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旋转不变的数据驱动稀薄流非线性本构计算方法

蒋励剑,赵文文,陈伟芳,尧少波   

  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

摘要: 针对现有稀薄过渡区多尺度非平衡流动模拟中NS方程连续性假设失效、粒子类方法计算效率低、占用内存大等瓶颈问题,在保证过渡流区计算精度与计算效率的需求下,文献已构建了一种基于数据驱动非线性本构方程数值计算方法(DNCR, Data-driven Nonlinear Constitutive Relations)。DNCR方法基于NS方程和UGKS方法的数值模拟结果作为流场样本训练数据,借助机器学习构建热流/应力与流场特征参数的高维复杂非线性回归关系模型,最终通过耦合数据驱动的非线性本构关系求解宏观量守恒方程得到待预测稀薄非平衡流数值解。现有DNCR方法的特征参数(速度、压力、密度等)和标记值(热流、应力张量等)不具备旋转不变特征,所得训练模型无法适用于坐标系旋转或平移后的计算网格。本文针对这一缺陷,构建全新且具有旋转不变性的特征参数与标记值,并结合典型算例预测结果与特征参数权重反馈优化所有训练集特征参数;同时瞄准回归模型预示范围与泛化性能提升,针对极端随机树开展选参与调参研究,最终发展了一种基于旋转不变量的改进DNCR方法。针对不同来流条件、不同几何外形条件下的二维高超声速圆柱绕流与顶盖方腔驱动流,评估了改进DNCR方法对比原始方法的计算精度提升效果,计算结果表明:使用旋转不变量能够显著提升训练模型对坐标系旋转、外形变化的适应能力,使DNCR方法具备更好的泛化性能。

关键词: 稀薄非平衡流, 极端随机树, 旋转不变性, 泛化性能, 数据驱动

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.

Key words: rarefied non-equilibrium flow, extremely randomized trees, rotation invariance, generalization ability, data-driven