Effect of outflow boundary conditions in global stability analysis of bluff body wakes

Global linear stability problems are solved using matrix-forming or time-stepping. While the former approach avoids the need to have a linearized direct numerical solver, it is limited due to the need to store the matrix in the memory, which might prevent its application to problems with many degrees of freedom. This study investigates the effect of outflow boundary conditions (BCs) in the matrix-forming approach, with emphasis on reduction of the computational domain size as much as possible. Incompressible bluff body wakes, including cylinders and airfoils, are examined, in particular when the global modes are spatially amplified downstream. It is shown that below a certain Reynolds number, when the global mode is stable, it is spatially amplified downstream even when the wake is virtually inexistent. The ability of various outflow BCs from the literature to adequately resolve such eigenmodes is discussed. The BCs include Dirichlet, Neumann, and Robin, where the latter is based on a Gaster-type transformation and incorporates predictions from local stability analysis of the outflow streamwise velocity profile. It is shown that appropriate BCs facilitate the convergence of the global mode, even when the computational domain size is reduced, thus appreciably improving the efficiency of the global stability analysis. Our findings pave the way towards application of the matrix-forming approach in more complex stability problems, such as Floquet analysis and compressible flows.