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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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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

On High-Order/Low-Order and Micro-Macro Methods for Implicit Time-Stepping of the BGK Model

In this paper, a high-order/low-order (HOLO) method is combined with a micro-macro (MM) decomposition to accelerate iterative solvers in fully implicit time-stepping of the Bhatnagar–Gross–Krook (BGK) equation for gas dynamics. The MM formulation represents a kinetic distribution as the sum of a local Maxwellian and a perturbation. In highly collisional regimes, the perturbation away from initial and boundary layers is small and can be compressed to reduce the overall storage cost of the distribution. The convergence behavior of the MM methods, the usual HOLO method, and the standard source iteration method is analyzed on a linear BGK model. Both the HOLO and MM methods are implemented using a discontinuous Galerkin (DG) discretization in phase space, which naturally preserves the consistency between high- and low-order models required by the HOLO approach. Furthermore, the accuracy and performance of these methods are compared on the Sod shock tube problem and a sudden wall heating boundary layer problem. Overall, the results demonstrate the robustness of the MM and HOLO approaches and illustrate the compression benefits enabled by the MM formulation when the kinetic distribution is near equilibrium.

BGK model↗
DOE OSTI2025

Dataset for manuscript "Equipartition and the temperature of maximum density of TIP4P/2005 water"

We simulate TIP4P/2005 water in the temperature range of 257 K to 318 K with time-steps 0.25, 0.50, 1.00, 2.00, and 4.00 fs. The density-temperature behavior obtained using 0.25 or 0.50 fs are in excellent agreement with each other but differ from those obtained using time-steps that have been shown earlier to lead to a breakdown of equipartition. The temperature of maximum density (TMD) is 277.15 K with time-step 0.25 or 0.50 fs, but is shifted to progressively lower values for longer time-steps, a trend that holds for different thermostat/barostat combinations. Enhancing the water-water dispersion interaction, as has been recommended for simulating disordered proteins in TIP4P/2005, degrades the description of the liquid-vapor phase envelope. We present a simple physically transparent reasoning to highlight the separation of the time-scales between translational and rotational motion. We also develop a metric, Chi, that we term the equipartition anomaly, to detect equipartition violations in simulations that include molecules that are treated as rigid objects. Calculating Chi is shown to be straightforward and sensitive to equipartition violations. A key takeaway from this study is that using sufficiently short time-steps (less than or equal to 0.5 fs) to preserve equipartition is essential for obtaining meaningful liquid water properties and for producing reliable simulation data, as correct-ensemble sampling is fundamental to ensure reproducibility across codes and simulation alogrithms. The included dataset provides the raw data used in the preparation of the graphs noted in the manuscript.

36 MATERIALS SCIENCE↗
DOE OSTI2025

A review of high order strong stability preserving two-derivative explicit, implicit, and IMEX methods

High order strong stability preserving time discretizations ensure the nonlinear non-inner-product strong stability properties of spatial discretizations suited for the stable simulation of hyperbolic PDEs in a wide variety of application areas including fluid dynamics, magnetohydrodynamics, semiconductor devices, electromagnetics, and astrophysics. Over the past decade multiderivative time-stepping have been increasingly used for the time-evolution hyperbolic PDEs, so that the strong stability properties of these methods have become important. In this work we review sufficient conditions for a two-derivative multistage method to preserve the strong stability properties of spatial discretizations in a forward Euler and different conditions on the second derivative. In particular we present the strong stability preserving theory for explicit and implicit two-derivative Runge–Kutta schemes, including a special condition on the second derivative under which these implicit methods may be unconditionally strong stability preserving. This special condition is natural for the stiff component of wide range of plasma physics problems, and can be useful in the context of strong stability preserving implicit-explicit multi-derivative Runge–Kutta schemes, where the time-step restriction is then independent of the stiff term. Lastly, we present the strong stability preserving theory for implicit-explicit multi-derivative general linear methods, and some novel second and third order methods where the time-step restriction is independent of the stiff term.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Explicit Monotone Stable Super-Time-stepping Methods for Finite Time Singularities

