Adjoint-Based Functional Correction for Unstructured Mesh Finite Volume Methods

The goal of this paper is to demonstrate the use of adjoint-based functional correction and mesh adaptation for aerodynamic flows with an unstructured mesh finite volume solver. A key feature of our approach is that all calculations are performed on a single mesh, unlike other error correction and mesh adaptation schemes. As using the original p-truncation error estimate is not helpful in improving the functional, we use a smoothed estimate of the truncation error to correct the functional for both inviscid and viscous flows. The correction term is based on the smoothed truncation error and the adjoint solution, with both the continuous and discrete adjoints. The same correction term is used as an adaptation indicator for goal-based mesh adaptation as well. Our results show the effectiveness of our method in improving the convergence rate for test cases of interest in computational aerodynamics.