Petrov-Galerkin model reduction for collisional-radiative argon plasma

TL;DR

This paper introduces a Petrov-Galerkin reduced-order model for collisional-radiative argon plasma that significantly reduces computational costs while accurately capturing complex plasma dynamics in high-speed flow simulations.

Contribution

The paper develops a novel Petrov-Galerkin ROM that balances state trajectories and sensitivities, enabling efficient and accurate simulation of nonequilibrium plasmas.

Findings

3x reduction in state dimension

Over 10x decrease in computational effort

Errors below 1% in key quantities

Abstract

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.