Search NASA⌕ Search

SEARCH · Search NASA

Results for “Numerical methods”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 271 records · Page 15

Estimating Eigenenergies from Quantum Dynamics: A Unified Noise-Resilient Measurement-Driven Approach

Ground state energy estimation in physical, chemical, and materials sciences is one of the most promising applications of quantum computing. In this work, we introduce a new hybrid approach that finds the eigenenergies by collecting real-time measurements and post-processing them using the machinery of dynamic mode decomposition (DMD). From the perspective of quantum dynamics, we establish that our approach can be formally understood as a stable variational method on the function space of observables available from a quantum many-body system. We also provide strong theoretical and numerical evidence that our method converges rapidly even in the presence of a large degree of perturbative noise, and show that the method bears an isomorphism to robust matrix factorization methods developed independently across various scientific communities. Our numerical benchmarks on spin and molecular systems demonstrate an accelerated convergence and a favorable resource reduction over state-of-the-art algorithms. The DMD-centric strategy can systematically mitigate noise and stands out as a leading hybrid quantum-classical eigensolver.

Shen, Yizhi↗

Resonant Raman in armchair graphene nanoribbons from first-principles

Resonant Raman spectra of armchair graphene nanoribbons (AGNRs) are computed using Density Functional Theory (DFT) and third-order perturbation theory. Results are benchmarked against available experimental data and compared to previously used theoretical approaches based on the Placzek approximation. Comparable agreement with experiments is found for both previously and presently used methods. In addition, a numerical analysis is carried out to provide a justification for the resonant modeling method based on the use of the frequency-dependent dielectric tensor in the Placzek approximation. Finally, this work also provides additional predictions and references for wide AGNRs that might be investigated with Raman scattering experiments in the future.

42 ENGINEERING↗

Numerical analysis of gas exhaust in Wendelstein 7-X using the direct simulation Monte Carlo method

The present work is focused on a 3D numerical assessment of the Wendelstein 7-X (W7-X) particle exhaust. For all the numerical simulations the direct simulation Monte Carlo solver of the DIVGAS workflow, has been employed. The complex 3D geometry of the sub-divertor region includes the pumping gap panel, supporting structures, cooling pipes as well as the cryo-vacuum pump. All the considered flow simulations correspond to the Standard magnetic configuration of W7-X. The main conclusions, which can be extracted from the present numerical analysis could be summarized as follows; The coupling between EMC3-EIRENE and DIVGAS, which considers the fact that the incoming neutral particle flux at the sub-divertor is based on realistic plasma background, has been demonstrated. Three plasma scenarios have been considered, for which is clearly seen that by increasing the heating power, the neutral pressure as well as the resulting pumping efficiency is increased. The obtained numerical results of the neutral pressure in the sub-divertor lie within a more general scan matrix, which assumes a wider range of incoming particle flux, namely 10 19 –10 24 (s −1 ). It has been observed that, the sub-divertor neutral pressure is proportional to the incoming neutral particle flux, with the effective pumping speed to be a constant of proportionality. The influence of switching off the cryo-vacuum pump on the sub-divertor pressure is rather modest and a weak increase of the neutral pressure in the sub-divertor is expected. Correlations of the sub-divertor pressure with the total incoming particle flux as well as the individual pumped flux at each of the AEH and AEP sections have been deduced. Moreover, it has been demonstrated that the influence of the incoming neutral particle flux on the albedo coefficient at the AEH and AEP pumping gaps is rather weak. All the above numerical findings will actively support the optimization of the W7-X particle exhaust, in view of future experimental campaigns.

