  Recently, meshless methods have become popular in numerically solving partial
differential equations and have been employed to solve equations governing
fluid flows, heat transfer, and species transport. In the present study, a
numerical solver is developed employing the meshless framework to efficiently
compute the hydrodynamic stability of fluid flows in complex geometries. The
developed method is tested on two cases of Taylor-Couette flows. The concentric
case represents the parallel flow assumption incorporated in the Orr-Sommerfeld
model and the eccentric Taylor-Couette flow incorporates a non-parallel base
flow with separation bubbles. The method was validated against earlier works by
Marcus [1], Oikawa et al. [2], Leclercq et al. [3], and Mittal et al. [4]. The
results for the two cases and the effectiveness of the method are discussed in
detail. The method is then applied to Taylor-Couette flow in an elliptical
enclosure and the stability of the flow is investigated.
