近年兴起的非线性耦合本构关系模型对于临近空间高超声速飞行器气动力预测具有一定的研究潜力与工程应用价值，然而对于特定条件的经典稀薄问题仍存在着线性化精度不足、碰撞频率修正过大、反向热流预测不准等不足。本项目将围绕传统矩方程的奇异“子激波”固有缺陷及修正方案，拟基于广义流体动力学Eu方程开展深入的理论分析和严谨数学推导，厘清Eu碰撞项累积量展开的推导过程，通过对Eu非平衡分布函数进行Chapmann-Enskog小扰动展开，构建一套新型广义流体动力学正则化封闭理论，完成Eu矩方程的高阶封闭和高阶矩本构建模，解决原有本构模型的准确性和适用范围问题，同时建立正则化Eu十三矩方程和高阶正则化非线性本构模型的有限体积计算方法，进一步提升对跨流域高超声速流动和飞行器气动特性的预示精度。

Nonlinear coupled constitutive relations model emerged in the recent years has certain research potential and engineering application value for aerodynamic prediction of hypersonic vehicles in near space. However, the model still suffers from the insufficient linearization accuracy, excessive correction of collision frequency, and inaccurate prediction of reverse heat flow in the classical rarefied problems under certain conditions. In this proposal, we will focus on the inherent defect of the “sub-shock” singularity problem encountered by the traditional moment equations and its correction scheme, and conduct in-depth theoretical analysis and rigorous mathematical derivation from Eu’s generalized hydrodynamic equations to clarify the mathematical derivation of the cumulant approximation of the Eu collision term. It is planned that, through the Chapmann-Enskog small perturbation expansion around the Eu’s non-equilibrium distribution manifold, a new regularization theory of generalized hydrodynamic equations is constructed to complete the high-order closure of Eu’s moment equations and the constitutive modeling for high-order moments, solving the problems related to the accuracy and validation scope of the original constitutive model. Meanwhile, the finite-volume computational method of Eu’s regularized 13 moment equations and the high-order regularized nonlinear constitutive model is established to further improve the accuracy of the prediction of the hypersonic flows and the aerodynamic characteristics of the hypersonic vehicle across the whole flow regimes.