Error estimation and grid adaptation using Euler adjoint method

An adjoint-based error estimation and grid adaptation study is conducted for three-dimensional inviscid flows with unstructured meshes. The error in an integral output functional of interest is estimated by a dot product of the residual error and adjoint variable vector. To suppress excessive mesh refinement in unnecessary regions due to high-frequency noise contained in the residual vector, the flow residual is smoothed using a volume-weighted averaging process. Regions to be adapted are selected based on the error contribution of a local node to the global error. The adaptive regions are refined by the bisection refinement algorithm. The present procedure is applied to three-dimensional transonic inviscid flows around ONERA M6 wing and ONERA M5 airplane models. The same level of prediction accuracy for drag is achieved with much less mesh points than uniformly refined fine meshes. It is found that the residual smoothing strategy remarkably improves the accuracy of error estimation, and there exists an optimum number of smoothing for accurate error estimation.