To overcome the defects of traditional rarefied numerical methods such as the Direct Simulation Monte Carlo (DSMC) method and unified Boltzmann equation schemes and extend the covering range of macroscopic equations in high Knudsen number flows, data-driven nonlinear constitutive relations (DNCR) are proposed first through the machine learning method. Based on the training data from both Navier-Stokes (NS) solver and unified gas kinetic scheme (UGKS) solver, the map between responses of stress tensors and heat flux and feature vectors is established after the training phase. Through the obtained off-line training model, new test cases excluded from training data set could be predicated rapidly and accurately by solving conventional equations with modified stress tensor and heat flux. Finally, conventional one-dimensional shock wave cases and two-dimensional hypersonic flows around a blunt circular cylinder are presented to assess the capability of the developed method through various comparisons between DNCR, NS, UGKS, DSMC and experimental results. The improvement of the predictive capability of the coarse-graining model could make the DNCR method to be an effective tool in the rarefied gas community, especially for hypersonic engineering applications.
The efficient and accurate prediction of the aeroheating performance of hypersonic vehicles is a challenging task in the thermal protection system structure design process, which is greatly affected by grid distribution, numerical schemes, and iterative steps. From the inspiration of the theoretical analysis and machine learning strategy, a new wall heat flux prediction framework is proposed first by establishing the relationship between the wall heat flux and the flow variables at an extreme temperature point (ETP) in the normal direction of the corresponding wall grid cell, which is named the machine learning (ML)-ETP method. In the training phase, the flow properties and their gradients at the ETP and the distance from the ETP normal to the wall are employed as feature values, and the accurate wall heat flux predicted by the converged fine grid is regarded as the tag value. With the assistance of the trained regression model, the heat flux of the same configuration with a coarse grid in the wall-normal direction could be predicted accurately and efficiently. Moreover, test cases of different configurations and inflow conditions with a coarse grid are also carried out to assess the model’s generalization performance. All comparison results demonstrate that the ML-ETP strategy could predict wall heat flux more rapidly and accurately than the traditional numerical method due to its nonstrict grid distribution requirements. The improvement of the predictive capability of the coarse-graining model could make the ML-ETP method an effective tool in hypersonic engineering applications, especially for unsteady ablation simulations or aerothermal optimizations.
Aerodynamic thermal prediction plays an important role in the design of hypersonic aircraft, especially in the design of the aircraft’s thermal protection system. The main challenges of the aerothermal prediction lie in the slow converging speed and the strict requirements of the computational grid. In this paper, a convolutional-neural-network-based hybrid-features deep-learning strategy is constructed to efficiently predict aerodynamic heating, which is named the convolutional neural network/hybrid-feature method. The hybrid features of this strategy consist of the normal distribution of physical quantities from the wall and the flow parameters at the extreme temperature point. The strategy, which extends through the multilayer perceptron regression layer method, constructs the relationship between the hybrid features and the wall heat flux to obtain a high-precision model trained by the flowfield data without gradient convergence. It is demonstrated that the model has a better inflow generalization ability to predict wall heat flux with different inflow conditions and angles of attack by zero-angle-of-attack training data, which has great potential in aircraft thermal protection system design and shape optimization.
To further improve the efficiency of the unified gas-kinetic wave-particle (UGKWP) method in hypersonic rarefied non-equilibrium flows, particularly the particle simulation process, we presented the first application of the three-dimensional UGKWP method to multiple graphics processing unit (GPU) devices in this study. The wave and particle evolution components of the method are addressed using cell and particle paralleling strategies, respectively, enabling the primary loop of the GPU-based UPKWP (GPU-UGKWP) to be executed entirely by the compute unified device architecture threads on GPU devices. Concurrently, communication issues between central processing unit (CPU) nodes are resolved by employing the message passing interface model. Additionally, we introduce a tailored memory management scheme for the GPU-UGKWP method, facilitating efficient access to the particle array. Performance comparisons reveal that, relative to a single Intel Xeon Gold 6148 CPU core, the Nvidia Tesla P100 achieves a total speedup of 34 using one GPU device, and 226 with eight GPU devices, and a single Nvidia Titan V GPU device attains a speedup of 62. The speedup outcomes on multiple CPU cores and GPU devices demonstrate that the GPU-based algorithm is better suited for computationally demanding tasks, particularly in particle-dominated simulations. As evidenced by the reduced calculation time for a hypersonic technology vehicle simulation performed on the P100 cluster, GPU devices significantly outperform their CPU counterparts.
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