A Reduced-Parameter-to-Mesh Framework for Rapid Local Mesh Deformation in Aerodynamic Shape Optimization

Repeated computational fluid dynamics (CFD)-based aerodynamic optimization requires both a compact design space and an inexpensive mesh-update procedure. This study presents a reduced-parameter-to-mesh framework in which low-dimensional variables act directly on the computational mesh instead of reconstructing the geometry and then perform global volume-mesh deformation. A parametric non-uniform free-form deformation (NFFD) method is developed using a body-fitted control lattice. Radial basis function interpolation (RBF) is restricted to the NFFD background control mesh, while nodes in the local deformation region are updated from precomputed local coordinates. This offline–online decomposition makes the node update independent across mesh points and avoids global RBF interpolation or a large-scale elasticity solve. Dimensionality reduction is then embedded in an extended point set comprising body-fitted control points and aerodynamic surface points; the reconstructed control points directly drive mesh deformation. Tests on 100 deformations of the RAE2822 airfoil and ONERA M6 wing show that the core mesh-update time is reduced from 156.9 ms and 482 ms to 36.5 ms for RAE2822 and from 156.258 s and 62.857 s to 0.253 s for M6, relative to conventional NFFD-RBF and elastic deformation, respectively. The design-space dimensions are reduced from 22 to 13 and from 42 to 24, while mesh quality remains stable. In the M6 optimization demonstration, total optimization time decreases from 30.35 h to 18.42 h. The results show that coupling reduced coordinates directly to a local parametric mesh-update operator can substantially lower the non-solver overhead of repeated aerodynamic optimization.