Acceleration of Adjoint-Based Adaptation through Sub-Iterations for Unsteady Simulations

Sub-iterations in adjoint-based adaptation refer to reusing primal states and fine-space adjoints, in multiple adaptive iterations. This technique has been demonstrated for steady compressible Navier-Stokes simulations, for which it achieved significant CPU time savings as compared to standard adjoint-based adaptation. In this paper, we extend the sub-iterations idea of formulating approximated and relatively accurate adaptive indicators by reusing solver information, to unsteady problems. The steady sub-iteration only needs to reconstruct in space in order to reuse the previous adaptation iteration's primal states and fine-space adjoints, while unsteady sub-iterations require both spatial and temporal reconstruction due to mismatched adapted time histories. In this paper, we present our results for simulations of the unsteady Navier-Stokes equations, with p adaptation.