DSMC method↗

Investigation of residual stress distribution in wire-arc directed energy deposited refractory molybdenum alloy utilizing numerical thermo-mechanical analysis and neutron diffraction method

Directed energy deposition (DED), a metal additive manufacturing (AM) technique, offers higher deposition rates and energy efficiency, making it suitable for fabricating components from refractory molybdenum alloys, such as molybdenum-titanium-zirconium (TZM). However, large thermal gradients and non-equilibrium thermal cycles in DED could generate high residual stress in the component, potentially deteriorating quality and performance. Thus, this study aims to investigate residual stress generation and its distribution in wire-arc DED of TZM thin-wall, utilizing thermo-mechanical analysis and high-fidelity neutron diffraction (ND) method. Two interpass temperatures (50°C and 200°C) have been considered to investigate their impact on residual stress formation. During experiments, in-situ thermal data has been recorded using thermocouples, which have been utilized for calibrating the thermal model. Thermocouple data shows a good agreement with the simulation results, having a difference of less than 10 %. Post-deposition part deformation has been observed, which is measured using a coordinate measuring machine, showing maximum values of 0.93 mm and 0.78 mm for interpass temperatures of 50°C and 200°C, respectively. Numerical predictions of distortion deviated by less than 15% from the experimental results. ND measurement and simulation results indicate that residual stress magnitude and evolution vary across the TZM deposits, revealing microstructural anisotropy in both conditions. Notably, lower interpass temperatures resulted in higher residual stresses, confirmed by experimental and simulation data. Further, this study demonstrated that an integrated experimental and thermo-mechanical analysis can potentially reveal the temperature history, part deformation, and residual stress formation in wire-arc DED TZM alloy.

36 MATERIALS SCIENCE↗

Enabling Low-Temperature (LTP) Ignition Technologies for Multi-Mode Engines through the Development of a Validated High-Fidelity LTP Model for Predicative Simulations Tools

The goal of multi-mode engine architectures is to extend current lean-burn dilution limits with renewable fuels, which requires spark plugs to deposit high energies (hundreds of mJ) in order to initiate ignition and complete combustion. At elevated energy deposition rates, spark plugs experience increased electrode erosion and thermal losses, which ultimately shortens the spark-plug lifetime and lowers ignition efficiency. As such, in order to safeguard the efficiency gains of multi-mode concepts, new and improved ignition technologies are required. Recently, non-equilibrium low-temperature plasmas (LTP) have been shown to promote energy-efficient ignition via quenching and transport of electronically excited atoms and molecules, selective radical production and fast heating of hydrocarbon/air mixtures [1-2]. Thus, LTP is seen as a technology that can potentially improve the energy extraction efficiency of fuels, while enabling kinetically controlled combustion modes towards fuel leaner conditions to realize current DOE VTO goals of improving the sustainability of future mobility [3]. Although many previous studies have demonstrated the efficacy of plasma-assisted ignition to enhance combustion, the detailed enhancement mechanisms remain largely unknown, especially for oxygenated fuels and at elevated pressures that are most relevant to practical engine conditions. These barriers hinder the development of accurate and comprehensive numerical models that seek to describe LTP-based ignition in existing engine design software tools and methods. Current state-of-the-art simulation capabilities for LTP ignition systems are in need of improvements since they deliver qualitative results only due to important limitations of existing approaches. Firstly, validated kinetic models with elementary steps for plasma discharges in oxygenated fuel/air mixtures of relevance to the transportation sector are required. Such kinetic models do not exist at present and will be developed and validated within this project. Secondly, plasma discharges and reactive mixture ignition are multi-scale, unsteady processes requiring high-performance numerical methods and software that execute efficiently on DOE supercomputers. Such software does not exist at present and will be developed and applied to practical LTP ignition scenarios as part of this project. Thirdly, experimental databases that are tailored to serve as benchmark in support of the development of predictive computational models of LTP ignition do not exist and will be part of this project.

