Computational Aspects of Pseudospectra in Hydrodynamic Stability Analysis

作者：Gerecht D^*; Rannacher R; Wollner W

来源：Journal of Mathematical Fluid Mechanics, 2012, 14(4): 661-692.

DOI：10.1007/s00021-011-0085-7

• Navier-Stokes equations
• Linearized stability
• Pseudospectrum
• Finite element method
• Arnoldi method
• Non-normal operators

This paper addresses the analysis of spectrum and pseudospectrum of the linearized Navier-Stokes operator from the numerical point of view. The pseudospectrum plays a crucial role in linear hydrodynamic stability theory and is closely related to the non-normality of the underlying differential operator and the matrices resulting from its discretization. This concept offers an explanation for experimentally observed instability in situations when eigenvalue-based linear stability analysis would predict stability. Hence the reliable numerical computation of the pseudospectrum is of practical importance particularly in situations when the stationary %26quot;base flow%26quot; is not analytically but only computationally given. The proposed algorithm is based on a finite element discretization of the continuous eigenvalue problem and uses an Arnoldi-type method involving a multigrid component. Its performance is investigated theoretically as well as practically at several two-dimensional test examples such as the linearized Burgers equations and various problems governed by the Navier-Stokes equations for incompressible flow.

• 出版日期2012-12