Unnikrishnan, AkashAkashUnnikrishnanNarayanan, VinodVinodNarayananVanka, Surya PratapSurya PratapVanka2025-08-312025-08-312024-06-0110.1063/5.02133252-s2.0-85195392437http://repository.iitgn.ac.in/handle/IITG2025/28901Recently, 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.falseArticle108976661 June 20241064103arJournal1WOS:001242219700006