A boundary element method for unsteady viscous flows

A potential vorticity method for the analysis of unsteady viscous incompressible flow past arbitrarily shaped objects is discussed which is based on the Helmholtz decomposition. It is found that the correct boundary condition to be imposed is on the normal component of the velocity for the cases of both inviscid and viscous flows. The no-slip condition is shown to be automatically satisfied for viscous flows. Numerical solutions for two-dimensional flow problems are given for attached flows in addition to those involving separation. The vorticity is confined, at least for the case of symmetric flows, to a small region in the immediate vicinity of the body, making possible the minimization of the number of node points in the field, and hence the computational time, without loss of accuracy.