High-Order Reconstruction of Defect Corrected Solutions on Unstructured Meshes

In spite of being more efficient than mesh refinement in terms of memory and computational work requirements, higher-order (greater than second-order) methods are not very common in commercial CFD codes because of stability issues. In previous work, we have shown that defect correction with a good estimate of the truncation error is an efficient alternative method in improving the accuracy of the control volume averages from a finite volume solver beyond second-order. In this paper, the higher-order accurate control volume average is used to get a piecewise continuous solution that mimics a higher-order reconstruction, which can be used to get better estimates of output functionals. The treatment of curved boundaries to get higher-order accurate integral functionals is also described.