The Importance of Eigenvectors for Local Preconditionersof the Euler


The design of local preconditioners to accelerate the convergence to a steady state for the compressible Euler equations has so far been solely based on eigenvalue analysis. However, numerical evidence exists that the eigenvector structure also has an in uence on the performance of preconditioners, and should therefore be included in the design process. In this paper, 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 ampli cation of perturbations. Several existing local preconditioners are shown to possess a highly nonnormal structure for low Mach numbers. This non-normality leads to signi cant robustness problems at stagnation points. A modi cation to these preconditioners which eliminates the non-normality is suggested, and numerical results are presented showing the marked improvement in robustness.

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@inproceedings{Darmofal1996TheIO, title={The Importance of Eigenvectors for Local Preconditionersof the Euler}, author={David L. Darmofal}, year={1996} }