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DOE OSTI2022

The Schwarz Alternating Method for the Seamless Coupling of Nonlinear Reduced Order Models and Full Order Models

Projection-based model order reduction allows for the parsimonious representation of full order models (FOMs), typically obtained through the discretization of a set of partial differential equations (PDEs) using conventional techniques (e.g., finite element, finite volume, finite difference methods) where the discretization may contain a very large number of degrees of freedom. As a result of this more compact representation, the resulting projection-based reduced order models (ROMs) can achieve considerable computational speedups, which are especially useful in real-time or multi-query analyses. One known deficiency of projection-based ROMs is that they can suffer from a lack of robustness, stability and accuracy, especially in the predictive regime, which ultimately limits their useful application. Another research gap that has prevented the widespread adoption of ROMs within the modeling and simulation community is the lack of theoretical and algorithmic foundations necessary for the “plug-and-play” integration of these models into existing multi-scale and multi-physics frameworks. This paper describes a new methodology that has the potential to address both of the aforementioned deficiencies by coupling projection-based ROMs with each other as well as with conventional FOMs by means of the Schwarz alternating method [41]. Leveraging recent work that adapted the Schwarz alternating method to enable consistent and concurrent multiscale coupling of finite element FOMs in solid mechanics [35, 36], we present a new extension of the Schwarz framework that enables FOM-ROM and ROM-ROM coupling, following a domain decomposition of the physical geometry on which a PDE is posed. In order to maintain efficiency and achieve computation speed-ups, we employ hyper-reduction via the Energy-Conserving Sampling and Weighting (ECSW) approach [13]. We evaluate the proposed coupling approach in the reproductive as well as in the predictive regime on a canonical test case that involves the dynamic propagation of a traveling wave in a nonlinear hyper-elastic material.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Resolution requirements for energy conservation in kinetic plasma simulations

The kinetic codes used to model the coupled dynamics of electromagnetic fields and charged particle transport have requirements for spatial, temporal, and charge resolution. These requirements may vary by the solution technique and scope of the problem. In this report, we investigate the resolution limits in the energy-conserving implicit particle-in-cell code CHICAGO. This report has the narrow aim of determining the maximum acceptable grid spacing for the dense plasmas generated in models of z-pinch target gases and power-flow electrode plasmas. In the 2D sample problem, the plasma drifts without external forces with velocity of 10 cm/µs. Simulations are scaled by plasma density to maintain uniform strides across the plasma and from the plasma to the boundaries. Additionally, the cloud-in-cell technique is used with 400 particles per cell and Δ t = 0.85× the Courant limit. For the linear cloud distribution, the criterion for conserving energy is Δ E/E tot < 0.01 for 50,000 time steps. The grid resolution is determined to crudely be Δx ≲ 3 l s , where l s is the electron collisionless skin depth. For the second-order cloud distribution the criterion is Δ E/E tot < 0.005 yielding Δx ≤ 15 l s . These scalings are functions of the chosen v d , Δ t , particles-per-cell, and number of steps.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2026

User Manual - HydraGNN v5.0: Distributed Implementation of Multi-Tasking Graph Neural Networks

This document serves as the user manual for HydraGNN v5.0, a scalable graph neural network (GNN) architecture for simultaneous prediction of multiple target properties using multi-task learning (MTL). This version of HydraGNN has been developed primarily to support the development, training, and deployment of predictive graph-based deep learning (DL) models for atomistic materials modeling. HydraGNN is templated over 13 message-passing policies, including invariant models (GIN, PNA, PNAPlus, GAT, MFC, CGCNN, SAGE, SchNet, DimeNet) and equivariant models (EGNN, PNAEq, PAINN, MACE), and supports distributed training via distributed data parallelism (DDP), DeepSpeed, and Fully Sharded Data Parallelism (FSDP) on leadership-class supercomputers. Although HydraGNN can be applied to problems beyond atomistic materials modeling, its current use is confined to homogeneous graphs. Additional capabilities include machine-learned interatomic potentials with energy-conserving forces, General, Powerful, and Scalable Graph Transformer (GraphGPS) global attention, periodic boundary conditions, hyperparameter optimization, mixed-precision training, and uncertainty quantification.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