We explore a novel way to numerically resolve the scaling behavior of finite-time singularities in solutions of nonlinear parabolic PDEs. The Runge–Kutta–Legendre (RKL) and Runge–Kutta–Gegenbauer (RKG) super-time-stepping methods were originally developed for nonlinear complex physics problems with diffusion. These are multistage single step second-order, forward-in-time methods with no implicit solves. The advantage is that the time-step size for stability scales with stage number 𝑠 as $\mathcal{O}$⁡(𝑠 2 ). Many interesting nonlinear PDEs have finite-time singularities, and the presence of diffusion often limits one to using implicit or semi-implicit time-step methods for stability constraints. Finite-time singularities are particularly challenging due to the large range of scales that one desires to resolve, often with adaptive spatial grids and adaptive time steps. Here, in this study, we show two examples of nonlinear PDEs for which the self-similar singularity structure has time and space scales that are resolvable using the RKL and RKG methods, without forcing even smaller time steps. Compared to commonly used implicit numerical methods, we achieve a significantly smaller run time while maintaining comparable accuracy. We also prove numerical monotonicity for both the RKL and RKG methods under their linear stability conditions for the constant coefficient heat equation, in the case of infinite domain and periodic boundary condition, leading to a theoretical guarantee of the superiority of the RKL and RKG methods over traditional super-time-stepping methods, such as the Runge-Kutta-Chebyshev and the orthogonal Runge-Kutta-Chebyshev methods. Code can be found at https://github.com/ZT220501/SRK-Singularity.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Role of Computational Parameters on Predicting Self-Consistent Residual Stress and Distortion during Wire Arc Additive Manufacturing

Production of three-dimensional metallic parts through integration of an articulated robot and gas metal arc welding, also known as wire arc additive manufacturing (WAAM), can produce large-scale components with moderate geometrical complexity. This technology is particularly appealing due to its high deposition rates, scalability, and cost-effective feedstock compared to other AM processes. Despite its advantages, WAAM adoption is hindered by challenges in ensuring geometric conformity without extensive distortion, defect-free structures, and consistent mechanical properties. Finite element analysis (FEA) is often used to address the challenge of geometrical conformity. As the size of parts increases, the best practices for mesh size and temporal resolution known in the literature become computationally unviable. This research examined the effects of mesh and time-step resolutions during transient FEA of a large-scale (248 layers) metallic part. The impact of computational parameters on the thermal history, displacement, and residual stress distributions were evaluated. The results showed that predicted distortion was consistent across resolutions, while time-step length significantly affected predicted thermal history, and mesh size influenced residual stress distributions. To investigate this relationship further, directionally biased meshes were considered and analyzed. The results indicated that increasing mesh resolution perpendicular to the welding path yielded stress predictions that aligned closely with higher-resolution models while offering substantial computational savings. In conclusion, the significances of this research are related to verification and validation of WAAM models for widespread industrial adoption and pragmatic guidelines for optimizing computation parameters for balancing computational efficiency and predictive accuracy of residual stress and distortion.

Solsbee, Brandon [Univ. of Tennessee, Knoxville, T↗
DOE OSTI2026

Parallel-in-Time Solution of Allen-Cahn Equations by Integrating Operator Learning into the Parareal Method

While recent advances in deep learning have shown promising efficiency gains in solving time-dependent partial differential equations (PDEs), matching the accuracy of conventional numerical solvers still remains a challenge. One strategy to improve the accuracy of deep learning-based solutions for time-dependent PDEs is to use the learned model as the coarse propagator in the Parareal method and a traditional numerical method as the fine solver. However, successful integration of deep learning into the Parareal method requires consistency between the coarse and fine solvers, particularly for PDEs exhibiting rapid changes such as sharp transitions. Here, to ensure this consistency, we propose using convolutional neural networks (CNNs) to learn the fully discrete time-stepping operator defined by the same numerical scheme employed as the fine solver. We demonstrate the effectiveness of the proposed method in solving the classical and mass-conservative Allen–Cahn (AC) equations. Through iterative updates in the Parareal algorithm, our approach achieves a significant computational speedup compared to traditional fine solvers while converging to high-accuracy solutions. Our results highlight that the proposed hybrid Parareal algorithm effectively accelerates simulations, particularly when implemented on multiple GPUs, and converges to the desired accuracy in only a few iterations. Another advantage of our method is that the CNN model is trained on trajectory-based data generated from random initial conditions, such that the trained model can be used to solve the AC equations with various initial conditions without retraining. This work demonstrates the potential of integrating neural network methods into parallel-in-time frameworks for efficient and accurate simulations of time-dependent PDEs.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Regularizing the linearly extrapolated BDF2 scheme for incompressible flows with time relaxation

