Stabilization of a linearized navier-stokes solver for turbomachinery aeroelasticity

The linear analysis of turbomachinery aeroelasticity relies on the assumption of small level of unsteadiness and requires the solution of both the nonlinear steady and the linear unsteady flow equations. The objective of the analysis is to compute a, complex flow solution which represents the amplitude and phase of the unsteady flow for the frequency of unsteadiness of interest. The solution procedure of the linear harmonic Euler/Navier-Stokes solver often consists of a, preconditioned fixed-point iteration which in some circumstances may become numerically unstable. The paper summarizes the use of the Recursive Projection Method and the Generalized Minimum Residuals algorithm to provide stabilization and presents a realistic application of both approaches.