With the rapid development of data-driven methods in recent years, deep neural networks have attracted significant attention for aerodynamic predictions and design optimizations. Among these methods, the multi-fidelity deep neural network (MFDNN), which can combine high-fidelity (HF) and low-fidelity (LF) data, has gained popularity. This paper systematically investigates the performances of employing MFDNN models in predicting aerodynamic coefficients and in performing aerodynamic shape optimizations (ASOs), especially the impact of using various HF/LF data ratios for training models. The results of the prediction accuracy of the aerodynamic coefficients of airfoils show that the less HF data used, the more advantages can be achieved by the MFDNN models than the single-fidelity models. The well-trained MFDNN models are then employed in an ASO problem of airfoil in the subsonic regime, and it is found that a higher HF/LF data ratio does not definitely result in a better performance in the ASO. As the insufficiency in the prediction accuracy of the optimal shapes appears when employing the non-updated MFDNN models, an update strategy is developed by tightly integrating the MFDNN models with the particle swarm optimization algorithm. To further reduce the time costs for updating models, a dual-threshold update strategy is then introduced, which can half the counts of evaluating HF data.

One major problem in the development of hypersonic vehicles is severe aerodynamic heating; thus, the implementation of a thermal protection system is required. A numerical investigation on the reduction of aerodynamic heating using different thermal protection systems is conducted using a novel gas-kinetic BGK scheme. This method adopts a different solution strategy from the conventional computational fluid dynamics technique, and has shown a lot of benefits in the simulation of hypersonic flows. To be specific, it is established based on solving the Boltzmann equation, and the obtained gas distribution function is used to reconstruct the macroscopic solution of the flow field. Within the finite volume framework, the present BGK scheme is specially designed for the evaluation of numerical fluxes across the cell interface. Two typical thermal protection systems are investigated by using spikes and opposing jets, separately. Both their effectiveness and mechanisms to protect the body surface from heating are analyzed. The predicted distributions of pressure and heat flux, and the unique flow characteristics brought by spikes of different shapes or opposing jets of different total pressure ratios all verify the reliability and accuracy of the BGK scheme in the thermal protection system analysis.

To improve the capacity for utilizing a higher number of design variables and handling complex geometries in the class-shape-transformation parameterization method, this paper introduces an alternative for the shape function that employs radial basis functions to interpolate the deformations of the control points throughout the entire shape function. Two representative airfoils are parameterized first, and the results indicate that the presented method can avoid the ill-conditioning problem encountered when using high-order Bernstein polynomials in the traditional method. Moreover, it is more effective in parameterizing complex geometries. A comprehensive test on a database containing 1433 airfoils reveals that the presented method can cover a larger design space with an increase in the number of design variables. The presented method is further employed and validated in two typical aerodynamic shape optimization tasks: an airfoil inverse design and a benchmark problem for drag minimization in transonic viscous flow. The results suggest that the presented method has potential advantages in gaining better optimized results when more design variables are employed.