A stabilized finite element method for global analysis of convective instabilities in nonparallel flows

Abstract

A new scheme for the global analysis of convective instabilities in nonparallel flows is proposed. The linearized perturbation equations for an incompressible flow are written in a moving frame of reference that travels with the perturbation. In the moving frame, the base flow varies with time. However, at t = 0, it is the same as the one in the stationary frame. Therefore, this analysis for determining the global convective instability is valid in an instantaneous sense. A stabilized finite element method is utilized to discretize these equations. A subspace iteration procedure is utilized to solve the resulting generalized eigenvalue problem. The scheme is applied to assess the stability of uniform flow past a circular cylinder. The critical Re for the onset of convective instability is found to be approximately 4. The results are in excellent agreement with the direct numerical simulation of the linearized flows equations. Unlike local analysis, the proposed method gives the global eigenmode and the corresponding growth rate.