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 flow around airfoils under various flow conditions. A lightweight and easily updatable data-driven model is built to predict roughly correct flowfield, and the DGM is then utilized 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-based radial basis function (RBF) is constructed to enhance the generalization capability of flowfield prediction. Numerical results demonstrate that the lightweight data-driven model 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 able to improve the computational efficiency and simulation robustness as compared to normal DGMs in simulating transonic inviscid/viscous airfoil flowfields on arbitrary grids, and further enables rapid aerodynamic evaluation of numerous sample points during the surrogate-based aerodynamic optimization.