This paper presents some of the first results of global linear stability analyses performed using a bespoke eigensolver that has recently been implemented in the next generation flow solver framework CODA. The eigensolver benefits from the automatic differentiation capability of CODA that allows computation of the exact product of the Jacobian matrix with an arbitrary complex vector. It implements the Krylov–Schur algorithm for solving the eigenvalue problem. The bespoke tool has been validated for the case of laminar flow past a circular cylinder with numerical results computed using the TAU code and those reported in the literature. It has been applied with both second-order finite volume and high-order discontinuous Galerkin schemes for the case of laminar flow past a square cylinder. It has been demonstrated that using high-order schemes on coarser grids leads to well-converged eigenmodes with a shorter computation time compared to using second-order schemes on finer grids.
