27308518-8194-4293-bde1-e3462bf4ff7420210527090102117wseas:wseasmdt@crossref.orgMDT DepositWSEAS TRANSACTIONS ON FLUID MECHANICS2224-347X1790-508710.37394/232013http://wseas.org/wseas/cms.action?id=40361420211420211610.37394/232013.2021.16https://wseas.org/wseas/cms.action?id=23282NitinKumarDepartment of Mechanical Engineering, G. B. Pant Institute of Engineering and Technology, Pauri, Uttarakhand, INDIASachinTejyanDepartment of Mechanical Engineering, G. B. Pant Institute of Engineering and Technology, Pauri, Uttarakhand, INDIASunilChamoliDepartment of Mechanical Engineering, G. B. Pant Institute of Engineering and Technology, Pauri, Uttarakhand, INDIAPawanKumar PantDepartment of Mechanical Engineering, G. B. Pant Institute of Engineering and Technology, Pauri, Uttarakhand, INDIAThe present study focuses on the development of a numerical framework for predicting the onset of vortex sheading due to flow past a square cylinder. For this a discrete linear stability analysis framework for two-dimensional laminar flows have used. Initially the frame work is validating by using the analysis of thermal stability of flows in the discrete numerical sense. The two-dimensional base flow for various values of the controlling parameter (Reynolds number for flow past a square cylinder and Rayleigh number for double-glazing problem) is computed numerically by using the lattice Boltzmann method. The governing equations, discretized using the finite-difference method in two-dimensions and are subsequently written in the form of perturbed equations with two-dimensional disturbances. These equations are linearized around the base flow and form a set of partial differential equations that govern the evolution of the perturbations. The eigenvalues, stability of the base flow and the points of bifurcations are determined using normal mode analysis. The eigenvalue spectrum predicts that the critical Reynolds number is 52 for the flow past a square cylinder. The results are consistent with the previous numerical and experimental observations.52720215272021109119https://www.wseas.org/multimedia/journals/fluid/2021/a245113-006(2021).pdf10.37394/232013.2021.16.11https://www.wseas.org/multimedia/journals/fluid/2021/a245113-006(2021).pdf10.1016/j.ast.2009.07.007Tsai, B.-J. and Y.-C. Fu, Design and aerodynamic analysis of a flapping-wing micro aerial vehicle, Aerospace Science and Technology, 13 (2009), 7, pp. 383-392. Chandrasekhar, S., Hydrodynamic and hydromagnetic stability, Courier Corporation Inc., New York, USA, 2013. Drazin, P.G. and W.H. 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