### 旋转不变的数据驱动稀薄流非线性本构计算方法

1. 浙江大学
• 收稿日期:2021-08-20 修回日期:2021-10-12 出版日期:2021-10-14 发布日期:2021-10-14
• 通讯作者: 赵文文
• 基金资助:
国家数值风洞项目;国家自然科学基金

### Data-driven rarefied nonlinear constitutive relations based on rotation invariants

• Received:2021-08-20 Revised:2021-10-12 Online:2021-10-14 Published:2021-10-14

Abstract: In order to overcome the defects of current numerical methods in transitional flow simulation such as the failure of continuum assumption in NS equation, the low computational efficiency and large memory occupation of particle method, a new numerical method based on data driven nonlinear constitutive relations (DNCR) has been proposed in literatures. Based on the numerical results of NS equation and UGKS method as the training data of flow field samples, the DNCR method constructs a high-dimensional complex nonlinear regression model of heat flux/stress tensor and flow field characteristic parameters. Finally, the macro conservation equations are solved by coupling data-driven nonlinear constitutive relations, and the numerical solution of the rarefied non-equilibrium flow to be predicted is obtained. However, not all features (velocity, pressure, density, etc.) and outputs (heat flow, stress tensor, etc.) of the existing DNCR method are rotation invariants and therefore the training model cannot be applied directly when coordinate system rotating or translating. Aiming at this defect, this paper constructs a set of new features and outputs with rotation invariant assumption, and optimizes all the features of training set by combining the prediction results of typical examples and the weight feedback. At the same time, aiming at the improvement of prediction range and generalization performance of regression model, the research of selecting and optimizing parameters for extreme random tree is also carried out, and finally proposed an improved DNCR based on rotation invariants. The improvement of the new method is evaluated by two-dimensional hypersonic flow around cylinder and lid driven flow under different flow conditions and different configurations compared with the original one. The results show that the use of rotation invariants can significantly improve the training model's ability to adapt to coordinate system rotation and shape changes, and make the DNCR have better generalization ability.