arXiv subjects

Daniel J. Bodony

Publications and source records attributed to Daniel J. Bodony.

12 recordsLinked to original sources

arXiv2026

From Coils to Surface Recession: Multiphysics Simulation of Ablation in ICP Wind Tunnels

This work presents a multi-solver, coupled computational framework for predicting the thermo-chemical material response of thermal protection systems in inductively coupled plasma (ICP) wind tunnels. The framework integrates a high-fidelity Navier-Stokes plasma solver, an electromagnetic field solver, and a discontinuous-Galerkin material response solver using a partitioned coupling strategy. This enables an ab initio, end-to-end simulation of the 350 kW Plasmatron X facility at the University of Illinois Urbana-Champaign (UIUC), including plasma generation, electromagnetic heating, near-wall thermochemistry, and time-accurate material ablation. The model captures key ICP physics such as vortex-mode recirculation, Joule-heating-driven plasma formation, and Lorentz-force-induced flow confinement, and accurately predicts the transition from subsonic to supersonic jet behavior at low pressures. Validation against cold-wall calorimetry shows that predicted stagnation-point cold-wall heat fluxes fall well within experimental uncertainty, while coupled ablation simulations accurately reproduce measured stagnation temperature histories and recession rates with errors below 12% and 10%, respectively. Remaining discrepancies are attributed to uncertainties in power-coupling efficiency, equilibrium ablation modeling, and material property datasets. Sensitivity analyses reveal that a 10% variation in system efficiency can induce changes of up to 11% in steady- state surface temperature and 17% in recession rate, whereas an equivalent variation in material thermal conductivity results in comparatively minor deviations of about 1.5% and 0.5%, respectively. Overall, the framework demonstrates strong predictive capability for ICP wind tunnel environments and provides a foundation for improved design, interpretation, and planning of hypersonic material testing campaigns.

physics.plasm-ph↗

arXiv2026

Beyond classical similitude: group theoretic extrapolation of hypersonic stagnation-point boundary layers

Motivated by the need to extrapolate the results from ground-based experiments to the conditions of high-speed flight, we present the Lie equivalence symmetry analysis of the hypersonic stagnation-point boundary layers. We demonstrate the application of the equivalence symmetry on the set of coupled ODEs which are physically relevant in hypersonics. By allowing the property laws to transform along with the independent and dependent variables, the invariants derived within the similarity-reduced stagnation-point ODE formulation identify families of non-linear maps that can be used to extrapolate the laboratory-scale predictions to flight. In practice, implementing these maps requires the laboratory-scale ODE solution together with the lab- and flight-side thermochemical property data, which are generally available from existing databases. The maps are derived for the similarity-reduced non-dimensional temperature across the boundary layer and are shown to {collapse with independently computed flight solutions} for a range of relevant cases.

physics.flu-dyn↗

arXiv2026

GasNiTROM: Model Reduction via Non-Intrusive Optimization of Oblique Projection Operators and Guaranteed-Stable Latent-Space Dynamics

Non-intrusive reduced-order modeling techniques are necessary for systems that are simulated using black-box solvers or known only from data. For systems exhibiting large transients and operating far away from equilibria, current non-intrusive models often exhibit poor forecasting accuracy and can even be unstable in infinite or finite time. Recent developments have addressed the stability issue by seeking structure-preserving latent-space architectures when reducing Hamiltonian or Lagrangian full-order dynamics, or by enforcing global stability via Lyapunov-informed parameterizations in the latent space. However, such developments do not necessarily improve the forecasting accuracy of the resulting models, since these formulations achieve dimensionality reduction using orthogonal projections that accidentally truncate dynamically-important states. In this paper, we address both issues by introducing a non-intrusive framework designed to simultaneously identify globally-asymptotically-stable latent-space dynamics, and oblique projection operators capable of capturing the sensitivity mechanisms of the system. In particular, given a Lyapunov-based parameterization of the latent-space tensors, and a matrix-manifold parameterization of the oblique projection operators, we fit a model against high-fidelity training trajectories. Furthermore, we show that the gradient of the objective function can be written in closed form using adjoint-based backpropagation in the latent space, eliminating the need for automatic differentiation. We compare our formulation with state-of-the-art methods on a three-dimensional system of ordinary differential equations, and a two-dimensional lid-driven cavity flow at Reynolds number Re=8300. We demonstrate that our models are not only globally asymptotically stable (as expected by construction), but they are also significantly more accurate.

math.NA↗

arXiv2026

Resolvent4py: a parallel Python package for analysis, model reduction and control of large-scale linear systems

