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Results for “Strang splitting”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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17 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS2013

On Spurious Numerics in Solving Reactive Equations

The objective of this study is to gain a deeper understanding of the behavior of high order shock-capturing schemes for problems with stiff source terms and discontinuities and on corresponding numerical prediction strategies. The studies by Yee et al. (2012) and Wang et al. (2012) focus only on solving the reactive system by the fractional step method using the Strang splitting (Strang 1968). It is a common practice by developers in computational physics and engineering simulations to include a cut off safeguard if densities are outside the permissible range. Here we compare the spurious behavior of the same schemes by solving the fully coupled reactive system without the Strang splitting vs. using the Strang splitting. Comparison between the two procedures and the effects of a cut off safeguard is the focus the present study. The comparison of the performance of these schemes is largely based on the degree to which each method captures the correct location of the reaction front for coarse grids. Here "coarse grids" means standard mesh density requirement for accurate simulation of typical non-reacting flows of similar problem setup. It is remarked that, in order to resolve the sharp reaction front, local refinement beyond standard mesh density is still needed.

Numerics↗
DOE OSTI2026

MFC 5.0: An exascale many-physics flow solver

Many problems of interest in engineering, medicine, and the fundamental sciences rely on high-fidelity flow simulation, making performant computational fluid dynamics solvers a mainstay of the open-source software community. Previous work MFC 3.0 was made a published, documented, and open-source solver via Bryngelson et al. Comp. Phys. Comm. (2021) with numerous physical features, numerical methods, and scalable infrastructure. MFC 5.0 is a significant update to MFC 3.0, featuring a broad set of well-established and novel physical models and numerical methods, as well as the introduction of GPU and APU (or superchip) acceleration. Here, we exhibit state-of-the-art performance and ideal scaling on the first two exascale supercomputers, OLCF Frontier and LLNL El Capitan. Combined with MFC’s single-accelerator performance, MFC achieves exascale computation in practice, and achieved the largest-to-date public CFD simulation at 200 trillion grid points as a 2025 ACM Gordon Bell Prize finalist. New physical features include the immersed boundary method, N-fluid phase change, Euler–Euler and Euler–Lagrange sub-grid bubble models, fluid-structure interaction, hypo- and hyper-elastic materials, chemically reacting flow, two-material surface tension, magnetohydrodynamics (MHD), and more. Numerical techniques now represent the current state-of-the-art, including general relaxation characteristic boundary conditions, WENO variants, Strang splitting for stiff sub-grid flow features, and low Mach number treatments. Weak scaling to tens of thousands of GPUs on OLCF Summit and Frontier and LLNL El Capitan achieves efficiencies within 5% of ideal to over 90% of their respective system sizes. Strong scaling results for a 16-times increase in device count show parallel efficiencies over 90% on OLCF Frontier. MFC’s software stack has undergone further improvements, including continuous integration, which ensures code resilience and correctness through over 300 regression tests; metaprogramming, which reduces code length while maintaining performance portability; and code generation for computing chemical reactions

Computational fluid dynamics↗
DOE OSTI2026

Quantum kinetic modeling of KEEN waves in a warm-dense regime

We report the first fully kinetic, quantum study of kinetic electrostatic electron nonlinear (KEEN) waves, showing that quantum diffraction systematically erodes the classical trapping mechanism, narrows harmonic locking to the fundamental, and hastens post-drive decay. Electrons are evolved with a second-order Strang-split 1D1V Wigner–Poisson solver that couples conservative semi-Lagrangian WENO advection to an analytic Fourier space update for the non-local Wigner term, while ions remain classical. We focus on collisionless dynamics in a weakly coupled regime, providing a controlled baseline before collisional extensions. Short, frequency-tuned ponderomotive pulses drive KEEN formation in a uniform Maxwellian plasma; as the dimensionless quantum parameter H rises from the classical limit to values relevant to warm-dense matter, doped semiconductors, and 2D electron systems, the drive threshold increases, higher harmonics are damped, trapped electron vortices diffuse, and the subplasma electrostatic energy relaxes to a lower stationary level, as confirmed by continuous wavelet analysis. These microscopic changes carry macroscopic weight. Ignition-scale capsules now compress matter to regimes where the electron de Broglie wavelength rivals the Debye length, making classical kinetic descriptions insufficient. By extending KEEN physics into this quantum domain, our results offer a potential diagnostic of non-equilibrium electron dynamics for next-generation inertial-confinement designs and high-energy-density platforms, indicating that predictive fusion modeling may benefit from the integration of kinetic fidelity with quantum effects.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Electric charge and strangeness-dependent directed flow splitting of produced quarks in Au+Au collisions

