An adaptive finite element method for unsteady compressible rotor airfoil aerodynamics

The accurate treatment of unsteady compressible rotor airfoil aerodynamic flows requires the capability to efficiently resolve the widely varying length scales of the flow physics as they evolve temporally. An adaptive finite element methodology suitable for this type of problem is developed in this thesis. It is based upon an automated adaptive environment consisting of the Finite Quadtree automatic mesh generator, a time-discontinuous Galerkin Least Squares finite element flow solver, an error indicator based upon interpolation estimates, and a mesh enrichment procedure. The time-discontinuous Galerkin Least Squares finite element flow solver is particularly well suited to handle problems with multiple relative motion. A linear space-time wedge element formulation was developed and implemented which is suitable for two dimensional problems with relative body motion. The mesh enrichment procedure developed to enable the solution process to be spatially adaptive (h-refinement) is edge based and stores no mesh enrichment history. Steady and unsteady transonic airfoil calculations show good correlation with other experimental and numerical data. Based upon these results it is concluded that this type of automated adaptive CFD technique is a viable computational tool capable of accurately resolving unsteady compressible flow features and should be developed further to handle three dimensional problems where multiple relative motion is important, i.e. the flow field around an entire helicopter.