This work presents a Streamline-Upwind Petrov–Galerkin (SUPG) framework with finite elements discretization for the prediction of non-ionized hypersonic flows in thermal non-equilibrium. The formulation is enhanced with a residual-based discontinuity-capturing (DC) operator. The numerical framework solves the set of Navier–Stokes equations for the compressible reacting flows with an additional equation for the vibrational–electronic energy conservation. The set of equations, which involves one continuity equation for each chemical species considered, is solved in the pressure-primitive variables. The numerical framework capabilities are assessed through several benchmark cases, including validation of the chemical model and its coupling with the two-temperature model in the context of critical flow features such as shock–shock and shock wave–boundary layer interactions. The accuracy of the results is assessed through the comparison with the numerical and experimental data available in the literature for all the test cases presented. The numerical results demonstrate the suitability of the formulation in predicting non-ionized reacting hypersonic flows in thermal non-equilibrium.

这项工作提出了一种具有有限元离散化的 Streamline-Upwind Petrov-Galerkin (SUPG) 框架，用于预测热非平衡中的非电离高超声速流动。该公式通过基于残差的不连续捕获 (DC) 算子得到增强。数值框架解决了可压缩反应流的 Navier-Stokes 方程组和振动-电子能量守恒的附加方程。方程组，其中每个方程都包含一个连续性方程所考虑的化学物种，在压力原始变量中求解。数值框架能力通过几个基准案例进行评估，包括在冲击-冲击和冲击波-边界层相互作用等关键流动特征的背景下验证化学模型及其与双温度模型的耦合。通过与文献中提供的所有测试用例的数值和实验数据进行比较，评估结果的准确性。数值结果表明该公式适用于预测热非平衡中的非电离反应高超声速流。