We report directed flow (v 1 ) of multistrange baryons (Ξ and Ω) and improved v1 data for $K¯$, $\bar{p}$, $\bar{Λ}$ and φ in Au+Au collisions at $\sqrt{s_{NN}} =27$ and 200 GeV from the STAR at the Relativistic Heavy Ion Collider (RHIC). We focus on particles whose constituent quarks are not transported from beam rapidity rather produced in the collisions. In midcentral collisions, we observe a coalescence sum rule for hadron combinations with identical quark content and a difference (“splitting”) in the slope of v 1 vs. rapidity for combinations having nonidentical quark content. The splitting strength appears to increase with the electric charge difference and strangeness content difference of the constituent quarks in the combinations, consistent with an electromagnetic effect. The peripheral collision statistics are insufficient to draw firm conclusions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

First benchmarked electron cooling simulations from first principles

We present the first microscopic electron cooling simulations from first principles with accurate prediction of cooling time. These simulations were performed using our previously developed numerical method, PHAD, which is the first efficient large-scale collisional numerical method in beam physics. The simulation results are benchmarked with the experimental data of the low energy bunched electron cooling of ion beams at the storage ring CSRm at the IMP facility in China. Here, we have accurately considered the nonlinear dynamics in the whole accelerator system in addition to the electron cooling section. As a result, our simulations correctly reproduced cooling times of the experiments from first principles and without any tuning or fitting parameters in the code.

43 PARTICLE ACCELERATORS↗
NASA NTRS1990

A new finite element method for solving compressible Navier-Stokes equations based on an operator splitting method and h-p adaptivity

A new finite element method solving compressible Navier-Stokes equations is proposed. The method is based on a version of Strang's operator splitting and an h-p adaptive finite element approximation in space. This paper contains the formulation of the method with a detailed discussion of boundary conditions, a sample adaptive strategy and numerical examples involving compressible viscous flow over a flat plate with Reynolds number Re = 1000 and Re = 10,000.

Demkowicz, L.↗
NASA NTRS1991

On the application of ENO scheme with subcell resolution to conservation laws with stiff source terms

Two approaches are used to extend the essentially non-oscillatory (ENO) schemes to treat conservation laws with stiff source terms. One approach is the application of the Strang time-splitting method. Here the basic ENO scheme and the Harten modification using subcell resolution (SR), ENO/SR scheme, are extended this way. The other approach is a direct method and a modification of the ENO/SR. Here the technique of ENO reconstruction with subcell resolution is used to locate the discontinuity within a cell and the time evolution is then accomplished by solving the differential equation along characteristics locally and advancing in the characteristic direction. This scheme is denoted ENO/SRCD (subcell resolution - characteristic direction). All the schemes are tested on the equation of LeVeque and Yee (NASA-TM-100075, 1988) modeling reacting flow problems. Numerical results show that these schemes handle this intriguing model problem very well, especially with ENO/SRCD which produces perfect resolution at the discontinuity.