Catalytic Bias of NADH-Dependent Reduced Ferredoxin: NADP+ Oxidoreductase (Nfn) and its Relevance to Ethanol Production in Thermoanaerobacterium Saccharolyticum

NADH-dependent reduced ferredoxin: NADP+ oxidoreductase (Nfn) enzyme catalyzes an energy-conserving flavin-based electron bifurcation (FBEB) reaction. In microbial metabolism, Nfn links redox pools of three electron carriers - ferredoxin (Fd), NAD(H), and NADP(H) - through the following FBEB reaction: 2 NADPH + NAD+ + 2 Fdox 2 NADP+ + NADH + 2 Fdred + H+ The forward reaction is termed electron bifurcation, and the reverse reaction is electron confurcation. Catalytic bias describes an enzyme's tendency to favor one direction of a reversible reaction over the other and is expressed as the ratio of activities in the two directions. Thermoanaerobacterium saccharolyticum (Tsac) is a thermophilic, ethanologenic bacterium that ferments hemicellulose to ethanol at yields above 90%. Its Nfn enzyme is known to support ethanol production, presumably by operating in the confurcating direction to balance cellular cofactors, but this has not previously been demonstrated. To investigate the Tsac Nfn further, we heterologously expressed, purified, and reconstituted the proteins NfnS (NfnA), NfnL (NfnB), and the putative partner Fd with iron-sulfur cluster and/or FAD cofactors. Activity assays monitoring the oxidation or reduction of Fd showed that, across pH 5-10, Tsac Nfn is catalytically biased towards the confurcating direction, favoring NADPH generation over NADPH oxidation by at least fivefold. Using protein electrochemistry, we also determined the reduction potentials of the cofactors in NfnL and Fd. These results indicate that the energetic landscape of FBEB in Tsac Nfn is similar to that in an ortholog. However, Tsac Fd has redox properties distinct from previously assayed Fds, suggesting that the identity and redox properties of Fd may help determine the catalytic bias of Nfn. Additionally, we confirmed the standalone ferredoxin: NADP+ oxidoreductase (FNOR) activity of NfnL but found it to be low and likely insignificant for in vivo redox conversion. We also show how the catalytic bias of Nfn integrates with the hydrogen cycling mechanism proposed in Tsac to better explain cofactor balancing for ethanol production. Our work advances the understanding of electron transfer processes within metabolic networks for the generation of valuable bioproducts.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1974

The MIST /MIUS Integration and Subsystems Test/ laboratory - A testbed for the MIUS /Modular Integrated Utility System/ program

The MIUS (Modular Integrated Utility System) concept is to be an energy-conserving, economically feasible, integrated community utility system to provide five necessary services: electricity generation, space heating and air conditioning, solid waste processing, liquid waste processing, and residential water purification. The MIST (MIUS Integration and Subsystem Test) integrated system testbed constructed at the Johnson Space Center in Houston includes subsystems for power generation, heating, ventilation, and air conditioning (HVAC), wastewater management, solid waste management, and control and monitoring. The key design issues under study include thermal integration and distribution techniques, thermal storage, integration of subsystems controls and displays, incinerator performance, effluent characteristics, and odor control.

Beckham, W. S., Jr.↗

NASA NTRS1975

Nonlinear hyperbolic theory of thermal waves in metals

A closed-form solution for cylindrical thermal waves in metals is given based on the nonlinear hyperbolic system of energy-conservation and heat-flux relaxation equations. It is shown that heat released from a line source propagates radially outward with finite speed in the form of a thermal wave which exhibits a discontinuous wave front. Unique nonlinear thermal-wave solutions exist up to a critical amount of driving energy, i.e., for larger energy releases, the thermal flow becomes multivalued (occurrence of shock waves). By comparison, it is demonstrated that the parabolic thermal-wave theory gives, in general, a misleading picture of the profile and propagation of thermal waves and leads to physical (infinite speed of heat propagation) and mathematical (divergent energy integrals) difficulties. Attention is drawn to the importance of temporal heat-flux relaxation for the physical understanding of fast transient processes such as thermal waves and more general explosions and implosions.

