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We describe a general framework for avoiding spurious eigenvalues --unphysical unstable eigenvalues that often occur in hydrodynamic stabilityproblems. In two example problems, we show that when system stability isanalyzed numerically using {\em descriptor} notation, spurious eigenvalues areeliminated. Descriptor notation is a generalized eigenvalue formulation fordifferential-algebraic equations that explicitly retains algebraic constraints.We propose that spurious eigenvalues are likely to occur when algebraicconstraints are used to analytically reduce the number of independent variablesin a differential-algebraic system of equations before the system isapproximated numerically. In contrast, the simple and easily generalizabledescriptor framework simultaneously solves the differential equations andalgebraic constraints and is well-suited to stability analysis in thesesystems.

Descriptor approach for eliminating spurious eigenvalues in hydrodynamic equations