2007/05/10 by M. Lisa Manning, Bassam Bamieh, Manning, M. Lisa +5
Engineering · Mathematics · Physics and Astronomy · #Computational Fluid Dynamics and Aerodynamics #Computational Physics (physics.comp-ph) #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Model Reduction and Neural Networks #Numerical methods for differential equations #physics.comp-ph #physics.flu-dyn
paper · pdf · doi:10.48550/arxiv.0705.1542
13 pages, 1 figure, revised for submission to SIAM Sci. Comp., moved background information to appendices
openalex publication_date 2007/05/10 · arxiv created 2008/12/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We describe a general framework for avoiding spurious eigenvalues -- unphysical unstable eigenvalues that often occur in hydrodynamic stability problems. In two example problems, we show that when system stability is analyzed numerically using \em descriptor notation, spurious eigenvalues are eliminated. Descriptor notation is a generalized eigenvalue formulation for differential-algebraic equations that explicitly retains algebraic constraints. We propose that spurious eigenvalues are likely to occur when algebraic constraints are used to analytically reduce the number of independent variables in a differential-algebraic system of equations before the system is approximated numerically. In contrast, the simple and easily generalizable descriptor framework simultaneously solves the differential equations and algebraic constraints and is well-suited to stability analysis in these systems.