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DOE OSTI2025

Direct Study of Changes in Catalyst Structure-Kinetic Properties During Redox Transitions

The Temporal Analysis of Products (TAP) pulse response methodology is a transient technique that provides the time resolution needed to deconvolve reaction steps from the complex networks typical in industrial catalytic processes. Traditionally, TAP measurements observe gas phase dynamics at the reactor exit but lack direct measurements of changes in the catalyst itself. Recently, a new operando technique was developed that couples gas phase transients to dynamic changes in metal centers with the precise TAP methodology for nanomole titration. Using an industrial CrOx/Al2O3 catalyst used for propane dehydrogenation, we demonstrate the capabilities of this unique device to reveal key catalytic processes: 1) total propane oxidation not associated with chromia centers, 2) reduction of Cr6+ to Cr3+ correlated with selective product formation, and 3) subsequent carbon accumulation. By utilizing incremental pulsing in a diffusion-only transport regime, the spectrokinetic device allows us to resolve detailed changes in catalyst structure, composition, and kinetic function that are otherwise indistinguishable in conventional operando devices. The unification of the TAP methodology with time-resolved spectroscopic measurements offers new and unique insights into the complex kinetic phenomena regulated by solid catalyst surfaces.

03 - NATURAL GAS↗

DOE OSTI2023

The physics basis to integrate an MHD stable, high-power hybrid scenario to a cool divertor for steady-state reactor operation

Abstract Coupling a high-performance core to a low heat flux divertor is a crucial step for ITER and a Fusion Pilot Plant or DEMO. Experiments in DIII-D recently expanded the steady-state hybrid scenario to high density and divertor impurity injection to study the feasibility of a radiating mantle solution. This work presents the physics basis for trade-offs between density, current drive and stability to tearing modes (TMs) at high β. EC power is crucial to tailor the plasma profiles into a passively stable state, and to eject impurities from the core. Off-axis EC depositions decrease the heating efficiency, but calculated electron heat transport coefficients show that this effect is partially mitigated by improved confinement inside the EC deposition. Additionally, the reduction in pressure is recovered by increasing the density. This favourable scaling of confinement with density was observed in high power plasmas for years, and this work provides a comprehensive explanation. ELITE predictions indicate that a path in peeling-ballooning stability opens up for certain conditions of density, power, q 95 and shaping, allowing the edge pressure to continue increasing without encountering a limit. In the core, calculated anomalous fast-ion diffusion coefficients are consistent with density fluctuation measurements in the toroidicity-induced Alfvén eigenmode range, showing that smaller fast-ion losses contribute to the enhanced confinement at high density. The edge integration study shows that divertor heat loads can be reduced with Ne and Ar injection, but this eventually triggers a cascade of n = 1, 2, 3 core TMs. We can now show that impurity radiation in the core is small and it is not the cause for the drop in confinement at high Ar and Ne injection rates. The overlap between the core TMs is consistent with the loss of pressure as estimated by the Belt model for the coupled rational surfaces. Optimization of these trade-offs has achieved plasmas with sustained H 98y2 = 1.7, f GW = 0.7 and ∼85% mantle radiation. The scenario and its variations at higher density and on- vs off-axis EC heating has been studied as a candidate for an integrated solution for several reactor designs, such as ITER, ARC, and the ARIES-ACT1 case, showing promising results in terms of fusion power and gain.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Visualization and analysis of coupling between plasmas self-organization and plasma-induced fluid circulation in 1 atm DC glows with liquid anode

The physical processes prevailing when plasma contacts liquid water are poorly understood; however, it is this very interaction that is the basis of new, exciting technologies for water purification, the treatment of cancer and disease and the production of new, high value chemical products. A chief impediment to widespread application of plasmas for the aforementioned applications is scale up and cost. Here we investigate plasma induced flows which facilitate transport of reactivity from the plasma to liquid water at rates much faster than diffusion. We find that this plasma induced motion varies depending on whether or not the plasma is self organized. The insight from this work paves the way to a better understanding of transport and ultimately informing plasma treatment technologies on how to best optimize the rate at which processes such as plasma based water purification occurs.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2026

Investigation of Drift Effects in UEDGE Simulations of NSTX-U Edge Plasma With Lithium Divertors