In this paper, we present resolvent4py, a parallel Python package for the analysis, model reduction and control of large-scale linear systems with millions or billions of degrees of freedom. This package provides the user with a friendly Python-like experience (akin to that of well-established libraries such as numpy and scipy), while enabling MPI-based parallelism through mpi4py, petsc4py and slepc4py. In turn, this allows for the development of streamlined and efficient Python code that can be used to solve several problems in fluid mechanics, solid mechanics, graph theory, molecular dynamics and several other fields.

physics.comp-ph↗

arXiv2025

Surface instabilities in laminar compressible boundary layers with sublimation

Surface patterns on ablating materials are observed in high-speed ground and flight tests, but the mechanisms behind their formation are not known. In this paper, the origin of surface patterns is investigated via a local linear stability analysis of compressible laminar boundary layers over a flat camphor plate. The effects of sublimation and conjugate heat transfer are included both on the baseflow and the linear fluctuations. This framework identifies one mode that fully characterizes the stability of the surface, which becomes unstable when the wall temperature exceeds that of an adiabatic wall, $T_{ad}$. These findings are consistent with experimental observations, where laminar flow conditions at adiabatic wall temperatures are found to be stable. The analysis also reveals that the nature of this surface mode varies as a function of the oblique angle $ψ= \tan^{-1}{β/α}$, where $α$ and $β$ are the streamwise and spanwise wavenumbers. Specifically, for baseflow temperatures below $\approx 1.15~T_{ad}$, the surface mode is most unstable at $ψ= 0$. Conversely, above $\approx 1.15~T_{ad}$ the surface is most unstable near the sonic angle $ψ_s = \cos^{-1}(1/M_e)$, which is the angle at which the normal Mach number equals one. Finally, a critical wavenumber is identified (i.e., one at which the temporal growth rate reaches a maximum) that is in good agreement with available experimental observations of turbulent flows.

physics.flu-dyn↗

arXiv2025

Petrov-Galerkin model reduction for collisional-radiative argon plasma

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.

physics.comp-ph↗

arXiv2024

Petrov-Galerkin model reduction for thermochemical nonequilibrium gas mixtures

State-specific thermochemical collisional models are crucial to accurately describe the physics of systems involving nonequilibrium plasmas, but they are also computationally expensive and impractical for large-scale, multi-dimensional simulations. Historically, computational cost has been mitigated by using empirical and physics-based arguments to reduce the complexity of the governing equations. However, the resulting models are often inaccurate and they fail to capture the important features of the original physics. Additionally, the construction of these models is often impractical, as it requires extensive user supervision and time-consuming parameter tuning. In this paper, we address these issues through an easily-implementable and computationally-efficient model reduction pipeline based on the Petrov-Galerkin projection of the nonlinear kinetic equations. Our approach is justified by the observation that kinetic systems in thermal nonequilibrium tend to exhibit low-rank dynamics that rapidly drive the state towards a low-dimensional subspace. Furthermore, despite the nonlinear nature of the governing equations, we observe that the dynamics of these systems evolve on subspaces that can be accurately identified using the linearized equations about thermochemical equilibrium, which significantly reduce the cost associated with the construction of the model. The approach is demonstrated on a rovibrational collisional model for the O$_2$-O system, and a vibrational collisional model for the combined O$_2$-O and O$_2$-O$_2$ systems. Our method achieves high accuracy, with relative errors of less than 1% for macroscopic quantities (i.e., moments) and 10% for microscopic quantities (i.e., energy levels population), while also delivering excellent compression rates and speedups, outperforming existing state-of-the-art techniques.

physics.comp-ph↗

arXiv2024

Data-driven model reduction via non-intrusive optimization of projection operators and reduced-order dynamics

Computing reduced-order models using non-intrusive methods is particularly attractive for systems that are simulated using black-box solvers. However, obtaining accurate data-driven models can be challenging, especially if the underlying systems exhibit large-amplitude transient growth. Although these systems may evolve near a low-dimensional subspace that can be easily identified using standard techniques such as Proper Orthogonal Decomposition (POD), computing accurate models often requires projecting the state onto this subspace via a non-orthogonal projection. While appropriate oblique projection operators can be computed using intrusive techniques that leverage the form of the underlying governing equations, purely data-driven methods currently tend to achieve dimensionality reduction via orthogonal projections, and this can lead to models with poor predictive accuracy. In this paper, we address this issue by introducing a non-intrusive framework designed to simultaneously identify oblique projection operators and reduced-order dynamics. In particular, given training trajectories and assuming reduced-order dynamics of polynomial form, we fit a reduced-order model by solving an optimization problem over the product manifold of a Grassmann manifold, a Stiefel manifold, and several linear spaces (as many as the tensors that define the low-order dynamics). Furthermore, we show that the gradient of the cost function with respect to the optimization parameters can be conveniently written in closed-form, so that there is no need for automatic differentiation. We compare our formulation with state-of-the-art methods on three examples: a three-dimensional system of ordinary differential equations, the complex Ginzburg-Landau (CGL) equation, and a two-dimensional lid-driven cavity flow at Reynolds number Re = 8300.

