Petrov-galerkin model reduction for nonequilibrium plasma simulations

Accurate simulation of nonequilibrium plasmas—central to applications in hypersonic re-entry, fusion energy, and astrophysical flows—requires state-specific collisional-radiative (CR) kinetic models, but the associated computational cost is often prohibitive. While traditional approaches reduce this burden through empirical or physics-based simplifications, they frequently compromise accuracy in strongly nonequilibrium regimes. 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 flow 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 the potential of the proposed model reduction strategy to enable high-fidelity simulation of reactive plasma flows at reduced computational cost, offering new capabilities for exploring high-speed fluid systems governed by coupled transport, wave propagation, and kinetic nonequilibrium.