Lithium is a low-Z material, and lithium-based plasma-facing components (PFCs) are planned for the National Spherical Torus Experiment Upgrade (NSTX-U) to explore potential benefits for divertor power exhaust and core plasma management. NSTX-U is a medium-sized spherical tokamak with up to 12 MW of auxiliary heating, capable of generating reactor-relevant plasma conditions. This work presents boundary plasma simulations for NSTX-U with lithium PFCs using the UEDGE code, incorporating full magnetic and 𝐄 ×𝐁 drift physics. The simulations show that drifts strongly influence heat and particle transport: they enhance convective transport, broaden the scrape-off layer heat-flux width 𝜆 𝑞 , and reduce the anomalous heat diffusivity 𝜒 required to reproduce predicted SOL heat-flux width. 𝐄 ×𝐁 drifts provide poloidal transport, while ∇𝐵 (which includes both gradB and curvature) drifts provide radial heat and particle transport. Lithium transport is also affected by drifts, with lithium ions migrating from the outer divertor to the inner divertor through the private flux region (PFR) following the 𝐄 ×𝐁 drifts flow, lowering upstream impurity lithium densities. UEDGE is self-consistently coupled with the Wall-Li model to study plasma lithium PFC interactions depending on the local lithium sourcing based on local plasma conditions and lithium surface temperature. In these simulations, lithium evaporation shows a vapor-shielding effect that reduces divertor heat flux and increases radiative losses once surface temperatures exceed 450°C. This research work provides a first step toward self-consistent modeling of lithium PFCs in NSTX-U, demonstrating the impact of drift-driven plasma transport in SOL and divertor regions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Physics-Informed Neural Network Method for Forward and Backward Advection-Dispersion Equations

Advection-dispersion equations (ADEs) are commonly used to describe transport phenomena in porous media. Even though mature discretization-based numerical methods for ADEs exist, some challenges still remain, especially when it comes to solving advection-dominated forward ADEs and diffusion-dominated backward ADEs. The latter problem usually arises in the source identification context and leads to numerically unstable grid-based solutions that require a form of regularization or should be treated as an inverse problem that is computationally more expensive because it requires solving the forward problem multiple times. In this study, we propose a discretization-free approach based on the physics-informed neural network (PINN) method for solving coupled ADE and Darcy flow equations with space-dependent hydraulic conductivity. In this approach, the hydraulic conductivity, hydraulic head, and concentration fields are approximated with deep neural networks (DNNs). We assume that the conductivity field is given by its values on a grid, and we use these values to train the conductivity DNN. The head and concentration DNNs are trained by minimizing the residuals of the flow equation and ADE and using the initial and boundary conditions as additional constraints. The PINN method is applied to one- and two-dimensional forward ADE problems, where its performance for various P\'{e}clet numbers ($Pe$) is compared with the analytical and numerical solutions. We find that the PINN method is accurate with errors of less than 1\% and outperforms some conventional discretization-based methods for $Pe$ larger that 100. Next, we demonstrate that the PINN method remains accurate for the backward ADEs, with the relative errors in most cases staying under 5\% compared to the reference concentration field. Finally, we show that when available, the concentration measurements can be easily incorporated in the PINN method and significantly improve (by more than 50\% in the considered cases) the accuracy of the PINN solution of the backward ADE.

He, Qizhi↗

DOE OSTI2020

Cluster Frustration in the Breathing Pyrochlore Magnet LiGaCr 4 S 8

We present a comprehensive neutron scattering study of the breathing pyrochlore magnet LiGaCr 4 S 8 . We observe an unconventional magnetic excitation spectrum with a separation of high and low-energy spin dynamics in the correlated paramagnetic regime above a spin-freezing transition at 12(2) K. By fitting to magnetic diffuse-scattering data, we parameterize the spin Hamiltonian. We find that interactions are ferromagnetic within the large and small tetrahedra of the breathing pyrochlore lattice, but antiferromagnetic further-neighbor interactions are also essential to explain our data, in qualitative agreement with density-functional theory predictions [Ghosh et al., npj Quantum Mater. 4, 63 (2019)]. We explain the origin of geometrical frustration in LiGaCr 4 S 8 in terms of net antiferromagnetic coupling between emergent tetrahedral spin clusters that occupy a face-centered lattice. Furthermore, our results provide insight into the emergence of frustration in the presence of strong further-neighbor couplings, and a blueprint for the determination of magnetic interactions in classical spin liquids.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Active learning of ternary alloy structures and energies

