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Solution of the eigenvalue problems resulting from global non-parallel flow stability analysis. (English) Zbl 0959.76045
Summary: We present an eigensolution method for global non-parallel flow stability analysis. The differential eigenvalue problem resulting from linear stability equations of non-parallel flow is discretized with the penalty FEM. The large-dimensional algebraic eigenvalue problem is solved with the use of subspace iteration method. Separation of eigenvalues interesting for the flow stability analysis is performed with the inverse Cayley transformation. It is shown that certain barriers resulting from large dimensions of the eigenvalue problem and limiting the non-parallel flow stability method can be overcome with this approach. To demonstrate the algorithm, we analyze the stability of the flow around circular cylinder.

76M10 Finite element methods applied to problems in fluid mechanics
76E09 Stability and instability of nonparallel flows in hydrodynamic stability
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