Three-dimensional Stability and Resolvent Analysis of External Flows Over Spanwise-homogeneous Immersed Bodies

We introduce a computationally efficient method to conduct three-dimensional stability and resolvent analyses of flow around nominally two-dimensional (spanwise homogeneous) bodies of arbitrary cross-sections. For incompressible flows, our method utilizes the immersed boundary (IB) method with a fast Lattice Green's Function (FLGF) solver for the associated Poisson-like equation and includes adaptive mesh refinement (AMR). We validate our algorithm by performing stability analyses of flow past a rotating cylinder and comparing our results with ones from the literature. We also demonstrate the capability of this algorithm by conducting a 2D resolvent analysis by considering the flow past a cylinder at Re = 100. Finally, we demonstrate the capability of this method to handle a wide range of length scales by conducting stability analysis of the flow past a cylinder at Re = 63 with a small control cylinder in its wake.