Continuous Adjoint Approach for Adaptive Mesh Refinement

Abstract

At present, all output-based mesh adaptation methods in the existing literature have adopted the discrete adjoint approach which, depending on the structure of the code, could be very complex to implement. In this work, we aim to investigate the continuous adjoint approach for adaptive mesh refinement, with an application to the compressible Euler equations. Both the primal and the adjoint equations are solved with the high-order spectral difference (SD) method. The approach is tested on steady subsonic and transonic flows over a NACA0012 airfoil on a C-mesh with p-refinement and isotropic h-refinement. The performance is assessed by looking at the trend of the local estimated error, as well as by the accuracy of capturing local flow features (e.g. shocks).