Chang, Shih-Hung↗
NASA NTRS1989

On the application of subcell resolution to conservation laws with stiff source terms

LeVeque and Yee recently investigated a one-dimensional scalar conservation law with stiff source terms modeling the reacting flow problems and discovered that for the very stiff case most of the current finite difference methods developed for non-reacting flows would produce wrong solutions when there is a propagating discontinuity. A numerical scheme, essentially nonoscillatory/subcell resolution - characteristic direction (ENO/SRCD), is proposed for solving conservation laws with stiff source terms. This scheme is a modification of Harten's ENO scheme with subcell resolution, ENO/SR. The locations of the discontinuities and the characteristic directions are essential in the design. Strang's time-splitting method is used and time evolutions are done by advancing along the characteristics. Numerical experiment using this scheme shows excellent results on the model problem of LeVeque and Yee. Comparisons of the results of ENO, ENO/SR, and ENO/SRCD are also presented.

Chang, Shih-Hung↗
NASA NTRS1988

A numerical study of ENO and TVD schemes for shock capturing

The numerical performance of a second-order upwind-based total variation diminishing (TVD) scheme and that of a uniform second-order essentially non-oscillatory (ENO) scheme for shock capturing are compared. The TVD scheme used is a modified version of Liou, using the flux-difference splitting (FDS) of Roe and his superbee function as the limiter. The construction of the basic ENO scheme is based on Harten, Engquist, Osher, and Chakravarthy, and the 2-D extensions are obtained by using a Strang-type of fractional-step time-splitting method. Numerical results presented include both steady and unsteady, 1-D and 2-D calculations. All the chosen test problems have exact solutions so that numerical performance can be measured by comparing the computer results to them. For 1-D calculations, the standard shock-tube problems of Sod and Lax are chosen. A very strong shock-tube problem, with the initial density ratio of 400 to 1 and pressure ratio of 500 to 1, is also used to study the behavior of the two schemes. For 2-D calculations, the shock wave reflection problems are adopted for testing. The cases presented in this report include flows with Mach numbers of 2.9, 5.0, and 10.0.

Chang, Shih-Hung↗
DOE OSTI2023

Observation of a critical charge mode in a strange metal

Understanding the strange metallic behavior that develops at the brink of localization in quantum materials requires probing the underlying electronic charge dynamics. Using synchrotron radiation–based Mössbauer spectroscopy, we studied the charge fluctuations of the strange metal phase of β-YbAlB 4 as a function of temperature and pressure. We found that the usual single absorption peak in the Fermi-liquid regime splits into two peaks upon entering the critical regime. Here, we interpret this spectrum as a single nuclear transition, modulated by nearby electronic valence fluctuations whose long time scales are further enhanced by the formation of charged polarons. These critical charge fluctuations may prove to be a distinct signature of strange metals.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Investigating the Electronic Structure of Prospective Water-Splitting Oxide BaCe 0.25 Mn 0.75 O 3-δ before and after Thermal Reduction

BaCe 0.25 Mn 0.75 O 3-δ (BCM), a non-stoichiometric oxide with a layered perovskite-like crystal structure, has recently emerged as a prospective contender for application in renewable energy harvesting by solar thermochemical hydrogen generation. Using solar-thermal energy and a reducing environment, oxygen vacancies can be created in high-temperature BCM, and the reduced crystal so obtained can, in turn, produce H 2 by stripping oxygen from H 2 O. Therefore, a first step toward understanding the working mechanism and optimizing the performance of BCM is a thorough and comparative analysis of the electronic structure of the pristine and the reduced material. In this paper, we probe the electronic structure of BCM using the combined effort of first-principles calculations and experimental O K-edge X-ray absorption spectroscopy (XAS). The computed projected density of states (PDOS) and orbital plots are used to propose a simplified model for orbital mixing between the oxygen and metal atoms. With the help of state-of-the-art simulations, we are able to find the origins of the XAS peaks and categorize them on the basis of contribution from Ce and Mn. For the reduced crystal, the calculations show that the change in electron density resulting from the reduction is strongly localized around the oxygen vacancy. Experimental measurements reveal a marked lowering of the first O K-edge peak in the reduced crystal. Using theoretical analysis, this is shown to result from lifting of spin degeneracy in the absorption peaks as well as from a diminished O 2p contribution to the frontier unoccupied orbitals, in accordance with the tight binding scheme. The simulated results serve as a reference for the extent of spectral change as a function of the percentage of oxygen vacancies in the reduced crystal. Here, our study paves the way for the investigation of the working mechanism of BCM and for computational and experimental efforts aimed at design and discovery of efficient water-splitting oxides.

