A velocity-stream function method for three-dimensional incompressible fluid flow

We describe a velocity-stream function method for computing incompressible fluid flow, extending earlier work in two- to three-dimensions. We present a strictly-divergence-free finite element in primitive variables in 3D as the curl of a (generalized) Hermite vector potential element with velocity degrees-of-freedom and show a method for its derivation. This linear velocity element is defined on a reference cube with 8 nodes, each node having 3 vector potential (stream function) and 3 velocity degrees-of-freedom. The method and element are applied to the lid-driven cavity problem and open duct flow in three dimensions.