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DOE OSTI2022

Centrifuge modeling and numerical analysis on lateral performance of mono-bucket foundation for offshore wind turbines

The lateral loading performance of the mono-bucket foundation for offshore wind turbines is investigated in this study through a series of centrifuge tests and numerical analysis. Six mono-bucket models are considered to assess the influences of aspect ratio under the ultimate condition. The FE model is validated against the centrifuge test results, and the failure mechanism of the foundation is revealed. The parametric study and sensitivity analysis of the soil parameters are performed in the numerical simulations. A modified theoretical calculation method is proposed to estimate the ultimate lateral capacity of the suction bucket foundation by solving the limit equilibrium equations. A correction term is added in the calculation using the “m” method. The position of the rotation center is calculated, demonstrating a better accuracy compared to the previously reported geometric method. The modified calculation method is verified against the field test, the centrifuge test, and the laboratory test. The method is proved to be applicable in estimating the lateral performance of the mono-bucket foundation in a general form. Finally, this study aims to provide well-documented data and design references for practical engineers.

17 WIND ENERGY↗

DOE OSTI2026

Axisymmetric hydrodynamics in numerical relativity: treating coordinate singularity, artificial heating and modeling MHD instabilities

Two-dimensional axisymmetric simulations of binary neutron star (BNS) merger remnant are a cheap alternative to 3D simulations. To maintain realism for secular timescales, simulations must avoid accumulated errors from drifts in conserved quantities and artificial heating, and they must model turbulent transport in a way that remains plausible throughout the evolution. It is also crucial to avoid numerical artifacts due to the polar coordinate axis singularity. Methods that behave well near the axis often break flux-conservative form of the hydrodynamic equations, resulting in significant drifts in conserved quantities. We present a flux-conservative scheme that maintains smoothness near the axis without sacrificing conservative formulation of the equations or incurring drifts in conserved global quantities. We compare the numerical performance of different treatments of the hydrodynamic equations when evolving a hypermassive neutron star resembling the remnant of a BNS merger. These simulations demonstrate that the new scheme combines the axis smoothness of non-conservative methods with the mass and angular momentum conservation of other conservative methods on $\sim 10^2$ ms timescales of viscous and neutrino-driven evolution. Because fluid profiles remain smooth in the remnant interior, it is possible to remove artificial heating by evolving the entropy density. We show how physical heating and cooling terms can be easily calculated from source terms of the conservative evolution variables and demonstrate our implementation. Finally, we discuss and implement improvements to the effective viscosity scheme to better model the effect of magnetohydrodynamic instabilities as the remnant evolves.

axisymmetry↗

DOE OSTI2022

Benchmark of few-level quantum theory vs ab initio numerical solutions for the strong-field Autler–Townes effect in photoionization of hydrogen

Abstract The temporal and spectral consequences of an intermediate resonance en route to photoionization are investigated theoretically in two ways: by solving few-level model equations and by ab initio numerical solution of the time-dependent Schrödinger equation, in both cases for hydrogen in three dimensions. The model consists of atomic states resonantly field-dressed in a three-level reduction of the hydrogen atom that consists of the 2 p –3 d (Balmer) transition and one energetically-distant continuum state. The model’s level occupation probabilities are derived from three Schrödinger amplitude equations and are benchmarked against an ab initio numerical solution for the hydrogen electron’s wavefunction under the same field. We examine contrasts between the results of the two approaches with a particular focus on Autler–Townes doublets that appear in the photoelectron spectrum.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2022

Numerical Investigation of the Spark Discharge Process in a Crossflow

The present study numerically investigates the spark discharge process under crossflow conditions using a thermal equilibrium plasma solver that fully couples the electromagnetic physics and fluid dynamics in a computational framework. Numerical results are validated by the comparison with experimental data. Here, the spark discharge experiment is performed in a constant volume vessel using an inductive coil ignition system for automotive applications, and the evolution of the spark channel is measured using high-speed imaging. The crossflow in the gap between the spark-plug electrodes is generated by a rotating fan with two different fan speeds, and the flow velocity across the gap is characterized by particle image velocimetry (PIV) measurement. A computational fluid dynamics (CFD) solver is employed to simulate the crossflow and provide the flow field variables (velocity, pressure, temperature) to the plasma solver. The crossflow velocity predicted in the flow simulation agrees well with the PIV data in that the non-uniform velocity profiles at monitoring points are reproduced by the CFD code. With the crossflow initialization in the plasma solver, the simulated spark discharge process from the breakdown to spark discharge matches the experimental data, including the voltage and circuit waveforms and the high-speed images of the spark channel evolution. The stretch of spark channel captured by plasma simulations agrees with the measured data. The plasma simulation reveals that the mean temperature of the spark channel is maintained at 5000 K during the discharge phase, and the temperature varies along the spark channel so that the highest value is obtained at the spark root on the center electrode. Overall, the results presented in this paper are meant to provide valuable information about the properties of the plasma generated by the spark discharge.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2026