Abstract Machine learning models with uncertainty quantification have recently emerged as attractive tools to accelerate the navigation of catalyst design spaces in a data-efficient manner. Here, we combine active learning with a dropout graph convolutional network (dGCN) as a surrogate model to explore the complex materials space of high-entropy alloys (HEAs). We train the dGCN on the formation energies of disordered binary alloy structures in the Pd-Pt-Sn ternary alloy system and improve predictions on ternary structures by performing reduced optimization of the formation free energy, the target property that determines HEA stability, over ensembles of ternary structures constructed based on two coordinate systems: (a) a physics-informed ternary composition space, and (b) data-driven coordinates discovered by the Diffusion Maps manifold learning scheme. Both reduced optimization techniques improve predictions of the formation free energy in the ternary alloy space with a significantly reduced number of DFT calculations compared to a high-fidelity model. The physics-based scheme converges to the target property in a manner akin to a depth-first strategy, whereas the data-driven scheme appears more akin to a breadth-first approach. Both sampling schemes, coupled with our acquisition function, successfully exploit a database of DFT-calculated binary alloy structures and energies, augmented with a relatively small number of ternary alloy calculations, to identify stable ternary HEA compositions and structures. This generalized framework can be extended to incorporate more complex bulk and surface structural motifs, and the results demonstrate that significant dimensionality reduction is possible in thermodynamic sampling problems when suitable active learning schemes are employed.

Chemistry↗

DOE OSTI2022

Deterministic modelling of the SPERT IV reactor transients using the multi-physics capability of WIMS

The ANSWERS WIMS reactor physics code is being developed for whole core multi-physics modelling. The established neutronics capability for lattice calculations has recently been extended to be suitable for whole core modelling of Small Modular Reactors (SMRs). A whole core transport, SP3 or diffusion flux solution is combined with fuel assembly resonance shielding. An integrated thermal hydraulic solver permits temperature and density variations to feedback to the neutronics calculation. This capability can be applied to both steady state and time dependent transient problems. Nuclear reactor design and safety case development requires assessment of a range of reactor transients, to inform both normal operation limitations and accident scenario analysis. This paper presents new methodology developed in WIMS to couple the core neutronics to the integrated core thermal hydraulics solver for the simulation of reactor transients in whole core models. To support the validation of the multi-physics capability of WIMS, this capability has been applied to the reactivity insertion transient experiments performed in the plate fuelled SPERT-IV reactor. This study employs WIMS using the whole core solver MERLIN, which calculates the time-dependent flux distribution and magnitude, coupled to ARTHUR, which solves for the time-dependent thermal hydraulics solution, and provides thermal feedback via the cross sections generated by GEOM, which performs resonance shielding calculations and generates cross section data for the plate geometry. This spatial kinetics model, with dynamic cross section generation, allows for variations in the temperature and neutron flux profile with time.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2024

Geochemical-hydromechanical couplings during water-serpentinized harzburgite interactions at 20° C and 30 bars

