Physically Consistent Outflow Boundary Conditions for Global Stability Analysis of Bluff Body Wakes

Abstract

Global linear stability analysis of bluff body wake flows is performed using the matrix-forming method based on finite-difference discretization. Particular emphasis is placed on the influence of outflow boundary conditions, with the aim of minimizing the required computational domain size without degrading accuracy or inducing spurious oscillations near the outlet. This study focuses on incompressible wakes behind bluff bodies such as cylinders and airfoils at high angle of attack, especially in regimes where global modes exhibit downstream spatial amplification. It is shown that below the critical Reynolds number -- where the global mode remains linearly stable -- significant spatial growth can persist far downstream, even when the wake is nearly absent. This behavior underscores the importance of imposing a physical boundary condition at the outlet. Several commonly used outflow boundary conditions are evaluated, including Dirichlet, Neumann, extrapolation, stress-free, sponge layer, and the Robin condition that incorporates predictions from local linear stability analysis at the outlet. The results demonstrate that, for different $Re$ cases, the Robin condition enables robust convergence of global modes within substantially truncated domains, thereby improving the efficiency of global stability analysis. These findings highlight the broader applicability of the matrix-forming approach for complex stability analyses, including Floquet analysis of time-periodic flows and extensions to compressible configurations.