Computational Aspects of Pseudospectra in Hydrodynamic Stability Analysis

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