C0 collocation solutions for weak-formulation Navier-Stokes equations

A global collocation procedure was attempted on two-D Navier-Stokes equations, but suffered from significant ringing. Historically, multi-element collocation has been based on Hermit shape functions for Navier-Stokes. Alternative, a weak formulation Navier-Stokes solution was developed using biquadratic Lagrangian functions on element boundaries and discrete Galerkin (collocation) expressions on interiors. To account for pressure, a penalty function expression was evaluated as part of a weighted integral, using bilinear shape functions. This method was exercised on flow through a duct that included a pivoting flap that protruded into the flow where the flap motion and fluid flow interacted.