Wilhelm, H. E.↗

NASA NTRS1978

A review of NASA's propulsion programs for civil aviation

Five NASA engine-oriented propulsion programs of major importance to civil aviation are presented and discussed. Included are programs directed at exploring propulsion-system concepts for (1) energy-conservative subsonic aircraft (improved current turbofans, advanced turbofans, and advanced turboprops), (2) supersonic cruise aircraft (variable-cycle engines), (3) general aviation aircraft (improved reciprocating engines and small gas turbines), (4) powered-lift aircraft (advanced turbofans), and (5) advanced rotorcraft. These programs reflect the opportunities still existing for significant improvements in civil aviation through the application of advanced propulsion concepts

Stewart, W. L.↗

NASA NTRS1984

Packed Alumina Absorbs Hypergolic Vapors

Beds of activated alumina effective as filters to remove hypergolic vapors from gas streams. Beds absorb such substances as nitrogen oxides and hydrazines and may also absorb acetylene, ethylene, hydrogen sulfide, benzene, butadiene, butene, styrene, toluene, and xoylene. Bed has no moving parts such as pumps, blowers and mixers. Reliable and energy-conservative. Bed readily adapted to any size from small portable units for use where little vapor release is expected to large stationary units for extensive transfer operations.

Thomas, J. J.↗

NASA NTRS1983

The influence of the tropics on the prediction of ultralong waves. I - Tropical wind field

The effects of tropical wind data from the FGGE and tropical latent heating on numerical modeling of ultralong waves are considered in a two-part study. The model studied is the global fourth-order GLAS general circulation model, an energy-conserving format with horizontal differences calculated with fourth-order accuracy. Data assimilation experiments were performed with and without the wind data, with account taken of eastward and northward wind components, the geopotential height, and the relative humidity, all over pressure surfaces. The initial conditions were used to generate six pairs of forecasts, and the tropical wind error decreased after two days of prediction when the initial conditions contained the wind data. The deviations from the measured planetary wave data were attributed to differences in the initial rotational wind field, which varied on a three-day basis. The latent heat initial data had a five-day period and extended its influence beyond the tropical zone. The tropical heat sources sustained the tropical westerlies in the GLAS model, and removal of the tropical heat sources reversed the wind to easterlies.

Baker, W. E.↗

NASA NTRS1984

On the effect of using the Shapiro filter to smooth winds on a sphere

Spatial differencing schemes which are not enstrophy conserving nor implicitly damping require global filtering of short waves to eliminate the build-up of energy in the shortest wavelengths due to aliasing. Takacs and Balgovind (1983) have shown that filtering on a sphere with a latitude dependent damping function will cause spurious vorticity and divergence source terms to occur if care is not taken to ensure the irrotationality of the gradients of the stream function and velocity potential. Using a shallow water model with fourth-order energy-conserving spatial differencing, it is found that using a 16th-order Shapiro (1979) filter on the winds and heights to control nonlinear instability also creates spurious source terms when the winds are filtered in the meridional direction.

Takacs, L. L.↗

NASA NTRS1986

Multigrid methods in structural mechanics

Although the application of multigrid methods to the equations of elasticity has been suggested, few such applications have been reported in the literature. In the present work, multigrid techniques are applied to the finite element analysis of a simply supported Bernoulli-Euler beam, and various aspects of the multigrid algorithm are studied and explained in detail. In this study, six grid levels were used to model half the beam. With linear prolongation and sequential ordering, the multigrid algorithm yielded results which were of machine accuracy with work equivalent to 200 standard Gauss-Seidel iterations on the fine grid. Also with linear prolongation and sequential ordering, the V(1,n) cycle with n greater than 2 yielded better convergence rates than the V(n,1) cycle. The restriction and prolongation operators were derived based on energy principles. Conserving energy during the inter-grid transfers required that the prolongation operator be the transpose of the restriction operator, and led to improved convergence rates. With energy-conserving prolongation and sequential ordering, the multigrid algorithm yielded results of machine accuracy with a work equivalent to 45 Gauss-Seidel iterations on the fine grid. The red-black ordering of relaxations yielded solutions of machine accuracy in a single V(1,1) cycle, which required work equivalent to about 4 iterations on the finest grid level.

