Adjoint-based Error Estimation for Grid Adaptation for Large Eddy Simulation

Goal-oriented grid adaptation for chaotic systems remains a challenging problem due to the instability of the adjoint system for long time integration. We propose two approximation methods to derive a single-solving adjoint system for statistically steady chaotic problems. The approaches are further applied to derive an adjoint-based error estimator for LES. The error estimator was validated using the SD7003 airfoil case. Tests were carried out for two different Reynolds numbers on coarse, fine and adapted grids. Numerical results were validated through a comparison against reference LES and experimental data and it was shown that the adjoint-adapted grid improves the prediction of the functional as well as the capture of pertinent flow structures.