Domain reduction strategy for the stability analysis of complex aerodynamic flows

Abstract

Stability analysis in the framework of fluid dynamics is often expressed in terms of a complex eigenvalue problem (EVP). The solution of this EVP describes underlying flow features and their stability characteristics. The main shortcoming of this approach is the high computational cost necessary to solve the EVP, limiting the applicability of this analysis to simple two-dimensional configurations. Many efforts have been focused on overcoming this limitation. Reducing the computational domain to encompass only those regions of physical interest may help alleviate the computational cost. However, the accuracy of the eigenmodes recovered from a reduced region needs to be carefully assessed. In this work, an in-depth analysis of the domain reduction (DR) strategy is presented, and an error estimation tool is provided. The applicability and limitations of this methodology are studied on the open-cavity problem. Next, the error estimation tool is exploited in the transonic buffet phenomenon on a NACA 0012 profile, giving valuable recommendations for the best use of this methodology. Finally, the DR strategy has been applied to investigate the asymmetries induced by jet cooling of turbine blades. K E Y W O R D S complex flows, domain reduction, eigenvalue problems, fluid dynamics, stability analysis 1 Int J Numer Meth Fluids. 2020;92:727-743. wileyonlinelibrary.com/journal/fld

Sensitivity gradients of surface geometry modifications based on stability analysis of compressible flows

“…This approach has, however, the drawback of the memory limitations related to the matrix storage, as the scaling of the full LU decomposition behaves as (N v × N ) 3 [38]. However, domain reduction strategies [39] and efficient matrix distribution [40] reduce memory demands and allows one to perform stability analyses of three-dimensional configurations [3].…”