Raju, I. S.↗

NASA NTRS1986

Kinetic efficiencies of stellar wind bubbles

The theoretical fraction of a stellar wind's energy converted into the kinetic energy of an expanding swept-up shell is 20 percent in the classical theory of stellar wind bubbles. Observational estimates of this conversion factor based on the amount of ionized material in wind-swept shells about Wolf-Rayet stars generally yield results of 1 percent. If there is a substantial amount of neutral material in the shell, it will not be counted and the kinetic efficiency will be underestimated. Presented here is a dynamical estimate which accounts for this neutral material in deducing the kinetic efficiencies of stellar wind bubbles. Bubbles classified as wind-blown shells have kinetic efficiencies in line with theoretical expectations for energy-conserving evolution in a homogeneous medium. Ringlike nebulae have significantly lower efficiencies, probably because they have been 'poisoned' by the photoevaporation of clouds engulfed during evolution into a cloudy substrate.

Van Buren, D.↗

NASA NTRS1989

Intersubband Auger recombination and population inversion in quantum-well subbands

The intersubband-Auger-recombination time of electrons under population-inversion conditions in a single quantum well is calculated by taking into account momentum- and energy-conservation rules, and by employing Fermi-Dirac statistics. The screened matrix element of the electron-electron interaction and the overlap integral are calculated for an infinitely deep quantum well. The results are in a good agreement with published experimental data. As a major nonradiative process, the Auger recombination is related to threshold current of infrared lasers based on intersubband transitions in quantum-well structures. The realization of these devices and other limitations to achieving population inversion are discussed. In view of the results, development of these lasers for emission wavelengths corresponding to energies below the LO-phonon energy seems feasible.

Borenstain, S.↗

NASA NTRS1990

A computational procedure for multibody systems including flexible beam dynamics

A computational procedure suitable for the solution of equations of motions for flexible multibody systems has been developed. The flexible beams are modeled using a fully nonlinear theory which accounts for both finite rotations and large deformations. The present formulation incorporates physical measures of conjugate Cauchy stress and covariant strain increments. As a consequence, the beam model can easily be interfaced with real-time strain measurements and feedback control systems. A distinct feature of the present work is the computational preservation of total energy for undamped systems; this is obtained via an objective strain increment/stress update procedure combined with an energy-conserving time integration algorithm which contains an accurate update of angular orientations. The procedure is demonstrated via several example problems.

Downer, J. D.↗

NASA NTRS1994

Gravity waves in Titan's atmosphere

Scintillations (high frequency variations) observed in the radio signal during the occultation of Voyager 1 by Titan (Hinson and Tyler, 1983) provide information concerning neutral atmospheric density fluctuations on scales on hundreds of meters to a few kilometers. Those seen at altitudes higher than 25 km above the surface were interpreted by Hinson and Tyler as being caused by linear, freely propagating (energy-conserving) gravity waves, but this interpretation was found to be inconsistent with the scintillation data below the 25-km altitude level. Here an attempt is made to interpret the entire scintillation profile between the surface and the 90-km altitude level in terms of gravity waves generated at the surface. Numerical calculations of the density fluctuations caused by two-dimensional, nonhydrostatic, finite-amplitude gravity waves propagating vertically through Titan's atmosphere are performed to produce synthetic scintillation profiles for comparison with the observations. The numerical model accurately treats the effects of wave transience, nonlinearity, and breakdown due to convective instability in the overturned part of the wave. The high-altitude scintillation data were accurately recovered with a freely propagating wave solution, confirming the analytic model of Hinson and Tyler. It is found that the low-altitude scintillation data can be fit by a model where a component of the gravity waves becomes convectively unstable and breaks near the 15 km level. The large-scale structure of the observed scintillation profile in the entire altitude range between 5 and 85 km can be simulated by a model where the freely propagating and breaking waves are forced at the surface simultaneously. Further analysis of the Voyager 1 Titan low-altitude scintillation data, using inversion theory appropriate for strong scattering, could potentially remove some of the ambiguities remaining in this analysis and allow a better determination of the strength and source of the waves.

