On the formulation of boundary conditions for vorticity in problems of the flow of a viscous incompressible fluid around bodies

For the stream function-vorticity formulation of the Navier–Stokes equations, vorticity boundary conditions are required on the body surface and the far-field boundary. A two-parameter approximating formula is derived that relates the velocity and vorticity on the outer boundary of the computational domain. The formula is used to construct an algorithm for correcting the conventional far-field boundary conditions. Specifically, a soft boundary condition is set for the vorticity and a uniform flux is specified for the transversal velocity. A third-order accurate three-parameter formula for the vorticity on the wall is derived. The use of the formula does not degrade the convergence of the iterative process of finding the vorticity as compared with a previously derived and tested two-parameter formula.