33 ADVANCED PROPULSION SYSTEMS↗

TRUST Contact Thermal Conductance (TRUST-CTC) Report: FY24

The objective of the Delivery Environments (DE) Testbeds to Reduce Uncertainties in Simulations and Tests (TRUST) project is to quantify and help increase confidence in specific areas of computational and experimental capabilities that are applicable to current and future delivery environments. More complete quantification of confidence in experimental and computational capabilities and the sufficient increase of confidence in those capabilities is critical to improving weapons engineering design, qualification, and assessment efforts that are critical to the current and future stockpile. Staff development will include cross-discipline collaboration to provide engineers with experience in both numerical simulations and experimental methods. This work uses and provides feedback on analysis tools and experimental results databases for efficient and responsive engineering which are currently under development. TRUST currently includes five testbeds and their associated engineering analysis baseline models (EABMs): 1. contact thermal conductivity, (CTC) 2. nonlinear dynamics, (ND) 3. sensors in environments for accelerometers, (SEA) 4. sensors in environments for fiber optic displacement gages, and (SEFOD) 5. sensors in environments for thermocouples (SETC). The TRUST project uses single-feature testbeds to quantify uncertainties in specific models and experiments and to identify capability development needs that can help to reduce these uncertainties. Each testbed is designed, configured, and tested in collaboration with groups with design and experimental capability: E-14 and MPA-CINT. The complementary simulations are conducted using W-13 analysis tools and stored in model repositories with plans for incremental progress toward EABM requirements. W-13 extends and exercises the testbed simulations in collaboration with experimentalists for uncertainty quantification of current and future materials, geometries, and environments. Additionally, TRUST is intended to provide engineers in W-13 and E-14 with experience in both numerical simulations and experimental methods through cross-discipline collaborations. Following the introduction to the TRUST project, the remainder of this report focuses on experimental and analytical efforts conducted in Fiscal Year (FY) 2024 relevant to the TRUST Contact Thermal Conductance (CTC) testbed.

42 ENGINEERING↗

Prediction of dynamic behavior of a system undergoing an exchange of components using a transmission simulator method

In systems with modular design, it is of interest to perform component exchanges to upgrade components and explore new system configurations. If the dynamics of the components are known, then dynamic substructuring can be used to obtain a prediction of system performance for the new configuration. The transmission simulator method is a substructuring technique that utilizes an additional fixture to apply an elastic boundary condition to a test article such that an appropriate dynamic response can be obtained for a given substructuring application, and the technique has been used widely for performing coupling and decoupling operations. Here, in this work, a modified transmission simulator method is proposed that allows a direct exchange of components to be performed. In a numerical demonstration, the proposed method is shown to accurately predict the dynamics of an assembly that has undergone a component exchange in which the exchanged components have different material properties and different geometric properties. This approach can be applied to dynamic qualification frameworks in which structures undergo modifications or upgrades rather than complete redesigns.

Component exchange↗

Compact representation and long-time extrapolation of real-time data for quantum systems using the ESPRIT algorithm

Representing real-time data as a sum of complex exponentials provides a compact form that enables both denoising and extrapolation. As a fully data-driven method, the Estimation of Signal Parameters via Rotational Invariance Techniques (ESPRIT) algorithm is agnostic to the underlying physical equations, making it broadly applicable to various observables and experimental or numerical setups. In this work, we consider applications of the ESPRIT algorithm primarily to extend real-time dynamical data from simulations of quantum systems. We evaluate ESPRIT's performance in the presence of noise and compare it to other extrapolation methods. We demonstrate its ability to extract information from short-time dynamics to reliably predict long-time behavior and determine the minimum time interval required for accurate results. We discuss how this insight can be leveraged in numerical methods that propagate quantum systems in time, and we show how ESPRIT can predict infinite-time values of dynamical observables, offering a purely data-driven approach to characterizing quantum phases.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Performing Numerical Analysis of Cybersecurity Options Using Dynamic Risk Analysis Tool EMRALD

