  Direct methods to obtain global stability modes are restricted by the
daunting sizes and complexity of Jacobians encountered in general
three-dimensional flows. Jacobian-free iterative approaches such as Arnoldi
methods have greatly alleviated the required computational burden. However,
operations such as orthonormalization and shift-and-invert transformation of
matrices with appropriate shift guesses can stll introduce computational and
parameter-dependent costs that inhibit their routine application to general
three-dimensional flowfields. The present work addresses these limitations by
proposing and implementing a robust, generalizable approach to extract the
principal global modes, suited for curvilinear coordinates as well as the
effects of compressibility. Accurate linearized perturbation snapshots are
obtained using high-order schemes by leveraging the same non-linear
Navier-Stokes code as used to obtain the basic state by appropriately
constraining the equations using a body-force. It is shown that with random
impulse forcing, dynamic mode decomposition (DMD) of the subspace formed by
these products yields the desired physically meaningful modes when
appropriately scaled. The leading eigenmodes are thus obtained without spurious
modes or the need for an iterative procedure. Further, since orthonormalization
is not required, large subspaces can be processed to capture converged low
frequency or stationary modes. The validity and versatility of the method are
demonstrated with numerous examples encompassing essential elements expected in
realistic flows, such as compressibility effects and complicated domains
requiring general curvilinear meshes. Favorable comparisons with Arnoldi-based
method, complemented with substantial savings in computational resources show
the potential of the current approach for relatively complex flows.
