An Output-Based Dynamic Order Re nement Strategy for Unsteady Aerodynamics

An output-based dynamic order re nement strategy is presented for unsteady simulations using the discontinuous Galerkin nite element method in space and time. A discrete unsteady adjoint solution provides scalar output error estimates and drives adaptive re nement of the space-time mesh. Space-time anisotropy is measured using projection of the adjoint onto semi-re ned spaces and is used to allocate degrees of freedom to additional time slabs or increased spatial order of individual space-time elements. The spatial re nement is dynamic in that the solution approximation order can change between time slabs. Results for the compressible Euler equations demonstrate bene ts of the dynamic order re nement strategy in terms of total degrees of freedom: at strict error tolerances, the savings approaches two orders of magnitude compared to uniform re nement, and a factor of two to three compared to output-based re nement with a static spatial mesh.