This paper presents a highly-efficient finite element scheme for the time relaxation model (TRM). The efficiency is achieved through the second-order BDF2 time-stepping scheme with linear extrapolation (BDF2LE). The accuracy of the scheme is also greatly enhanced through the use of the divergence-free Scott-Vogeulis finite elements, and van Cittert approximate deconvolution. A complete finite element analysis is provided, which includes rigorous proofs for the stability, well-possessedness, and convergence of both velocity and pressure solutions. Furthermore, we also demonstrate that the inclusion of the linear time relaxation term preserves the long-time stability of the unregularized BDF2LE scheme. Finally, numerical experiments are presented that demonstrate the added stability and accuracy that time relaxation can provide.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Numerical schemes for 3-wave kinetic equations: A complete treatment of the collision operator

In our previous work Walton and Tran (2023), numerical schemes for a simplified version of 3-wave kinetic equations, in which only the simple forward-cascade terms of the collision operators are kept, have been successfully designed, especially to capture the long time dynamics of the equation given the multiple blow-up time phenomenon. In this second work in the series, we propose numerical treatments for the complete 3-wave kinetic equations, in which the complete, much more complicated collision operators are fully considered based on a novel conservative form of the equation. Here we then derive an implicit finite volume scheme to solve the equation. The new discretization uses an adaptive time-stepping method which allows for the simulations to be carried to very long times. Our computed solutions are compared with previously derived long-time asymptotic estimates for the decay rate of total energy of time-dependent solutions of 3-wave kinetic equations and found to be in excellent agreement.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Equipartition and the Temperature of Maximum Density of TIP4P/2005 Water

Here, we simulate TIP4P/2005 water in the temperature range of 257 to 318 K with time-steps δ = 0.25, 0.50, 1.00, 2.00, and 4.00 fs. The density–temperature behavior obtained using 0.25 or 0.50 fs is in excellent agreement with each other but differs from those obtained using time steps that have been shown earlier to lead to a breakdown of equipartition. For δt = 0.25 or 0.50 fs, the temperature of maximum density (TMD) is 277.15 K and the density value is in close agreement with experiments. For δt = 1.00 fs, the TMD is 277.15 K, but the density value is shifted higher. For the other time steps considered here, the TMD is shifted to progressively lower values for longer time steps, a trend that holds for different thermostat/barostat combinations. Enhancing the water–water dispersion interaction, as has been recommended for simulating disordered proteins in TIP4P/2005, degrades the description of the liquid–vapor phase envelope. We present a simple physically transparent explanation that highlights the separation of the time scales between translational and rotational motion. We also develop a metric, χ, that we term the equipartition anomaly, to detect equipartition violations in simulations that include molecules that are treated as rigid objects. Calculating χ is shown to be straightforward and sensitive to equipartition violations. A key takeaway from this study is that using sufficiently short time steps (≤0.5 fs) to preserve equipartition is essential for obtaining meaningful liquid water properties and for producing reliable simulation data, as correct ensemble sampling is fundamental to ensure reproducibility across codes and simulation algorithms.

Asthagiri, Dilipkumar N. [Oak Ridge National Labor↗
DOE OSTI2026

The Energy Exascale Earth System Model Version 3: 2. Overview of the Coupled System

The Energy Exascale Earth System Model version 3 (E3SMv3) represents the latest advancement in Earth system modeling developed by the U.S. Department of Energy (DOE). Building upon previous versions, E3SMv3 introduces significant updates across its coupled components to enhance capability and improve fidelity. The atmosphere component incorporates advancements in chemistry, aerosol-cloud interactions, convection, and microphysics. The ocean features a new time-stepping scheme and a higher-resolution unstructured mesh with sub-ice-shelf cavities, while the sea ice model integrates advanced snow and ice physics for more realistic cryospheric simulations. The land model introduces prognostic vegetation dynamics and a new sub-grid topographic treatment of solar radiation. A new tri-grid configuration harmonizes the horizontal grids of the land and river components for improved process coupling. It is enabled by a new non-linear remapping between the atmosphere and land. E3SMv3 underwent extensive testing through a comprehensive simulation campaign, including pre-industrial control, idealized CO 2 experiments, and historical simulations spanning 1850–2024. The model demonstrates significant improvements in simulating the evolution of the historical surface temperature, particularly addressing the “pothole cooling” bias in earlier versions. Reduced aerosol-related forcing contributes to more realistic radiative forcing and better alignment with the observational record. Ocean heat content (OHC) and sea ice trends are also improved as a result.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Advancing simulations of coupled electron and phonon nonequilibrium dynamics using adaptive and multirate time integration

