Descriptor approach for eliminating spurious eigenvalues in hydrodynamic equations

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dc.creatorManning, M. Lisa
dc.creatorBamieh, B.
dc.creatorCarlson, J. M.
dc.date2007-05-10
dc.date2008-12-01
dc.date.accessioned2026-07-07T12:05:14Z
dc.date.available2026-07-07T12:05:14Z
dc.descriptionWe 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.
dc.description13 pages, 1 figure, revised for submission to SIAM Sci. Comp., moved background information to appendices
dc.identifierhttps://arxiv.org/abs/0705.1542
dc.identifierhttp://arxiv.org/abs/0705.1542
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/208321
dc.subjectComputational Physics
dc.subjectFluid Dynamics
dc.titleDescriptor approach for eliminating spurious eigenvalues in hydrodynamic equations
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