Interaction of groundwater with the serpentinized harzburgites of the upper mantle plays an important role in the geologic carbon cycle and serpentinization processes. Here, in this study, an intact serpentinized harzburgite with more than 60% lizardite from the Semail ophiolite in Oman was reacted with water at near neutral pH and low PCO 2 to observe its dissolution behavior and reaction path within the CaO-MgO-SiO 2 -CO 2 -H 2 O system at 20 °C and 30 bars. In the experiment, mass (i.e. H 2 O, ions) transfer is by diffusion and the selected temperature and pressure conditions mimic water-rock interactions at the shallow portions of most ultramafic rock hosted aquifers. Equilibrium activity-activity diagrams and thermodynamic data were used to compare the experimentally determined reaction path with the theoretical stability boundaries for minerals involved to investigate the evolution of bulk chemical composition, mineralogy, and water composition. The experiments demonstrated that (i) the water-rock interactions increased the pH of the aqueous phase from 5.9 to 7.5 over a period of 18 weeks; (ii) the dissolution of lizardite, orthopyroxene (enstatite), and clinopyroxene (diopside and augite) increased the concentration of Mg, Ca, and Si in the aqueous phase; (iii) the dissolution was incongruent with respect to Mg and Si, favoring Si release at pH > 6 due to (a) breaking of more reactive cation‑oxygen bonds that is consistent with the stoichiometry of magnesium for proton exchange reaction which favors a surface that is enriched in Mg at basic conditions, and (b) preferential dissolution of clinopyroxene Mg 1.30 Ca 0.52 Fe 0.06 Si 2 O 6 ; (iv) the aqueous phase was undersaturated with respect to carbonate (e.g. calcite, magnesite, and hydromagnesite) and hydrous (e.g. lizardite, chrysotile, brucite, and talc) minerals; (v) the bulk chemical composition and mineralogy of the intact serpentinized harzburgite matrix did not change; (vi) the thermodynamic data can successfully predict water-intact serpentinized harzburgite behavior if the water chemical composition can be constrained; and (vii) no detectable macroscopic form of damage (e.g. microcracks forming as a result of differential stress fields due to changes in volume during chemical reaction) was observed.

Carbonation↗

DOE OSTI2023

Diffused trenches for high fill-factor Low-Gain Avalanche Diodes

Low-Gain Avalanche Diodes (LGADs) are a class of silicon detectors that have been specifically designed for the fast detection of minimum ionizing particles (mips) in High-Energy Physics experiments. While they provide timing resolution on the order of a few tens of picoseconds, they cannot achieve high spatial resolution due to the intrinsic characteristics of their structures. Thus, active R&D is on-going to develop detectors based on LGADs to improve their spatial resolution while maintaining the timing performance of the LGADs. Such devices are, for example, AC-coupled LGADs and Deep-Junction LGADs. Another device option is the Trench-Isolated LGAD (TI LGAD), where trenches etched at the periphery of the pixels isolate them while providing a high fill-factor. Here, in this paper, we present a variation of this latter approach, demonstrating its feasibility by means of 2-dimensional TCAD simulations.

47 OTHER INSTRUMENTATION↗

DOE OSTI2024

ASb 3 Mn 9 O 19 (A = K or Rb): New Mn-Based 2D Magnetoplumbites with Geometric and Magnetic Frustration

Magnetoplumbites are one of the most broadly studied families of hexagonal ferrites, typically with high magnetic ordering temperatures, making them excellent candidates for permanent magnets. However, magnetic frustration is rarely observed in magnetoplumbites. Herein, the discovery, synthesis, and characterization of the first Mn-based magnetoplumbite, as well as the first magnetoplumbite involving pnictogens (Sb), ASb 3 Mn 9 O 19 (A = K or Rb) are reported. The Mn 3+ ( S = 2) cations, further confirmed by DC magnetic susceptibility and X-ray photoelectron spectroscopy, construct three geometrically frustrated sublattices, including Kagome, triangular, and puckered honeycomb lattices. Magnetic properties measurements revealed strong antiferromagnetic spin–spin coupling as well as multiple low-temperature magnetic features. Heat capacity data does not show any prominent λ-anomaly, suggesting minimal associated magnetic entropy. Moreover, neutron powder diffraction (NPD) implied the absence of long-range magnetic ordering in KSb 3 Mn 9 O 19 down to 3 K. However, several magnetic peaks are observed in RbSb 3 Mn 9 O 19 at 3 K, corresponding to an incommensurate magnetic structure. Interestingly, strong diffuse scattering is seen in the NPD patterns of both compounds at low angles and is analyzed by reverse Monte Carlo refinements, indicating short-range spin ordering related to frustrated magnetism as well as 2D magnetic correlations in ASb 3 Mn 9 O 19 (A = K or Rb).