math-ph↗

arXiv2023

Multi-domain analysis and prediction of the light emitted by an inductively coupled plasma jet

Inductively coupled plasma wind tunnels are crucial for replicating hypersonic flight conditions in ground testing. Achieving the desired conditions (e.g., stagnation-point heat fluxes and enthalpies during atmospheric reentry) requires a careful selection of operating inputs, such as mass flow, gas composition, nozzle geometry, torch power, chamber pressure, and probing location along the plasma jet. The study presented herein focuses on the influence of the torch power and chamber pressure on the plasma jet dynamics within the 350 kW Plasmatron X ICP facility at the University of Illinois at Urbana-Champaign. A multi-domain analysis of the jet behavior under selected power-pressure conditions is presented in terms of emitted light measurements collected using high-speed imaging. We then use Gaussian Process Regression to develop a data-informed learning framework for predicting Plasmatron X jet profiles at unseen pressure and power test conditions. Understanding the physics behind the dynamics of high-enthalpy flows, particularly plasma jets, is the key to properly design material testing, perform diagnostics, and develop accurate simulation models

physics.plasm-ph↗

arXiv2023

An Extended B' Formulation for Ablating-Surface Boundary Conditions

The B' formulation can be understood as a mass and energy conservation formalism at a reacting singular surface. In hypersonics applications, it is typically used to compute the chemical equilibrium properties of gaseous mixtures at ablating surfaces, and to estimate the recession velocity of the interface. In the first half of the paper, we derive the B' formulation to emphasize first principles. In particular, while we eventually specialize to the commonly considered case of chemical equilibrium boundary layers that satisfy the heat and mass transfer analogy, we first derive a general interface jump condition that lets us highlight all the underlying assumptions of the well-known B' equations. This procedure helps elucidate the nature of the B' formalism and it also allows us to straightforwardly extend the original formulation. Specifically, when applied at the interface between a porous material and a boundary layer (as in thermal protection systems applications), the original formulation assumes unidirectional advective transport of gaseous species from the porous material to the boundary layer (i.e., blowing). However, under conditions that may appear in hypersonic flight or in ground-based wind tunnels, boundary layer gases can enter the porous material due to a favorable pressure gradient. We show that this scenario can be easily handled via a straightforward modification to the B' formalism, and we demonstrate via examples that accounting for gas entering the material can impact the predicted recession velocity of ablating surfaces. In order to facilitate the implementation of the extended B' formulation in existing material response codes, we present a short algorithm in section 5 and we also refer readers to a GitHub repository where the scripts used to generate the modified B' tables are publicly available.

physics.flu-dyn↗

arXiv2022

Adjoint-based Control of Three Dimensional Stokes Droplets

We develop a continuous adjoint formulation and implementation for controlling the deformation of clean, neutrally buoyant droplets in Stokes flow through farfield velocity boundary conditions. The focus is on dynamics where surface tension plays an important role through the Young-Laplace law. To perform the optimization, we require access to first-order gradient information, which we obtain from the linearized sensitivity equations and their corresponding adjoint by applying shape calculus to the space-time tube formed by the interface evolution. We show that the adjoint evolution equation can be efficiently expressed through a scalar adjoint transverse field. The optimal control problem is discretized by high-order boundary integral methods using Quadrature by Expansion coupled with a spherical harmonic representation of the droplet surface geometry. We show the accuracy and stability of the scheme on several tracking-type control problems.

physics.comp-ph↗

arXiv2019

Reduced-order control using low-rank Dynamic Mode Decomposition

In this work we perform full-state LQR feedback control of fluid flows using non-intrusive data-driven reduced-order models. We propose a model reduction method called low-rank Dynamic Mode Decomposition (lrDMD) that solves for a rank-constrained linear representation of the dynamical system. lrDMD is shown to have lower data reconstruction error compared to standard Optimal Mode Decomposition (OMD) and Dynamic Mode Decomposition (DMD), but with an increased computational cost arising from solving a non-convex matrix optimization problem. We demonstrate model order reduction on the complex linearized Ginzburg-Landau equation in the globally unstable regime and on the unsteady flow over a flat plate at a high angle of attack. In both cases, low-dimensional full-state feedback controller is constructed using reduced-order models constructed using DMD, OMD and lrDMD. It is shown that lrDMD stabilizes the Ginzburg-Landau system with a lower order controller and is able to suppress vortex shedding from an inclined flat plate at a cost lower than either DMD or OMD. It is further shown that lrDMD yields an improved estimate of the adjoint system, for a given rank, relative to DMD and OMD.

physics.flu-dyn↗