稀薄非平衡流域内连续介质假设已经失效，主要围绕Boltzmann方程及模型方程对稀薄非平衡流开展理论与计算研究，统一气体动理论格式（UGKS）是其中一种代表性方法。在稀薄非平衡流数值模拟中，Navier-Stokes （N-S）方程连续介质假设已经失效，不能有效描述流场非平衡特征。UGKS方法虽然计算精度高，但速度空间离散导致计算效率低下，多维高速条件下数值计算难以开展。基于数据驱动的思想，在N-S方程与UGKS方法的研究基础上发展出了一种稀薄非平衡流非线性本构关系求解方法（DNCR）。该方法以N-S与UGKS求解器获得的流场数值模拟计算结果作为训练数据集，基于流场特征参数采用极端随机树算法生成机器学习模型，对预测流场中线性黏性应力项与热流项进行非线性修正，并耦合非线性本构关系求解宏观守恒方程得到目标状态稀薄非平衡流动数值解。针对DNCR方法中所采用的机器学习方法-极端随机树模型，通过二维顶盖驱动方腔流算例对高维非线性建模涉及的特征参数选取、参数调优开展了相关验证工作，选取若干典型状态对极端随机树模型的泛化性能开展研究，并评估了相关模型与方法的计算精度与计算效率。
The continuum medium hypothesis in the rarefied non-equilibrium flow field has been invalid, and the rarefied non-equilibrium flow is mainly researched around the Boltzmann equation with the Unified Gas-Kinetic Scheme (UGKS) as a representative method. In numerical simulation of the rarefied non-equilibrium flow, the Navier-Stokes (N-S) equation has high efficiency but low accuracy while the UGKS method has high accuracy but low efficiency. In this paper, a Data-driven method for the solution of the Nonlinear Constitutive Relations of the rarefied non-equilibrium flow based on the N-S equation and the UGKS method (DNCR) is proposed. The flow field numerical simulation results of the N-S solver and the UGKS solver are used as the data set. Based on the characteristic parameters of the flow field, an extremely randomized trees algorithm is adopted to nonlinearly correct the linear viscous stress term and heat flux term of the N-S equation. The numerical solution of the rarefied non-equilibrium flow is obtained by solving the N-S macro-conservation equation via coupling nonlinear constitutive relations. A two-dimensional lid-driven cavity case is used to select and tune the characteristic parameters involved in high-dimensional non-linear modeling. Several typical states are selected for the study of the generalization ability of the extremely randomized trees model. Finally, the evaluation of calculation accuracy and efficiency shows the superiority of the method proposed in this paper.
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