A Variational Finite Element Method for Solving Unsteady Viscous-Flow Problems

The effects of a two-dimensional ‘real’ vortex convected along by an incompressible free stream impinging on a flat plate of finite length, situated midway between two parallel sides of a channel and near to the entrance of the channel, were studied analytically using the variational approach. Of particular interest were the effects of the free stream vorticity on the behaviour of the viscous layer developed on the plate. In the solution, the vorticity (Helmholtz) and stream function (Poisson) equations were integrated in space, using the finite element method and a weighted-average marching scheme in the direction of time. Results have been compiled for the variation of the pressure and shear along the plate with time and also for the variation of lift, drag forces, and pitching moment about the leading edge of the plate.