标题： Petrov-Galerkin 降阶模型用于碰撞-辐射氩等离子体 显示英文标题

标题： Petrov-Galerkin model reduction for collisional-radiative argon plasma

摘要： 高保真非平衡等离子体模拟——对电推进、高超音速再入和天体物理流动应用至关重要——需要特定状态的碰撞辐射（CR）动力学模型，但这些模型计算成本很高。传统上，通过经验或基于物理的控制方程简化来减轻这种成本。然而，这些方法通常无法保留原始动力学的基本特征，特别是在强非平衡条件下。为了解决这些限制，我们开发了一种基于斜投影的Petrov-Galerkin降阶模型（ROM），用于CR氩等离子体，该模型最优地平衡了全阶状态轨迹与系统输出灵敏度的协方差。这种构建确保了ROM既捕捉到主要能量模式，又捕捉到对输入输出行为最相关的方向。在零维环境下使用非线性前向和伴随模拟进行离线训练后，ROM被耦合到有限体积求解器中，并应用于一维（1D）和二维（2D）电离激波管问题。该ROM实现了状态维度3$\times$的减少，并在浮点运算上节省了超过一个数量级，同时保持宏观量的误差低于1%。在1D和2D中，它能够稳健地再现复杂的非定常等离子体特征——如周期性波动、电子雪崩、三重点和细胞状电离模式——与标准ROM策略不同，在这些具有挑战性的条件下，标准ROM会变得不稳定或不准确。这些结果表明，所提出的基于投影的ROM能够在保持非平衡等离子体物理中的关键物理机制的同时实现显著的模型压缩，为高速等离子体流动的快速、可靠模拟铺平了道路。 显示英文摘要

摘要： High-fidelity simulation of nonequilibrium plasmas -- crucial to applications in electric propulsion, hypersonic re-entry, and astrophysical flows -- requires state-specific collisional-radiative (CR) kinetic models, but these come at a prohibitive computational cost. Traditionally, this cost has been mitigated through empirical or physics-based simplifications of the governing equations. However, such approaches often fail to retain the essential features of the original dynamics, particularly under strong nonequilibrium conditions. To address these limitations, we develop a Petrov-Galerkin reduced-order model (ROM) for CR argon plasma based on oblique projections that optimally balance the covariance of full-order state trajectories with that of the system's output sensitivities. This construction ensures that the ROM captures both the dominant energetic modes and the directions most relevant to input-output behavior. After offline training in a zero-dimensional setting using nonlinear forward and adjoint simulations, the ROM is coupled to a finite-volume solver and applied to one- (1D) and two-dimensional (2D) ionizing shock-tube problems. The ROM achieves a 3$\times$ reduction in state dimension and more than one order of magnitude savings in floating-point operations, while maintaining errors below 1% for macroscopic quantities. In both 1D and 2D, it robustly reproduces complex unsteady plasma features -- such as periodic fluctuations, electron avalanches, triple points, and cellular ionization patterns -- in contrast to standard ROM strategies, which become unstable or inaccurate under these challenging conditions. These results demonstrate that the proposed projection-based ROM enables substantial model compression while preserving key physical mechanisms in nonequilibrium plasma physics, paving the way for fast, reliable simulation of high-speed plasma flows.