A Lightweight Data-Driven Model Enhanced Discontinuous Galerkin Method for Rapidly Simulating Transonic Airfoil Flowfields (Communications in Computational Physics, 2025)
Accurate and rapid prediction of flowfields is crucial for aerodynamic design. This work proposes a discontinuous Galerkin method (DGM) whose performance can be enhanced with increasing data, for rapid simulation of transonic flowaround airfoils under various flow conditions. A lightweight and easily updatabledata-driven model is built to predict roughly correct flowfield, and the DGM is thenutilized as the CFD solver to refine the detailed flow structures and provide the corrected data. During the construction of the data-driven model, a zonal proper orthogonal decomposition (POD) method is designed to reduce the dimensionality of flowfield while preserving more near-wall flow features, and a weighted distance-basedradial basis function (RBF) is constructed to enhance the generalization capability offlowfield prediction. Numerical results demonstrate that the lightweight data-drivenmodel can predict the flowfield around a wide range of airfoils at Mach numbers ranging from 0.7 to 0.95 and angles of attack from $−5^◦$ to $5^◦$ by learning from sparse data,and maintains high accuracy of the location and essential features of flow structures(such as shock waves). In addition, the data-driven model enhanced DGM is ableto improve the computational efficiency and simulation robustness as compared tonormal DGMs in simulating transonic inviscid/viscous airfoil flowfields on arbitrarygrids, and further enables rapid aerodynamic evaluation of numerous sample pointsduring the surrogate-based aerodynamic optimization.