Electronic structure calculations in the time domain provide a deeper understanding of nonequilibrium dynamics in materials. The real-time Boltzmann equation (rt-BTE), used in conjunction with accurate interactions computed from first principles, has enabled reliable predictions of coupled electron and lattice dynamics. However, the timescales and system sizes accessible with this approach are still limited, with two main challenges being the different timescales of electron and phonon interactions and the cost of computing collision integrals. As a result, only a few examples of these calculations exist, mainly for two-dimensional (2D) materials. Here we leverage adaptive and multirate time integration methods to achieve a major step forward in solving the coupled rt-BTEs for electrons and phonons. Relative to conventional (non-adaptive) time-stepping, our approach achieves a 10x speedup for a target accuracy, or greater accuracy by 3–6 orders of magnitude for the same computational cost, enabling efficient calculations in both 2D and bulk materials. This efficiency is showcased by computing the coupled electron and lattice dynamics in graphene up to ~100 ps, as well as modeling ultrafast lattice dynamics and thermal diffuse scattering maps in bulk materials (silicon and gallium arsenide). In addition to improved efficiency, our adaptive method can resolve the characteristic rates of different physical processes, thus naturally bridging different timescales. This enables simulations of longer timescales and provides a framework for modeling multiscale dynamics of coupled degrees of freedom in matter. Our work opens new opportunities for quantitative studies of nonequilibrium physics in materials, including driven lattice dynamics with phonons coupled to electrons, spin, and other degrees of freedom.

Yao, Jia [California Institute of Technology (CalT↗
DOE OSTI2026

Accelerating kinetic plasma simulations with machine-learning-generated initial conditions

Computational models of plasma technologies often solve for the system operating conditions by time-stepping an initial value problem to a quasi-steady solution. However, the strongly nonlinear and multi-timescale nature of plasma dynamics often necessitate millions, or even hundreds of millions, of steps to reach convergence, reducing the effectiveness of these simulations for computer-aided engineering. We consider acceleration of kinetic plasma simulations via data-driven machine-learning-generated initial conditions, which initialize the simulations close to their final quasi-steady-state, thereby reducing the number of steps to reach convergence. Three machine-learning models are developed to predict the density and ion kinetic profiles of capacitively coupled plasma discharges relevant to the microelectronics industry. The models are trained on kinetic simulations over a range of device operating frequencies and pressures. Best performance was observed when simulations were initialized with ion kinetic profiles generated by a convolutional neural network, reducing the mean number of steps to reach convergence by 17.1× when compared to initialization with a zero-dimensional global model. We also outline a workflow for continuous data-driven model improvement and simulation speedup, with the aim of generating sufficient data for full device digital twins.

Artificial neural networks↗
DOE OSTI2026

Verification of an energy-conserving semi-implicit electrostatic particle-in-cell scheme for modeling high-density plasma at scale

A verification study of a semi-implicit energy-conserving electrostatic particle-in-cell algorithm is presented. The algorithm relaxes the time-step and mesh-size constraints that require resolution of the plasma period and Debye length associated with traditional explicit momentum-conserving particle-in-cell algorithms. Physical implications and applicability of using the semi-implicit scheme for modeling high-density plasmas are discussed. Where possible, numerical results are compared against analytical solutions. The simulation results indicate that the algorithm is stable at time steps larger than twice the inverse plasma frequency and cell sizes larger than the Debye length. It is found that the algorithm gives adequate results, provided that the distribution function and the spatiotemporal scales dictating the physics of the problem are resolved. As such, the algorithm may provide a robust method for kinetic modeling of high-density plasmas at scale.

Cyclotron resonance↗
DOE OSTI2025

Towards modelling AR Sco: calibration – reproducing high-energy pulsar emission and testing convergence to Aristotelian electrodynamics

In recent years, kinetic simulations have been crucial to further our understanding of pulsar electrodynamics. Yet, due to the large-scale separation between the gyro-period and the stellar rotation period, resolving the particle gyration has been computationally unfeasible for realistic pulsar parameters. The main aim of this work is comparing our gyro-phase-resolved model with a gyro-centric pulsar model, where our model solves the general equations of motion with included radiation reaction using a higher order numerical solver with adaptive time-steps. Specifically, we aim to (i) reproduce a pulsar’s high-energy emission maps, namely one with 10 per cent of the surface B-field strength of Vela, and the spectra produced by an independent gyro-centric pulsar emission model; and (ii) test convergence of these results to the radiation-reaction limit of Aristotelian electrodynamics. (iii) Additionally, we identify the effect that a large $E_{\parallel }$-field has on the trajectories and radiation calculations. We find that we can reproduce the curvature radiation emission maps and spectra well, using 10 per cent field strengths of the Vela pulsar and injecting our particles at a higher altitude in the magnetosphere. Using sufficiently large $E_{\parallel }$-fields, our numeric results converge to the analytic radiation-reaction limit trajectories. Additionally, we illustrate the importance of accounting for the $\mathbf {E}\times \mathbf {B}$-drift in the particle trajectories and radiation calculations, validating the Harding and collaborators’ model approach. Lastly, we found that our model deals very well with the high-radiation-reaction and high-field regimes present in pulsars.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Operator dynamics in Floquet many-body systems

