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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.

MSC:
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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