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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 “Simulation of Taylor-Couette flow. Part 1. Numerical methods and comparison with experiment,” J. Fluid Mech. 146, 45–64 (1984), Oikawa et al. “Stability of flow between eccentric rotating cylinders,” J. Phys. Soc. Jpn. 58, 2355–2364 (1989), Leclercq et al. “Temporal stability of eccentric Taylor–Couette–Poiseuille flow,” J. Fluid Mech. 733, 68–99 (2013), and Mittal et al. “A finite element formulation for global linear stability analysis of a nominally two-dimensional base flow,” Numer. Methods Fluids 75, 295–312 (2014). 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.
Unnikrishnan et al. (Sat,) studied this question.