Cyberattacks can have many different attack paths, durations, and goals. There are also many different mitigation options involving hardware, software, and/or humans. Considering a cyber threat should involve defense-in-depth methods and a quantitative or numerical evaluation of overall effectiveness against dynamic, time-dependent attacks to make cost and risk-informed decisions. Typical cyberattack modeling methods only provide a qualitative evaluation. The main areas of cybersecurity are confidentiality, integrity, and availability. For companies with cyber-physical systems such as advanced nuclear reactors, cyber-related safety is a requirement set by North American Electric Reliability and the U.S. Nuclear Regulatory Commission. They are also concerned about availability or reliability as a business case. As cyber threats are evolving to a business-for-hire structure, more attacks may focus on disrupting business success and reliability, causing financial and economic stability risk. Companies want to know business reliability and recovery from those threats, and that requires modeling physical behavior of the targets. Dynamic-state-based and Markov-based modeling provides a method for better cyber scenario modeling with different tools having issues such as state-base explosion. Dynamic modeling enables time and conditional features not found in other numerical evaluation methods. EMRALD (Event Modeling Risk Assessment using Lined Diagrams) is a dynamic risk analysis modeling and simulation tool and has features that reduce modeling issues. It has been used to model different time-dependent events including plant behavior and operator procedures. As a general modeling tool, EMRALD can also be used to model cyberattack scenarios with varying mitigation options and quantify effectiveness, producing numerical data for risk-informed decisions. This paper uses EMRALD to demonstrate that dynamic numerical risk analysis can be used for cyber threat modeling to provide insights for design decision-making and optimize defense strategies. Keywords: cyber modeling; cyber-physical systems; numerical cyber modeling

97 - MATHEMATICS AND COMPUTING↗

pyDecay: A CRAM-Based Isotope Decay Solver

This module (pyDecay) implements a Chebyshev Rational Approximation Method (CRAM) for solving isotope decay equations, based on the work of M. Pusa. It provides a numerically stable and efficient method for evaluating the matrix exponential involved in nuclear decay calculations. This implementation of CRAM relies on the incomplete partial factorization (IPF) algorithm published by Pusa [3], with corrections noted by Romano et al.

Skutnik, SteveEugene [Oak Ridge National Laborator↗

Robust Iterative Method for Symmetric Quantum Signal Processing in All Parameter Regimes

Here, this paper addresses the problem of solving nonlinear systems in the context of symmetric quantum signal processing (QSP), a powerful technique for implementing matrix functions on quantum computers. Symmetric QSP focuses on representing target polynomials as products of matrices in SU(2) that possess symmetry properties. We present a novel Newton’s method tailored for efficiently solving the nonlinear system involved in determining the phase factors within the symmetric QSP framework. Our method demonstrates rapid and robust convergence in all parameter regimes, including the challenging scenario with ill-conditioned Jacobian matrices, using standard double precision arithmetic operations. For instance, solving symmetric QSP for a highly oscillatory target function α cos(1000x) (polynomial degree ≈ 1433) takes 6 iterations to converge to machine precision when α = 0.9, and the number of iterations only increases to 18 iterations when α = 1 – 10 -9 with a highly ill-conditioned Jacobian matrix. Leveraging the matrix product state structure of symmetric QSP, the computation of the Jacobian matrix incurs a computational cost comparable to a single function evaluation. Moreover, we introduce a reformulation of symmetric QSP using real-number arithmetics, further enhancing the method’s efficiency. Extensive numerical tests validate the effectiveness and robustness of our approach, which has been implemented in the QSPPACK software package.

97 MATHEMATICS AND COMPUTING↗

New particle pusher with hadronic interactions for modeling multimessenger emission from compact objects

We propose novel numerical schemes based on the Boris method in curved spacetime, incorporating both hadronic and radiative interactions for the first time. Once the proton has lost significant energy due to radiative and hadronic losses, and its gyroradius has decreased below typical scales on which the electromagnetic field varies, we apply a guiding center approximation (GCA). We fundamentally simulate collision processes either with a Monte-Carlo method or, where applicable, as a continuous energy loss, contingent on the local optical depth. To test our algorithm for the first time combining the effects of electromagnetic, gravitational, and radiation fields including hadronic interactions, we simulate highly relativistic protons traveling through various electromagnetic fields and proton backgrounds. We provide unit tests in various spatially dependent electromagnetic and gravitational fields and background photon and proton distributions, comparing the trajectory against analytic results. We propose that our method can be used to analyze hadronic interactions in black hole accretion disks, jets, and coronae to study the neutrino abundance from active galactic nuclei.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