Hybrid Symbolic-Numerical Modeling and Parametric Stability Analysis of DC–AC Power Systems

Hybrid DC-AC power systems integrating diverse inverter-based resources (IBRs) and multi-terminal high-voltage direct current (MTDC) networks represent a promising architecture for future power grids, while introducing challenges for modeling, stability analysis, and control design. This paper develops a hybrid symbolic-numerical modeling framework and tool to characterize the parametric small-signal stability of DC-AC coupled power systems. The proposed approach constructs parametric state-space models to enable efficient representation of system dynamics under varying control parameters and network configurations, with target parameters retained as symbolic variables and the remainder treated numerically. The stability analysis framework covers eigenvalue, sensitivity, and stability boundary and region characterization. Enhanced linear matrix inequality (LMI) techniques are proposed to directly certify small-signal stability over regions of parameter space while also reducing the conservativeness and computational burden. The resulting tools and frameworks enable rapid parametric model construction across diverse grid conditions, thereby facilitating stability-informed control and operation in complex DC–AC power systems.

DC–AC power systems↗

DOE OSTI2022

Dissecting Tensor Cores via Microbenchmarks: Latency, Throughput and Numeric Behaviors

Tensor Cores have been an important unit to accelerate Fused Matrix Multiplication Accumulation (MMA) in all NVIDIA GPUs since Volta Architecture. To program Tensor Cores, users have to use either legacy wmma APIs or current mma APIs. Legacy wmma APIs are more easy-to-use but can only exploit limited features and power of Tensor Cores. Specifically, wmma APIs support fewer operand shapes and can not leverage the new sparse matrix multiplication feature of the newest Ampere Tensor Cores. However, the performance of current programming interface has not been well explored. Furthermore, the computation numeric behaviors of low-precision floating points (TF32, BF16, and FP16) supported by the newest Ampere Tensor Cores are also mysterious. In this paper, we explore the throughput and latency of current programming APIs. Further, we intuitively study the numeric behaviors of Tensor Cores MMA and profile the intermediate operations including multiplication, addition of inner product, and accumulation. All codes used in this work can be found in https://github.com/sunlex0717/DissectingTensorCores.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Fast Solution of Fully Implicit Runge--Kutta and Discontinuous Galerkin in Time for Numerical PDEs, Part II: Nonlinearities and DAEs

Fully implicit Runge--Kutta (IRK) methods have many desirable accuracy and stability properties as time integration schemes, but high-order IRK methods are not commonly used in practice with large-scale numerical PDEs because of the difficulty of solving the stage equations. This paper introduces a theoretical and algorithmic framework for solving the nonlinear equations that arise from IRK methods (and discontinuous Galerkin discretizations in time) applied to nonlinear numerical PDEs, including PDEs with algebraic constraints. Several new linearizations of the nonlinear IRK equations are developed, offering faster and more robust convergence than the often-considered simplified Newton, as well as an effective preconditioner for the true Jacobian if exact Newton iterations are desired. Inverting these linearizations requires solving a set of block 2 x 2 systems. Under quite general assumptions, it is proven that the preconditioned 2 x 2 operator's condition number is bounded by a small constant close to one, independent of the spatial discretization, spatial mesh, and time step, and with only weak dependence on the number of stages or integration accuracy. Moreover, the new method is built using the same preconditioners needed for backward Euler-type time stepping schemes, so can be readily added to existing codes. The new methods are applied to several challenging fluid flow problems, including the compressible Euler and Navier--Stokes equations, and the vorticity-streamfunction formulation of the incompressible Euler and Navier--Stokes equations. Up to 10th-order accuracy is demonstrated using Gauss IRK, while in all cases fourth-order Gauss IRK requires roughly half the number of preconditioner applications as required by standard Singly diagonally implicit Runge--Kutta methods.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Numerical modeling and experimental validation of low velocity impact of woven GFRP/CFRP composites

Low-velocity impact of 2D woven glass fiber reinforced polymer (GFRP) and carbon fiber reinforced polymer (CFRP) composite laminates was studied experimentally and numerically. Hybrid laminates containing blocked layers of GFRP/CFRP/GFRP with all plies oriented at 0° were investigated. Relatively high impact energies were used to obtain full perforation of the laminate in a low-velocity impact setup. Numerical simulations were carried out using the in-house transient dynamics finite element code, Sierra/SM, developed at Sandia National Laboratories. A three-dimensional continuum damage model was used to describe the response of a woven composite ply. Two methods for handling delamination were considered and compared: (1) cohesive zone modeling and (2) continuum damage mechanics. The reduced model size achieved by omission of the cohesive zone elements produced acceptable results at reduced computational cost. Further, the comparison between different modeling techniques can be used to inform modeling decisions relevant to low velocity impact scenarios. The modeling was validated by comparing with the experimental results and showed good agreement in terms of predicted damage mechanisms and impactor velocity and force histories.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Predictive numerical modeling of plasma-induced surface roughness and wettability evolution in LM-PAEK/CF tape

