Stabilization of a linearized Navier-Stokes solver for turbomachinery aeroelasticity

Abstract. The linear analysis of turbomachinery aeroelasticity relies on the assump-tion of small level of unsteadiness and requires the solution of both the nonlinear steady and the linear unsteady ow equations. The objective of the analysis is to com-pute a complex ow solution which represents the amplitude and phase of the unsteady ow for the frequency of unsteadiness of interest. The solution procedure of the lin-ear harmonic Euler/Navier-Stokes solver often consists of a preconditioned xed-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.