Adjoint Error Estimation and Adaptive Refinement for Embedded-Boundary Cartesian Meshes

We present an approach for the computation of error estimates in output functionals such as lift or drag for an embedded-boundary Cartesian mesh method. The approach relies on the solution of an adjoint equation and provides error estimates that can be used to both improve the accuracy of the functional and guide a mesh refinement procedure. This is a significant step in our research toward automating the simulation process for flows in complex geometries. The accuracy of the approach is verified on an analytic model problem and validated against common results in the literature. The robustness of the approach is examined for two test cases in three dimensions, namely, an isolated wing in transonic flow and a canard-controlled missile in supersonic flow. The results demonstrate that the approach is tolerant of coarse initial meshes. A practical advantage of the approach is that the adaptive mesh refinement may be performed with a fixed surface triangulation. In all cases considered, the approach provided reliable estimates of the output functional on computationally affordable meshes. I