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Ring polymers have a special topology which are devoid of any terminal ends. Studying the dynamics of such polymer chains become important because of their application in cloning of bacterial DNA in biotechnology, rheology modifiers in food processing industry, paint manufacturing and also useful from the perspective of modelling diffusion of active matter (such as bacteria) through porous medium, which has applications in treatment of diseases. In this work we focus on studying the rheology of ring polymer solutions in the single chain limit and in the limit of finite concentration by using Brownian dynamics simulations. The work involves mesoscale modelling of ring polymers by using bead-spring chain model and we carry out extensive numerical simulations using Brownian dynamics algorithm under various flow conditions (such as shear and extensional flows) to study the macroscopic rheology and correlate them with the microscopic configurational changes.