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Comparison of “Harmonic Functions” and “Freeform Deformation” techniques for the concurrent geometry and computational grid deformation

Antonakakis Georgios

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Summary

The optimization of an airfoil’s aerodynamic shape aims at improving the value of an objective function under specific constraints. A typical example is the maximization of the lift-to-drag ratio while maintaining structural strength. This process requires the generation of a computational grid and the solution of CFD models, which entails high computational cost. Since every geometric modification demands a new mesh, the iterative process becomes increasingly computational expensive, making mesh adaptation methods essential.This dissertation investigates and compares two mesh morphing techniques: Free-Form Deformation (FFD) and the Amended Harmonic Functions Method (AHFM). FFD is based on a parametric NURBS lattice, where the displacement of control points enables smooth geometric deformation. In contrast, the AHFM employs the B-spline basis functions as harmonic functions along the mesh boundary. The B-spline curve used as boundary is also the geometry to be deformed. boundary deformations are transmitted to the interior of the computational mesh.The comparison is carried out on an airfoil subjected to various deformations, with mesh quality evaluated using metrics such as aspect ratio, skewness, and orthogonal quality. Results indicate that both methods are effective, though they exhibit different advantages. FFD performs well across the full range of deformations, but its main drawbacks are the high computational cost and the approximate representation of the airfoil’s Cartesian coordinates. Conversely, AHFM offers consistency for minor deformations, improved computational efficiency and exact coordinate determination through analytical relations, though it shows limitations under large deformations.The study highlights the significance of mesh adaptation in aerodynamic shape optimization and suggests directions for future research, particularly focusing on further improvements to the AHFM algorithm.

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