Linear stability of Euler equations in cylindrical domain. (English) Zbl 1426.35182

Chleboun, J. (ed.) et al., Programs and algorithms of numerical mathematics 14. Proceedings of the seminar, Dolní Maxov, Czech Republic, June 1–6, 2008. Prague: Academy of Sciences of the Czech Republic, Institute of Mathematics. 53-58 (2008).
Summary: The linear stability problem of inviscid incompressible steady flow between two concentric cylinders is investigated. Linearizing the transient behavior around a steady state solution leads to an eigenvalue problem for linearized Euler equations. The discrete eigenvalue problem is obtained by the spectral element method. The algorithm is implemented in MATLAB. The developed program serves as a simple tool for numerical experimenting. It enables to state rough dependency of the stability on various input velocity profiles.
For the entire collection see [Zbl 1194.65013].


35Q31 Euler equations
76M22 Spectral methods applied to problems in fluid mechanics
76B99 Incompressible inviscid fluids
76E99 Hydrodynamic stability