We study operator dynamics in many-body quantum systems, focusing on generic features of systems that are ergodic, spatially extended, and lack conserved densities. Quantum circuits of various types provide simple models for such systems. We focus on Floquet quantum circuits, comparing their behavior with what has been found previously for circuits that are random in time. Floquet circuits, which have discrete time-translation symmetry, represent an intermediate case between circuits that are random in time and lack any symmetry, and systems with a time-independent Hamiltonian and continuous time-translation invariance. By making this comparison, one of our aims is to identify signatures of time-translation symmetry in Floquet operator dynamics. To characterize behavior we examine a variety of quantities in solvable models and numerically: operator autocorrelation functions; the partial spectral form factor; the out-of-time-order correlator (OTOC); and the paths in operator space that make the dominant contributions to the ensemble-averaged autocorrelation functions. Our most striking result is that ensemble-averaged autocorrelation functions show behavior that is distinctively different in Floquet systems compared to systems in which successive time-steps are independent. Specifically, while average autocorrelation functions decay on a microscopic timescale for circuits that are random in time, in Floquet systems they have a late-time tail with a duration that grows parametrically with the size of the operator support. In the simplest models this tail is separated from the initial decay by a minimum, so that the average autocorrelation function has an intermediate-time peak. The existence of these tails provides a way to understand deviations of the spectral form factor from random matrix behavior at times shorter than the Thouless time. In contrast to this feature in autocorrelation functions, we find no new aspects to the behavior of OTOCs for Floquet models compared to random-in-time circuits. We show that this difference between averaged autocorrelation functions and OTOCs can be understood in terms of the paths in operator space that contribute to the two quantities: paths for the former retain a limited support at late times, while paths for the latter are dominated by operator spreading. Published by the American Physical Society 2025

Yoshimura, Takato (ORCID:0000000309159846)↗
DOE OSTI2025

Adaptive Graph Learning with Transformer for Multi-Reservoir Inflow Prediction

Reservoir inflow prediction is crucial for water resource management, yet existing approaches mainly focus on single-reservoir models that ignore spatial dependencies among interconnected reservoirs. We introduce AdaTrip as an adaptive, time-varying graph learning framework for multi-reservoir inflow forecasting. AdaTrip constructs dynamic graphs where reservoirs are nodes with directed edges reflecting hydrological connections, employing attention mechanisms to automatically identify crucial spatial and temporal dependencies. Evaluation on thirty reservoirs in the Upper Colorado River Basin demonstrates superiority over existing baselines, with improved performance for reservoirs with limited records through parameter sharing. Additionally, AdaTrip provides interpretable attention maps at edge and time-step levels, offering insights into hydrological controls to support operational decision-making. Our code is available at https://github.com/humphreyhuu/AdaTrip.

Hu, Pengfei [ORNL] (ORCID:0009000367130950)↗
DOE OSTI2025

Machine Learned Empirical Numerical Integrator from Simulated Data

Recently, a number of state-of-the-art surrogate machine learning (ML) models have been designed for global weather and climate prediction, which have been trained using reanalysis data products. Reanalysis data products are constructed using numerical model simulations that combine numerical integration of partial differential equations and parameterization schemes. These products are typically only archived and made available using coarsened spatial and temporal resolutions. This study explores the impact of the numerical generation methods used to produce the training datasets and the temporal resolution of those datasets on machine learning surrogate models. Using the nonlinear vector autoregression (NVAR) machine as an explainable ML technique, simple dynamical systems are emulated with ML models trained on data produced by three classical numerical integration schemes. NVAR is validated as a skillful ML method, capable of producing accurate predictions and, more importantly, reconstructing both the underlying dynamics and the numerical integration scheme used to generate the training data. However, the machine fails to generalize predictions on unseen test data generated by different numerical integration schemes, despite the underlying dynamical system being the same. This result provides a word of caution for the growing field of machine learning emulation of weather and climate dynamics. Furthermore, we illustrate using NVAR that training on temporally coarsened data may increase the required complexity of ML models and potentially introduce new numerical challenges. Finally, we discover that empirical integration schemes with arbitrary time-stepping sizes can be constructed directly from the data, which implies a potential for the development of empirical numerical integration schemes.

54 ENVIRONMENTAL SCIENCES↗