08 HYDROGEN↗
DOE OSTI2023

Chapter 14: Surface plasmon resonance enhanced artificial photosynthesis of chemical fuels for energy storage

Nanostructured noble metals such as Au, Ag, and Cu have interesting optical properties because of the oscillation motions of their surface electrons upon strong coupling with light under resonance conditions. This resonant oscillation motion of conduction electrons refers to surface plasmon resonance (SPR) and localized SPR (LSPR) when localized near the surface of a nanoparticle. The extinction spectrum of a solution of plasmonic nanoparticles has tunable wavelength responses from UV to NIR due to strong light scattering and absorption which are highly sensitive to the permittivity of the nanoparticles, their sizes and shapes, and chemical environment. Strong light scattering due to the LSPR of plasmonic nanoparticles creates a strong localized and far-field intensity capable of enhancing light absorption characteristics of a chromophore near a plasmonic surface. Engineering the chromophores’ radiative decay dynamics can be done by 1) increasing its radiative decay rate to increase its photoluminescence intensity and 2) increasing its nonradiative decay rates associated to direct charge transfer to the metal surface. Such interesting photophysical properties of a chromophore can be extended to other light-absorbing materials such as semiconductor thin films and nanostructures. This plasmonic effect on the photophysics of a light-absorbing material can be theoretically and experimentally validated. The phenomenon has also been applied to advanced optoelectronic devices such as organic light-emitting diodes (OLED)1 and organic photovoltaics (OPV).2-4 The local field created by the SPR can provide an intense EM field to enhance photoluminescence emission of an organic chromophore5-8 and Raman scattering of an organic molecule, and single-molecule Raman9-10 can be detected on specially designed LSPR substrate. (Figure 1 on SPR for energy) Recent studies suggest that LSPR can be incorporated in light-harvesting and conversion systems to increase energy conversion in a solar cell and photoelectrochemical cell and chemical transformations of CO2 to chemical fuels.11-12 Plasmonic active metals naturally exhibit catalytic activities for electrochemical fuel conversion that can be enhanced by engineering their structures to form unique catalytic structures such as symmetry-broken Au-Cu Janus nanocrystals.13 These studies are critical to addressing the global challenges of energy14-15 and CO2 emission from nonrenewable sources such as coal, petroleum, and natural gas.16-17 Electrochemical systems comprised of unique photonic structures and functions that enable efficient and affordable energy harvesting/conversion/storage are highly desired for providing safe and environment-friendly energy sources. This chapter reviews our recent work of LSPR enabled photoelectrochemical water splitting and recent advances in LSPR-enabled CO2 reduction and photochemical reactions reported in the literature. Scientific and technical challenges of applying LSPR to enhance these energy conversion and storage systems are discussed at the conclusion of this chapter.

Pan, Shanlin↗
DOE OSTI2023

Formation of Ba 3 Nb 0.75 Mn 2.25 O 9 -6H during thermochemical reduction of Ba 4 NbMn 3 O 12 -12R

The resurgence of interest in hydrogen-related technologies has stimulated new studies aimed at advancing lesser-developed water-splitting processes, such as solar thermochemical hydrogen production (STCH). Progress in STCH has been largely hindered by a lack of new materials able to efficiently split water at a rate comparable to ceria under identical experimental conditions. BaCe 0.25 Mn 0.75 O 3 (BCM) recently demonstrated enhanced hydrogen production over ceria and has the potential to further our understanding of two-step thermochemical cycles. A significant feature of the 12R hexagonal perovskite structure of BCM is the tendency to, in part, form a 6H polytype at high temperatures and reducing environments ( i.e. , during the first step of the thermochemical cycle), which may serve to mitigate degradation of the complex oxide. An analogous compound, namely BaNb 0.25 Mn 0.75 O 3 (BNM) with a 12R structure was synthesized and displays nearly complete conversion to the 6H structure under identical reaction conditions as BCM. The structure of the BNM-6H polytype was determined from Rietveld refinement of synchrotron powder X-ray diffraction data and is presented within the context of the previously established BCM-6H structure.