2-D magnetic correlation↗

DOE OSTI2025

Decoherence and Brownian motion of a polarizable particle near a medium

Optically levitated nanoparticles are ideal experimental testbeds for investigating macroscopic superpositions and microscopic thermodynamics. Integrating such levitated nanoparticles with photonic structures can enable strong coupling between their center-of-mass motion and guided photonic modes, facilitating enhanced control and probing of their motion. When coupling a particle to a photonic structure, such as a waveguide, the effects of fluctuations become prominent at nanoscales. In this work, we analyze the classical and quantized center-of-mass motion of a polarizable particle interacting with the fluctuations of the electromagnetic field in the presence of a medium. We derive a position localization master equation for the particle's quantized center of mass, and examine its classical center-of-mass momentum diffusion, elucidating correspondences between classical and quantum Brownian motion of polarizable particles near media. We study the decoherence rate of the particle in the presence of a planar surface as a function of temperature and distance from the surface, comparing it to common sources of decoherence. Our results are pertinent to experiments aimed at preparing levitated nanospheres in macroscopic quantum states and investigating their Brownian dynamics.

Brownian motion↗

DOE OSTI2024

Solvent-mediated oxide hydrogenation in layered cathodes

Self-discharge and chemically induced mechanical effects degrade calendar and cycle life in intercalation-based electrochromic and electrochemical energy storage devices. In rechargeable lithium-ion batteries, self-discharge in cathodes causes voltage and capacity loss over time. The prevailing self-discharge model centers on the diffusion of lithium ions from the electrolyte into the cathode. Here, we demonstrate an alternative pathway, where hydrogenation of layered transition metal oxide cathodes induces self-discharge through hydrogen transfer from carbonate solvents to delithiated oxides. In self-discharged cathodes, we further observe opposing proton and lithium ion concentration gradients, which contribute to chemical and structural heterogeneities within delithiated cathodes, accelerating degradation. Hydrogenation occurring in delithiated cathodes may affect the chemo-mechanical coupling of layered cathodes as well as the calendar life of lithium-ion batteries.

25 ENERGY STORAGE↗

DOE OSTI2025

Coupled geomechanical investigation of depletion-induced fault reactivation

Fault reactivation during subsurface fluid production pose significant challenges to safe and sustainable resource extraction. Here, this study presents a three-dimensional coupled geomechanical framework to investigate the processes driving fault reactivation, capturing the interactions between reservoir dynamics and geomechanical responses. Verification against theoretical estimations based on linear poroelasticity confirms the model's capacity in representing reservoir background stress responses. However, the study reveals that relying solely on background stress states can underestimate or overestimate fault reactivation potential, emphasizing the importance of including localized stress perturbations such as differential compaction and stress redistribution. Applied to a fault (M1) inspired by the geological characteristics of the Groningen field, the model shows slip initiation at 2965 m depth with 16.0 MPa depletion, aligning with field observations where seismicity occurred at approximately 3 km depth after 15.8 MPa depletion. Parametric studies reveal: (1) inelastic reservoir compaction delays fault reactivation and mitigates fault slip by reducing stress concentration, (2) higher intermediate in-situ stress magnitudes decrease the Coulomb Failure Stress (CFS) increase rate and reduce fault slip, (3) larger fault offsets amplify shear stress near the offset zone, promoting earlier reactivation and longer rupture propagation, and (4) fault permeability significantly influences pressure diffusion, with low-permeability faults leading to sharper stress changes and earlier fault destabilization. These insights highlight the critical role of geological and mechanical parameters in fault reactivation and provide a predictive framework for mitigating induced seismicity risks.

Coupled geomechanical modeling↗

DOE OSTI2020

Non-compact oxide-island growth induced by surface phase transition of the intermetallic NiAl during vacuum annealing

Crystal structure and composition are inter-dependent and decoupling their effects on surface reactivity is challenging. Using low-energy electron microscopy to spatially and temporally resolve the oxide film growth during the oxidation of NiAl(100), we differentiate such coupled effects by monitoring oxide growth while simultaneously fine-tuning the surface structure and composition during oxidation. We demonstrate that the oxidation of chemically ordered surfaces results in compact oxide island growth whereas non-compact oxide growth during the surface phase transition. By incorporating the surface phase transition induced chemical disordering into kinetic Monte Carlo simulations, we illustrate that the non-compact oxide growth is induced by the composition effect on the surface diffusion of oxygen, which can be described by the concept of “ant in the labyrinth”.

