - ELETTRONICO. - 139:(2024), pp. 102.1-102.9. [10.1140/epjp/s13360-024-04886-w]
Barletta A.; Brandão Pedro.; Celli M.
File in questo prodotto:
File Dimensione Formato  
s13360-024-04886-w-1.pdf

accesso aperto

Tipo: Versione (PDF) editoriale
Licenza: Creative commons
Dimensione 1.59 MB
Formato Adobe PDF
1.59 MB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/958318
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 1
  • ???jsp.display-item.citation.isi??? 1
social impact