### Numerical method of data-driven rarefied nonlinear constitutive relations coupled with clustering

• Received:2022-06-30 Revised:2022-09-20 Online:2022-09-22 Published:2022-09-22

Abstract: Owing to the rarefied nonequilibrium effect encountered in near space environment, the existing numerical methods are difficult to describe the multi-scale flow phenomena efficiently and accurately at the same time. By integrating the machine learning methods rising in recent years, Data-driven nonlinear constitutive relations (DNCR) paved a new way for solving the nonequilibrium problem as a data-driven modeling approach. In order to further improve the generalization capability and model training efficiency of the DNCR method, Gaussian Mixture Model (GMM) and Sparse Principal Component Analysis (SPCA) for preprocessing the data of training set and prediction set are introduced into DNCR method for the first time in this paper. The prediction results of relevant cases show that the dominant parameters in different flow fields are extracted by GMM and SPCA without relying on artificial experience, which could improve the interpretability and robustness of DNCR. On the other hand, GMM and SPCA can accurately cluster the data points under a large number of flow field samples to eliminate the interference of redundant information and reduce the training and prediction time of the regression model, which is crucial to the updating and maintenance of the model when adding new sample data in future. For prediction accuracy, the coupled DNCR could improve the computational efficiency without losing accuracy in simple flows and further elevate the precision significantly in complex flows coupled with different flow characteristics.