Numerical solution for the steady motion of a viscous fluid inside a circular boundary using integral conditions (Q685845)

The problem of determining the two-dimensional steady motion of a viscous incompressible fluid which is injected radially over one small arc of a circle and ejected radially over another arc is considered and examples are given of both symmetrical and asymmetrical flows. The motion is governed by the Navier-Stokes equations and the method of solution is based on the use of truncated Fourier series representations for the stream function and vorticity in the angular polar coordinate. The Navier-Stokes equations are reduced to ordinary differential equations in the radial variable and these sets of equations are solved using finite- difference methods, but with the boundary vorticity calculated using global integral conditions rather than local finite-difference approximations.