Error estimation and adaptation for functional outputs in time-dependent flow problems

The paper presents an adjoint-based approach for determining global error in the time domain that is relevant to functional outputs from unsteady flow simulations. The algorithm is derived for the unsteady Euler equations that are discretized for second-order accuracy in both space and time and takes into account the effect of dynamic meshes. In addition to error due to temporal resolution, the formulation also takes into account algebraic error arising from partial convergence of the governing equations at each implicit time-step. The resulting error distributions are then used to drive adaptation of the temporal resolution and the convergence tolerances for the governing equations at each time-step. The method is demonstrated in the context of both time-integrated and instantaneous functionals and the results are compared against traditional adaptation methods.