A multi-mesh approach for accurate computation of multi-target functionals in aerodynamics design

Aerodynamic optimal design is crucial for enhancing performance of aircrafts, while calculating multi-target functionals through solving dual equations with arbitrary right-hand sides remains challenging. In this paper, a novel multi-target framework of DWR-based mesh refinement is proposed and analyzed. Theoretically, an extrapolation method is generalized to expand multi-variable functionals, which guarantees that the dual equations of different objective functionals can be calculated separately. Numerically, an algorithm of calculating multi-target functionals is designed based on the multi-mesh approach, which can help to obtain different dual solutions simultaneously. One feature of our framework is that the algorithm is easy to implement with the help of the hierarchical geometry tree structure and the calculation avoids the Galerkin orthogonality naturally. The framework takes a balance between different targets even when they are not the same orders of magnitude. While existing approach uses a linear combination of different components in multi-target functionals for adaptation, it introduces additional coefficients for adjusting. With each component calculated under a dual-consistent scheme, this multi-mesh framework addresses challenges such as the lift-drag ratio and other kinds of multi-target functionals, ensuring smooth convergence and precise calculations of dual solutions.