On utilizing the finite element method on unstructured meshes for stability analysis of flows in channels of constant cross-section

Earlier a technique for numerical analysis of incompressible fluid flows in channels of constant cross section was developed. This technique is based on original effective algorithms of differential-algebraic systems analysis, which arise following the spatial approximation of the equations governing flow of viscid incompressible fluid, linearized around the main flow under investigation. The utilized algorithms are designed for matrices not of large dimensions. It is proposed in this study to look into the possibility of extending the technique to approximations leading to large sparse matrices. In particular, using a new effective Newton-type method is intended for solving partial eigenvalues problems, which arise in flows stability investigation. Performance ability of the proposed approach is demonstrated with the Poiseuille flow in a channel of circular cross-section and the finite element method approximation.