High-Fidelity, Low-Dissipation/Symmetry-Preserving Numerical Scheme for Solving the Euler Equations with Unstructured, Metric-Based Mesh Adaptation

This work presents an overview of a high-fidelity compressible Euler solver that utilizes the continuous Galerkin (CG) method with added artificial numerical diffusion for stabilization to solve a variety of unsteady and steady benchmark inviscid flow problems. This work shows that discretizing the Euler equations with this CG approach and first order basis functions produces a cost-effective stencil as well as simple well-posed boundary conditions. We show through convergence testing with manufactured solutions that the reduced stencil of CG, combined with the low amount of artificial diffusion required when using the stabilization method outlined in this work, leads to stable and highly accurate results for a variety of unsteady and steady applications. When combined with the adaptive mesh refinement approach used for many of the cases in this work, our results show that the flow solver achieves even more accurate results. A variety of inviscid flow cases are presented in this work, including transient 2D cases with complex shock structures and several steady 3D airfoils sections with a constant span.

Doetsch, Kevin [ORNL] (ORCID:0000000267051705)↗

Drift kinetic electrostatic simulations of the edge localized mode heat pulse

In the present work, electrostatic drift kinetic simulations of parallel plasma transport within the tokamak scrape-off layer (SOL) are conducted using the COGENT code. The SOL configuration is represented in one-dimensional slab geometry, incorporating a heat source localized in the midplane. The heat source parameters correspond to those characterizing edge-localized modes observed in the Joint European Torus (JET) tokamak. The numerical model includes kinetic treatment of both ions and electrons, a simplified model for the gyrokinetic Poisson equation that allows one to step over short time scales associated with fast electrostatic shear Alfvèn waves, and the logical sheath boundary condition (LSBC) that enforces global system quasineutrality. A third-order accurate LSBC is derived to be consistent with the third-order accurate upwind advection scheme utilized in the code, and it was shown to noticeably impact the simulation results, especially parallel heat flux at the target plate. The findings of this study are in agreement with results from preceding fluid and kinetic simulations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Quantifying Groundwater Response and Uncertainty in Beaver‐Influenced Mountainous Floodplains Using Machine Learning‐Based Model Calibration

Abstract Beavers ( Castor canadensis ) alter river corridor hydrology by creating ponds and inundating floodplains, and thereby improving surface water storage. However, the impact of inundation on groundwater, particularly in mountainous alluvial floodplains with permeable gravel/cobble layers overlain by a soil layer, remains uncertain. Numerical modeling across various floodplain structures considers topographic and sediment complexity and multidirectional flow, linking inundation to groundwater response. This study develops a model‐data integration workflow to address uncertainty in groundwater response to beaver‐induced inundations in a mountainous alluvial floodplain in the Upper Colorado River Basin. Uncertain factors include seasonal hydrologic dynamics, hydraulic conductivities, floodplain structures, and meteorological forcings. We employed an ensemble of groundwater models, based on geophysical and hydrologic data, with machine learning‐based calibration using a neural density estimator. This allowed us to quantify the vertical flux from the soil layer to the permeable gravel bed, the down‐valley underflow within the gravel bed, and their ratios. Results show a significant increase in the vertical flux relative to down‐valley underflow, from 2 during dry pond periods to 20 during wet periods, serving as an analogy for conditions without and with beaver ponds. The study highlights the influence of floodplain structure on groundwater storage, water balance, and water quality impacted by beaver ponds. A thick gravel bed layer, with a large down‐valley underflow, minimizes the effect of beaver‐induced inundation on water quality. We emphasize the need for field‐scale measurements of floodplain structure and improved characterization of evapotranspiration changes to reduce uncertainty in groundwater response. Plain Language Summary Beavers change the flow of water in river corridors by creating ponds, expanding wetlands, and flooding floodplains. This increases surface water area, promotes plant growth, and enhances biodiversity. However, the impact of this flooding on groundwater flow is not well understood, especially in mountainous areas with gravel layers where water moves easily beneath soil. In this study, we used numerical modeling to investigate how beaver ponds influence groundwater in a mountainous floodplain of the Upper Colorado River Basin. We adapted a machine learning method to validate our numerical models using multiple field data sets. Our findings show that beaver ponds significantly increase vertical water flow from the soil to the gravel during wet periods, compared to when the ponds are fully drained. The study also highlights the importance of floodplain structure in controlling both water flow in gravel layers along the river direction and vertical flow from the soil to the gravel with the presence of beavers. To reduce uncertainty in groundwater response, we emphasize the need for more field‐scale measurements of floodplain structure, hydraulic properties, and evapotranspiration changes. Key Points Floodplain structures and hydraulic conductivities are important for groundwater response with beaver ponds in mountainous floodplains Large down‐valley underflow in permeability‐stratified floodplains reduces beaver‐induced impacts on groundwater storage and water quality Machine learning‐based model calibration methods are effective for estimating posterior distributions of groundwater model parameters

