| Abstrakt: |
Summary: We recently proposed a second‐order accurate ψ‐v formulation of the steady‐state Navier‐Stokes (N‐S) equations on compact Cartesian nonuniform grids. In the current work, we extend the ideas of the aforesaid formulation and propose a second‐order spatially compact, implicit, stable ψ‐v formulation for the unsteady incompressible N‐S equations. Contrary to the existing ψ‐v finite difference formulations which use grid transformation, the proposed scheme is developed for nonuniform Cartesian grids without transformation specifically designed for two‐dimensional laminar flow past bluff bodies. It has been implemented on problems of internal flows inside curved regions as well as those involving fluid‐embedded body interaction. However, the robustness of the scheme is highlighted by the accurate resolution of a host of complex flows past bluff bodies with different physical set‐ups and boundary conditions. It was seen to handle problems involving both uniform and accelerated flows across a wide range of structures of varied shape, namely, a flat plate, a circular cylinder, inclined square cylinder, and a wedge in channel hinged to the wall. Apart from elegantly capturing all the details of the shedded vortex structures under different circumstances, the scheme was also able to handle both Dirichlet and Neumann boundary with equal ease. In all the cases, our results are found to be extremely close to the available numerical and experimental results. [ABSTRACT FROM AUTHOR] |
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