Solution of the eigenvalue problems resulting from global non-parallel flow stability analysis

Abstract

The eigensolution method, more flexible and efficient than previously used for global non-parallel flow stability analysis, is presented. 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 the eigenvalues interesting for the flow stability analysis is performed with the inverse Cayley transformation. It is shown that certain barriers, resulting from very large dimensions of the eigenvalue problem and limiting the non-parallel flow stability method can be overcome with this approach. To demonstrate the algorithm, the stability of the flow around circular cylinder is analyzed.