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The importance of eigenvectors for local preconditioners of the Euler equations. (English) Zbl 0860.76054
We present the mathematical framework for the eigenvector analysis of local preconditioners for the multi-dimensional Euler equations. The non-normality of the preconditioned system is crucial in determining the potential for transient amplification of perturbations. Several existing local preconditioners are shown to possess a highly non-normal structure for low Mach numbers. This non-normality leads to significant robustness problems at stagnation points. A modification of these preconditioners which eliminates the non-normality is suggested, and numerical results are presented showing the marked improvement in robustness.

76M20 Finite difference methods applied to problems in fluid mechanics
76G25 General aerodynamics and subsonic flows
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
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