Chebyshev polynomial method in solving the stability Orr-Sommerfeld equation of pipe flow. (Chinese. English summary) Zbl 0953.76557
Summary: The Orr-Sommerfeld equation is solved numerically for pipe Poiseuille flow by using the Chebyshev polynomial method. All the eigenvalues are proved to be negative, and it is shown that the circular Poiseuille flow is stable with axisymmetric infinitesimal disturbances. The numerical results are of high accuracy.
MSC:
| 76M25 | Other numerical methods (fluid mechanics) (MSC2010) |
| 76E05 | Parallel shear flows in hydrodynamic stability |