Wang, Lijing↗

Magnetic Reconnection

Magnetic reconnection is a fundamental plasma physics process ubiquitous in astrophysics, and important in both magnetic confinement fusion and space weather. The MARZ fundamental science program was recently established on Z to enable the first laboratory astrophysics platform able to access and study the strongly radiatively cooled magnetic reconnection regime. Simulations of this system have successfully used a resistive-MHD approach, but in some regions of parameter space Hall physics has the potential to be important. We describe implementation of a Hall method on a staggered grid resistive-MHD method (compatible with the approach used to model MARZ experiments. We then present a different Hall method based on cell-centered field quantities. Both approaches have been implemented in the Sandia KRAKEN code, to enable us to contrast different numerical Hall-MHD methods within the same HED code.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

A transient near to far field transformation method and verification benchmarking procedure

The numerical calculation of electromagnetic far fields in the time-domain requires a near to far field transformation (NTFF) method. While time-domain NTFF methods for popular finite-difference time-domain (FDTD) approaches are well established, there is little discourse on NTFF methods for finite-element time-domain (FETD) codes. Here, this work is concerned with the development of an NTFF method for the Empire FETD code, which utilizes curl and divergence conforming elements. This discretization presents a difficulty in obtaining the equivalent electric current for the NTFF. Straightforward finite element interpolation of the fields is shown to give poor accuracy. Alternative interpolation methods are recommended. An expanding magnetic quadrupole pulse benchmark problem, which is fully developed in the appendices, provides the basis for quantitative comparison.

FETD↗

Projection-to-Born-improved subtractions at NNLO

While the current frontier in fixed-order precision for collider observables is N 3 LO, important steps are necessary to consolidate NNLO cross-section predictions with improved stability and efficiency. Slicing methods have been successfully applied to obtain NNLO and N 3 LO predictions, but have shown poor performance in the presence of fiducial cuts due to large kinematical power corrections. In this paper we implement Projection-to-Born-improved q T (P2B q T ) and jettiness (P2Bτ 0 ) subtractions for a large class of color singlet processes in MCFM. This method allows for the efficient evaluation of fiducial power corrections in any non-local subtraction scheme using a Projection-to-Born subtraction. We demonstrate the significant numerical improvements of this method based on fiducial Drell-Yan and Higgs cross-sections. Moreover, with fiducial power corrections removed via this method, the leading-logarithmic power corrections that have only been calculated without fiducial cuts can be included, further improving the calculations. For di-photon production with photon isolation, we devise a novel method in combination with P2B-improved subtractions, which we name P2B γ τ 0 , and P2B γ q T for the two subtraction schemes, respectively. This method allows the inclusion of both fiducial power corrections due to kinematic cuts on the photons and a set of isolation power corrections in the fragmentation channel where a quark may enter the isolation cone. We find significant improvements in the convergence of NNLO di-photon cross-sections with photon isolation cuts, demonstrating that it is possible to achieve a stable and efficient calculation of di-photon cross-sections using slicing methods.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