Adjoint-based error estimation for grid adaptation for large eddy simulation

Abstract

Goal-oriented grid adaptation for chaotic systems remains a challenging problem due to the tremendous computational and storage costs as well as the instability of the adjoint system for long time backward time integration. We propose two approximation methods to derive a single-solve adjoint system for statistically steady chaotic problems. The first approximation leads to an adjoint system based on the time-averaged Jacobian and the sensitivity of the functional; while, the second approximation is based on converting the LES flow solution to a Reynolds-averaged Navier–Stokes (RANS)-type steady flow solution, on which the steady adjoint approach could be applied. 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-based adapted grids lead to fast convergence of the prediction of the functional as well as the capture of pertinent flow structures compared to feature-based and manually adapted grids.