A finite element analysis of steady viscous flow in triangular cavities

A finite element formulation of the Navier-Stokes equations, written in ter ms of the stream function, Psi, and vorticity, omega, for a Newtonian fluid in the absence of body forces, is used to solve the problem of flow in a t riangular cavity, driven by the uniform motion of one of its side walls. A key feature of the numerical method is that the difficulties associated wit h specifying w at the corners are addressed and overcome by applying analyt ical boundary conditions on w near these singularities. The computational r esults are found to agree well with previously published data and, for smal l stagnant corner angles, reveal the existence of a sequence of secondary r ecirculations whose relative sizes and strengths are in accord with Moffatt 's classical theory. It is shown that, as the stagnant corner angle is incr eased beyond approximately 40 degrees, the secondary recirculations diminis h in size rapidly.