Grid Adaptation for Functional Outputs: Application to Two-Dimensional Inviscid Flows

This paper presents an error estimation and grid adaptive strategy for estimating and reducing simulation errors in integral outputs (functionals) of partial differential equations. Adaptive criteria are derived using an adjoint-based error correction technique that relates the local residual errors of both the primal and adjoint solutions to the global error in the prescribed functional. This relationship allows local error contributions to be used as indicators in a grid adaptive strategy designed to produce specially tuned grids for accurately estimating the chosen functional. In this paper, attention is limited to two-dimensional inviscid flows using a standard finite volume discretization, although the procedure may be readily applied to other types of multidimensional problems and discretizations. Numerical examples demonstrate that the proposed adaptive procedure compares favorably in terms of accuracy, efficiency, and robustness relative to a commonly used gradient-based adaptive method.