Adjoint-based mesh adaptation method serves as an effective approach to improve the predictive accuracy of aerodynamic characteristics. However, viscous boundary layer grids often encounter issues such as hanging nodes, negative volumes, and directional constraints during adaptation, significantly limiting their practical application. To address these challenges, this study proposes an innovative polyhedral conversion strategy. Cells containing hanging nodes resulting from refinement are converted into polyhedra, effectively eliminating topological constraints between adjacent mesh elements. This approach is combined with surface-conforming projection and distance function-based mesh deformation techniques to ensure precise geometric representation and high mesh quality after adaptation. Numerical experiments demonstrate that the proposed viscous boundary layer mesh adaptation strategy successfully handles both refinement and coarsening of boundary layer grids. In a typical high-angle-of-attack case for the NACA0012 airfoil, the adjoint-based mesh adaptation method reduced lift coefficient error from 4.21% to 0.30% after four adaptation cycles. For the CHN-F1 low-aspect-ratio flying wing configuration, the method reduced the lift discrepancy from 10.05% to 6.65% at 40° angle of attack. The polyhedral conversion approach effectively resolves common challenges in viscous boundary layer mesh adaptation, providing a robust solution for high-fidelity prediction of aerodynamic characteristics with significantly improved accuracy.
Cui et al. (Thu,) studied this question.