Friedson, A. James↗

NASA NTRS1995

Large-eddy simulation of flow past a circular cylinder

Some of the most challenging applications of large-eddy simulation are those in complex geometries where spectral methods are of limited use. For such applications more conventional methods such as finite difference or finite element have to be used. However, it has become clear in recent years that dissipative numerical schemes which are routinely used in viscous flow simulations are not good candidates for use in LES of turbulent flows. Except in cases where the flow is extremely well resolved, it has been found that upwind schemes tend to damp out a significant portion of the small scales that can be resolved on the grid. Furthermore, it has been found that even specially designed higher-order upwind schemes that have been used successfully in the direct numerical simulation of turbulent flows produce too much dissipation when used in conjunction with large-eddy simulation. The objective of the current study is to perform a LES of incompressible flow past a circular cylinder at a Reynolds number of 3900 using a solver which employs an energy-conservative second-order central difference scheme for spatial discretization and compare the results obtained with those of Beaudan & Moin (1994) and with the experiments in order to assess the performance of the central scheme for this relatively complex geometry.

Mittal, R.↗

NASA NTRS2019

Predicting the X-Ray Spectra of Stellar-mass Black Holes from Simulations

We describe results from a new technique for the prediction of complete, self-consistent X-ray spectra from three-dimensional general relativistic magnetohydrodynamic (GRMHD) simulations of black hole accretion flows. Density and cooling rate data from a harm3d GRMHD simulation are post-processed by an improved version of the Monte Carlo radiation transport code pandurata (in the corona) and the Feautrier solver PTRANSX (in the disk), with xstar subroutines. The codes are run in a sequential, iterative fashion to achieve globally energy-conserving and self-consistent radiation fields, temperature maps, and photoionization equilibria. The output is the X-ray spectrum as seen by a distant observer, including features, such as the Fe Kα emission line and corresponding K-edge absorption trough, due to disk reprocessing of coronal power. For the example cases we consider—a non-rotating 10 M(sub ⊙) black hole with solar abundances, accreting at 0.01, 0.03, 0.1, or 0.3 Eddington—we find spectra resembling actual observations of stellar-mass black holes in the soft or steep power-law state: broad thermal peaks (at 1–3 keV), steep power laws extending to high energy (Γ = 2.7–4.5), and prominent, asymmetric Fe Kα emission lines with equivalent widths in the range 40–400 eV (larger EW at lower accretion rates). By starting with simulation data, we obviate the need for parameterized descriptions of the accretion flow geometry—no a priori specification of the corona's shape or flux, or the disk temperature or density, etc., is needed. Instead, we apply the relevant physical principles to simulation output using appropriate numerical techniques; this procedure allows us to calculate inclination-dependent spectra after choosing only a small number of physically meaningful parameters: black hole mass and spin, accretion rate, and elemental abundances.

Kinch, Brooks E.↗

NASA NTRS2019

The Role of Magnetic Helicity in Coronal Heating

One of the greatest challenges in solar physics is understanding the heating of the Sun's corona. Most theories for coronal heating postulate that free energy in the form of magnetic twist/stress is injected by the photosphere into the corona where the free energy is converted into heat either through reconnection or wave dissipation. The magnetic helicity associated with the twist/stress, however, is expected to be conserved and appear in the corona. In previous works, we showed that the helicity associated with the small-scale twists undergoes an inverse cascade via stochastic reconnection in the corona and ends up as the observed large-scale shear of filament channels. Our "helicity condensation" model accounts for both the formation of filament channels and the observed smooth, laminar structure of coronal loops. In this paper, we demonstrate, using helicity- and energy-conserving numerical simulations of a coronal system driven by photospheric motions, that the model also provides a natural mechanism for heating the corona. We show that the heat generated by the reconnection responsible for the helicity condensation process is sufficient to account for the observed coronal heating. We study the role that helicity injection plays in determining coronal heating and find that, crucially, the heating rate is only weakly dependent on the net helicity preference of the photospheric driving. Our calculations demonstrate that motions with 100% helicity preference are least efficient at heating the corona; those with 0% preference are most efficient. We discuss the physical origins of this result and its implications for the observed corona.

Knizhnik, K. J.↗