AI 中文总结
本研究提出带激波捕获的PASSC框架，结合SUPG、YZβ激波捕获技术与PINN，模拟马赫数2.0-12.0的圆柱绕流，提升激波数值表征精度。
AI 中文摘要
本研究提出一种混合计算框架，用于模拟氮气（N₂）绕圆柱的无反应无粘高速流动。由于可压缩欧拉方程具有强对流主导特性，研究将可压缩流动流线迎风/Petrov-Galerkin（SUPG）格式与YZβ激波捕获技术结合，以在强间断存在时稳定有限元离散化。基于稳定化解，采用物理信息神经网络（PINN）作为后处理校正阶段（带激波捕获的PINN增强SUPG——PASSC）。该网络通过激波加权数据一致性损失锚定有限元解，同时以保守时空控制体积形式控制方程，辅以宏观守恒窗口、熵容许惩罚项及基础问题的边界条件。对自由来流马赫数2.0至12.0的二维流动进行模拟，结果与解析正激波及滞止关系、半经验Billig关联式及文献参考解进行评估。该校正旨在通过减少局部离散诱导振荡和网格尺度锯齿，同时保持稳定化解与解析及半经验参考量的一致性，以改进激波的数值表征。
英文摘要
This study presents a hybrid computational framework for simulating non-reacting inviscid high-speed flows of nitrogen gas (N$_2$) around a circular cylinder. Owing to the strongly convection-dominated nature of the compressible Euler equations, the compressible-flow streamline-upwind/Petrov--Galerkin (SUPG) formulation is combined with the YZ$β$ shock-capturing technique to stabilize the finite element discretization in the presence of strong discontinuities. Building upon the stabilized solution, a physics-informed neural network (PINN) is employed as a post-processing correction stage (\underline{P}INN-\underline{A}ugmented \underline{S}UPG with \underline{S}hock-\underline{C}apturing---PASSC). The network is anchored to the finite element solution through a shock-weighted data-consistency loss, while the governing equations are enforced in a conservative space--time control-volume form supplemented by macroscopic conservation windows, an entropy-admissibility penalty, and the boundary conditions of the underlying problem. Two-dimensional simulations are performed for free-stream Mach numbers ranging from $2.0$ to $12.0$, and the results are assessed against analytical normal-shock and stagnation relations, the semi-empirical Billig correlation, and reference solutions from the literature. The correction is designed to improve the numerical representation of shocks by reducing localized discretization-induced oscillations and mesh-scale serrations while preserving the agreement of the stabilized solution with the analytical and semi-empirical reference quantities.
