We present a new local, adaptive, higher order, tree-based quadrature and point insertion method to describe 3-D vortex sheet motion. The main new contribution is a hierarchical tree representation of the vortex sheet surface, which allows us to insert new computational particles locally as leaves of the tree as opposed to the insertion of a complete new filament as in the previous approach. We have also developed 4th order accurate integration, point insertion, and derivative calculation schemes, compared to the 2nd order schemes available before. It appears that at the later stages of...