Output-Based Space-Time Mesh Adaptation for Unsteady Aerodynamics

An adjoint-based output error estimation algorithm is presented for unsteady problems discretized on static meshes with a space-time discontinuous Galerkin finite element method. An approximate factorization technique is used to solve both the forward and the discrete adjoint problems. A space-time anisotropy measure based on projection of the adjoint solution is used to attribute the error to spatial or temporal resolution. This measure drives a fixed-growth adaptive strategy that employs hanging-node refinement in the spatial domain and slab bisection in the temporal domain. Adaptive results for convection-dominated flows in two dimensions, including those governed by the compressible Navier-Stokes equations, demonstrate the effectivity of the output error estimate and the degree-of-freedom benefits of output-based adaptation compared to uniform space-time refinement and to cheaper heuristic indicators.