A vorticity-velocity formulation for solving the two-dimensional Navier-Stokes equations

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 tr ansport equation with a vorticity boundary condition. The Biot-Savart integ ral is evaluated to compute the velocity field from a vorticity distributio n over a fluid domain. The Green's scalar identity is employed to solve the total pressure in an integral approach. Global coupling between the vortic ity and the pressure boundary conditions is considered when this integro-di fferential approach is employed. For the early stage development of the flo w 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. (C) 1999 The Japan Society of Fl uid Mechanics and Elsevier Science B.V. All rights reserved.