Massively Parallel Solution of the BiGlobal Eigenvalue Problem Using Dense Linear Algebra

Linearinstabilityofcomplex! owsmaybeanalyzedbynumericalsolutionsofpartial-derivative-based eigenvalue problems;the concepts are,respectively, referredto asBiGlobal orTriGlobalinstability, dependingonwhether two or three spatial directions are resolved simultaneously. Numerical solutions of the BiGlobal eigenvalue problems in ! ows of engineering signi" cance, such as the laminar separation bubble in which global eigenmodes have been identi" ed,revealthatrecoveryof(two-dimensional) amplitudefunctionsofgloballystable butconvectivelyunstable ! ows (i.e., ! ows which sustain spatially amplifying disturbances in a local instability analysis context) requires resolutions well beyond the capabilities of serial, in-core solutions of the BiGlobal eigenvalue problems. The present contribution presents a methodology capable of overcoming this bottleneck via massive parallel solution of the problem at hand; the approach discussed is especially useful when a large window of the eigenspectrum is sought. Twoseparated! owapplications, onein theboundary-layer ona! atplate andoneinthe wakeof astalledairfoil, are brie! y discussed as demonstrators of the class of problems in which the present enabling technology permits the study of global instability in an accurate manner.