Automated adaptive time-discontinuous finite element method for unsteady compressible airfoil aerodynamics

An adaptive finite element methodology for unsteady compressible aerodynamics is presented. The automated adaptive environment consists of the finite quadtree automatic mesh generator, a time-discontinuous Galerkin least-squares finite element flow solver, an error indicator based on interpolation estimates, and a mesh enrichment procedure. Specifically, a linear space-time wedge element formulation was developed and implemented for two-dimensional problems with relative body motion. The mesh enrichment procedure is developed to enable the solution process to be spatially adaptive (h refinement), is edge based, and stores no mesh enrichment history.