Petrov-Galerkin Model Reduction

Projection-based reduced-order models (ROMs) are a powerful tool for accelerating simulations of high-dimensional dynamical systems by projecting the governing equations onto a carefully chosen low-dimensional subspace. This reduces computational cost significantly while retaining the system’s essential dynamics.

Traditional ROMs typically rely on orthogonal (Galerkin) projection using energy-optimal bases such as Proper Orthogonal Decomposition (POD). In more challenging systems, low-energy directions can still influence the dynamics and affect accuracy. Oblique (Petrov-Galerkin) projection uses distinct trial and test spaces, providing additional flexibility for stable and accurate reduced models.

Application to Nonequilibrium Flows

Simulating thermochemical nonequilibrium flows poses significant challenges due to the high dimensionality introduced by detailed, state-specific kinetics. While full state-to-state (StS) models provide the highest physical accuracy, they are computationally intractable when embedded directly into multidimensional solvers.

To address this, I worked on a reduced-order modeling strategy based on an extension of the CoBRAS framework, a method that constructs oblique projection operators for nonlinear systems by balancing statistical information from both forward and adjoint trajectories.

In this work, the ROM is first built and tested in zero-dimensional settings, then integrated into a finite-volume solver for multidimensional simulations. The goal is to produce efficient surrogate models that preserve the relevant physical behavior.

📚 Selected Publications

I. Zanardi, A. Padovan, D. J. Bodony, and M. Panesi.
“Petrov‑Galerkin model reduction for thermochemical nonequilibrium gas mixtures”.
In: Journal of Computational Physics 533 (Apr. 2025).
DOI

I. Zanardi, A. Meini, A. Padovan, D. J. Bodony, and M. Panesi.
“Petrov‑Galerkin model reduction for collisional‑radiative argon plasma”.
In: Physics of Plasmas 33 (Jan. 2026).
DOI