Smoothed truncation error in functional error estimation and correction using adjoint methods in an unstructured finite volume solver

The goal of this paper is to develop a reliable truncation error estimator for finite-volume schemes and to use this truncation error estimate to correct the output functional of interest. The rough modes in the truncation error for unstructured mesh are dominant and if p-truncation error estimation is used, functional correction has a poor performance. So, we are trying to obtain a smooth estimate of the truncation error to improve the performance of output error estimation. The correction term is based on the truncation error and the adjoint solution. Both discrete and continuous adjoint solutions are used for correcting the functional. Our results for a variety of governing equations suggest that the smoothing scheme can improve the correction process significantly.