An adaptive unstructured method has been developed for simulating two-dimensional unsteady, viscous, incompressible flows. The pressure-based approach coupled with a mesh adaptation method is employed to better capture the details of flow physics for time dependent problems by optimizing computational cost with respect to accuracy. The mesh adaptation for locally refining and coarsening hybrid unstructured grid is based on hanging node approach. The time dependent calculations is further enhanced by virtue of parallel computing which is the most powerful for large scale intensive computation at the present time. The proposed method is validated by comparison with experimental results of low Reynolds number flow over a shedding circular cylinder.

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