Title: High-order meshless global stability analysis of Taylor-Couette flows in complex domains

Abstract: 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.