Descriptor approach for eliminating spurious eigenvalues in hydrodynamic equations

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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.
13 pages, 1 figure, revised for submission to SIAM Sci. Comp., moved background information to appendices

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Computational Physics, Fluid Dynamics

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http://salesiana.dossiersoluciones.com/handle/123456789/208321

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0705.1542
 http://arxiv.org/abs/0705.1542

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arXiv