36 MATERIALS SCIENCE↗

DOE OSTI2024

A Lake Biogeochemistry Model for Global Methane Emissions: Model Development, Site‐Level Validation, and Global Applicability

Abstract Lakes are important sentinels of climate change and may contribute over 30% of natural methane (CH 4 ) emissions; however, no earth system model (ESM) has represented lake CH 4 dynamics. To fill this gap, we refined a process‐based lake biogeochemical model to simulate global lake CH 4 emissions, including representation of lake bathymetry, oxic methane production (OMP), the effect of water level on ebullition, new non‐linear CH 4 oxidation kinetics, and the coupling of sediment carbon pools with in‐lake primary production and terrigenous carbon loadings. We compiled a lake CH 4 data set for model validation. The model shows promising performance in capturing the seasonal and inter‐annual variabilities of CH 4 emissions at 10 representative lakes for different lake types and the variations in mean annual CH 4 emissions among 106 lakes across the globe. The model reproduces the variations of the observed surface CH 4 diffusion and ebullition along the gradients of lake latitude, depth, and surface area. The results suggest that OMP could play an important role in surface CH 4 diffusion, and its relative importance is higher in less productive and/or deeper lakes. The model performance is improved for capturing CH 4 outgassing events in non‐floodplain lakes and the seasonal variability of CH 4 ebullition in floodplain lakes by representing the effect of water level on ebullition. The model can be integrated into ESMs to constrain global lake CH 4 emissions and climate‐CH 4 feedback.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2025

Toward Establishing Uniqueness of Experimentally Determined Transference Numbers

The passage of current through a battery results in the development of concentration gradients in the electrolytic phase. For a fully characterized binary electrolyte, where the conductivity, salt diffusion coefficient, cation transference number, and the thermodynamic factor are known, concentration and potential gradients in the electrolytic phase can be modeled using Newman’s concentrated solution theory. We report two methods for measuring the transference number: the standard method based on electrochemical measurements ( t + , echem 0 ) and electrophoretic NMR ( t + , eNMR 0 ). The electrochemical approach requires combining measurements from multiple experiments; the equations used to determine the cation transference number and the thermodynamic factor are coupled, nonlinear algebraic equations. In the electrophoretic-NMR-based approach, however, the equations used to determine the cation transference number and the thermodynamic factor are decoupled. We find for a liquid electrolyte comprised of a lithium salt dissolved in tetraglyme, the values of the transference numbers obtained by these two methods are distinct. For example, at 30 °C, t + , echem 0 = −1.02 ± 1.11 and t + , eNMR 0 = 0.25 ± 0.04. The corresponding thermodynamic factors are also different. While the magnitude of the predicted concentration gradients based on the two sets of parameters are different, the predicted current-voltage relationships are similar.

Hickson, Darby T. (ORCID:0000000251339755)↗

DOE OSTI2021

Data-Driven Reduced-Order Modeling of Convective Heat Transfer in Porous Media

This work presents a data-driven Reduced-Order Model (ROM) for parametric convective heat transfer problems in porous media. The intrusive Proper Orthogonal Decomposition aided Reduced-Basis (POD-RB) technique is employed to reduce the porous medium formulation of the incompressible Reynolds-Averaged Navier–Stokes (RANS) equations coupled with heat transfer. Instead of resolving the exact flow configuration with high fidelity, the porous medium formulation solves a homogenized flow in which the fluid-structure interactions are captured via volumetric flow resistances with nonlinear, semi-empirical friction correlations. A supremizer approach is implemented for the stabilization of the reduced fluid dynamics equations. The reduced nonlinear flow resistances are treated using the Discrete Empirical Interpolation Method (DEIM), while the turbulent eddy viscosity and diffusivity are approximated by adopting a Radial Basis Function (RBF) interpolation-based approach. The proposed method is tested using a 2D numerical model of the Molten Salt Fast Reactor (MSFR), which involves the simulation of both clean and porous medium regions in the same domain. For the steady-state example, five model parameters are considered to be uncertain: the magnitude of the pumping force, the external coolant temperature, the heat transfer coefficient, the thermal expansion coefficient, and the Prandtl number. For transient scenarios, on the other hand, the coastdown-time of the pump is the only uncertain parameter. The results indicate that the POD-RB-ROMs are suitable for the reduction of similar problems. The relative L2 errors are below 3.34% for every field of interest for all cases analyzed, while the speedup factors vary between 54 (transient) and 40,000 (steady-state).

German, Péter (ORCID:0000000307285283)↗