08 HYDROGEN↗
DOE OSTI2025

Large-scale experimental validation of thermochemical water-splitting oxides discovered by defect graph neural networks

Thermochemical water-splitting (TCH) based on 2-step thermal redox cycles in metal oxides is a promising approach to generating H 2 , but state-of-the-art (SOTA) CeO 2 has several practical limitations, which has motivated continued materials discovery efforts in this field. Here, in this study, we improve upon a SOTA defect graph neural network (dGNN) surrogate model's oxygen vacancy predictions and combine them with materials project phase diagrams to down-select and discover structurally diverse, experimentally known metal oxides whose TCH performance was previously unknown. Amongst twelve candidates selected based on our high-throughput screening and down-selection criteria, we achieved ∼80% accuracy in identifying materials with stable redox cycling and hydrogen production in stagnation flow reactor water-splitting experiments. Closer to 100% accuracy can be achieved if higher-accuracy, hybrid DFT-predicted vacancy formation energies were computed and used in lieu of the most uncertain dGNN-based screening predictions, as they correct false positives to true negatives. Notably, two discovered candidates, Sr 3 PrMn 2 O 8 and Ba 2 Fe 2 O 5 , display hydrogen yields greater than CeO 2 under specific redox conditions. In conclusion, these results demonstrate our ability to computationally predict and experimentally validate promising candidate TCH materials that have the potential to compete with CeO 2 .

08 HYDROGEN↗
DOE OSTI2026

Machine-Learning-Driven Discovery of Water Splitting BaFe 2 O 4 and Human-in-the-Loop Improvement via Al-Substitution for Increased Thermal Stability

Thermochemical hydrogen (TCH) production offers a promising method for converting thermal energy into hydrogen fuel through heat-driven redox cycles of metal oxides. Here, in this work a defect graph neural network (dGNN) was used to predict oxygen vacancy formation energies ΔH V O combined with Materials Project predictions of oxygen chemical potential stability to screen candidate oxides via high-throughput database analysis. BaFe 2 O 4 was identified as a promising material for experimental validation based on its predicted ΔH V O , oxygen chemical potential stability range, and potential for tunable substitutions to improve thermal properties. Experimental validation using thermogravimetric analysis (TGA), stagnation flow reactor (SFR), X-ray diffraction (XRD), and electron microscopy confirmed positive water-splitting behavior but also revealed limitations in thermal stability under aggressive reduction conditions. To address this, a human-in-the-loop modification strategy was employed introducing Al substitution in BaFe 2–x Al x O 4 ; this modification improves thermal stability, alters the crystal structure and enhances overall performance. These results demonstrate a combined computational and experimental workflow in which machine learning accelerates identification of promising candidates, while targeted experimental design enables optimization of functional performance. This approach advances the development of robust, cost-effective TCH materials and highlights the importance of integrating data-driven discovery with human-guided materials design in paving the way for scalable hydrogen production technologies.

organic↗
DOE OSTI2025

Electric-charge-dependent directed flow splitting of produced quarks in Au+Au collisions

We report directed flow (v 1 ) of multistrange baryons ($Ξ$ and Ω) and improved v 1 data for K – ,$\overline{p}$, $\overline{Λ}$, and ϕ in Au+Au collisions at $\sqrt{s_{NN}}$ = 27 and 200 GeV from the STAR experiment at the Relativistic Heavy Ion Collider (RHIC). We focus on particles whose constituent quarks are not transported from the incoming nuclei but instead are produced in the collisions. At intermediate impact parameters, we examine quark coalescence behavior for particle combinations with identical quark content, and search for any departure from this behavior (“splitting”) for combinations having non-identical quark content. Under the assumption of quark coalescence for produced quarks, the splitting strength appears to increase with the electric charge difference of the constituent quarks in the combinations, consistent with electromagnetic effect expectations.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