Abstract
This paper describes a vorticity-based integro-differential formulation for the numerical solution of the two-dimensional incompressible Navier–Stokes equations. A finite volume scheme is implemented to solve the vorticity transport equation with a vorticity boundary condition. The Biot–Savart integral is evaluated to compute the velocity field from a vorticity distribution over a fluid domain. The Green's scalar identity is employed to solve the total pressure in an integral approach. Global coupling between the vorticity and the pressure boundary conditions is considered when this integro-differential approach is employed. For the early stage development of the flow about an impulsively started circular cylinder, the computational results with our numerical method are compared with known analytical solutions in order to validate the present formulation.
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