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

Global linear stability analysis of bluff body wakes must be carried out on truncated computational domains, even though the physical problem is unbounded. Because the global eigenfunctions are not known a priori, the outlet location and the outflow boundary condition are often selected heuristically and validated a posteriori by inspecting the computed eigenspectrum and eigenfunctions. In practice, standard outflow treatments can create a localized non-physical region near the outlet, which is then identified in post-processing and excluded from physical interpretation. To mitigate these outlet effects, the downstream boundary is often moved farther away by extending the computational domain, increasing the computational cost.

This seminar presents a matrix-forming BiGlobal stability framework based on finite-difference discretization and assesses how the outflow boundary condition influences the predicted eigenspectrum and eigenmodes. Common outlet closures (Dirichlet, Neumann, and extrapolation-type) are compared with a physically consistent Robin boundary condition that incorporates local linear stability theory information at the outlet. For steady, incompressible, low Reynolds number (of order of 100) wakes of cylinders and airfoils at high angles of attack, the proposed Robin condition eliminates outlet-induced artifacts and yields robust convergence, even when the computational domain is severely truncated. Our findings pave the way for efficient and accurate computations of global eigenfunctions in more complex flows.