Plasma surface modification effectively enhances adhesion in thermoplastic composites, yet its impacts on high-performance polymers like low-melting polyaryletherketone (LM-PAEK) remain inadequately quantified. Here, this study integrates experimental analysis and numerical modeling to characterize surface roughness and wettability changes in LM-PAEK/carbon fiber composites treated with atmospheric plasma. Atomic Force Microscopy quantified surface topography (n = 10 per condition for contact angles), while static contact-angle assessments measured wettability. Roughness rapidly increased from ∼0.2 nm to 1.6 nm, and contact angle reduced from ∼90° to 24°, both stabilizing after 25–30 s of exposure. A semi-empirical, physics-informed framework was calibrated to these data, coupling surface chemistry via the Owens–Wendt decomposition with topography via the Wenzel roughness factor, and evaluated using out-of-sample (cross-validated) tests, while static contact angle assessments measured wettability. Numerical predictions matched experimental results closely (RMSE <5%, R 2 > 0.95). Incorporating material-specific parameters, the calibrated model supports plasma-treatment optimization and provides quantitative guidance for improving interfacial adhesion in thermoplastic composite manufacturing.

Atomic Force Microscopy↗

DOE OSTI2021

Resiliency in numerical algorithm design for extreme scale simulations

Here this work is based on the seminar titled ‘Resiliency in Numerical Algorithm Design for Extreme Scale Simulations’ held March 1–6, 2020, at Schloss Dagstuhl, that was attended by all the authors. Advanced supercomputing is characterized by very high computation speeds at the cost of involving an enormous amount of resources and costs. A typical large-scale computation running for 48 h on a system consuming 20 MW, as predicted for exascale systems, would consume a million kWh, corresponding to about 100k Euro in energy cost for executing 10 23 floating-point operations. It is clearly unacceptable to lose the whole computation if any of the several million parallel processes fails during the execution. Moreover, if a single operation suffers from a bit-flip error, should the whole computation be declared invalid? What about the notion of reproducibility itself: should this core paradigm of science be revised and refined for results that are obtained by large-scale simulation? Naive versions of conventional resilience techniques will not scale to the exascale regime: with a main memory footprint of tens of Petabytes, synchronously writing checkpoint data all the way to background storage at frequent intervals will create intolerable overheads in runtime and energy consumption. Forecasts show that the mean time between failures could be lower than the time to recover from such a checkpoint, so that large calculations at scale might not make any progress if robust alternatives are not investigated. More advanced resilience techniques must be devised. The key may lie in exploiting both advanced system features as well as specific application knowledge. Research will face two essential questions: (1) what are the reliability requirements for a particular computation and (2) how do we best design the algorithms and software to meet these requirements? While the analysis of use cases can help understand the particular reliability requirements, the construction of remedies is currently wide open. One avenue would be to refine and improve on system- or application-level checkpointing and rollback strategies in the case an error is detected. Developers might use fault notification interfaces and flexible runtime systems to respond to node failures in an application-dependent fashion. Novel numerical algorithms or more stochastic computational approaches may be required to meet accuracy requirements in the face of undetectable soft errors. These ideas constituted an essential topic of the seminar. The goal of this Dagstuhl Seminar was to bring together a diverse group of scientists with expertise in exascale computing to discuss novel ways to make applications resilient against detected and undetected faults. In particular, participants explored the role that algorithms and applications play in the holistic approach needed to tackle this challenge. This article gathers a broad range of perspectives on the role of algorithms, applications and systems in achieving resilience for extreme scale simulations. The ultimate goal is to spark novel ideas and encourage the development of concrete solutions for achieving such resilience holistically.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2019

Deep Direct-Use Feasibility Study Numerical Modeling and Uncertainty Analysis using iTOUGH2 for West Virginia University

To reduce the geothermal exploration risk, a feasibility study is performed for a deep direct-use system proposed at the West Virginia University (WVU) Morgantown campus. This study applies numerical simulations to investigate reservoir impedance and thermal production. Because of the great depth of the geothermal reservoir, few data are available to characterize reservoir features and properties. As a result, the study focuses on the following three aspects: 1. model choice for predicting reservoir impedance and thermal breakthrough: after investigating three potential models (one single permeability model and two dual permeability models) for flow through fractured rock, it is decided to use single permeability model for further analysis; 2. well placement (horizontal vs. vertical) options: horizontal well placement seems to be more robust to heterogeneity and the impedance is more acceptable; 3. Prediction uncertainty: the most influential parameters are identified using a First-Order-Second-Moment uncertainty propagation analysis, and the uncertain range of the model predictions is estimated by performing a Monte Carlo simulation. Heterogeneity has a large impact on the perdition, therefore, is considered in the predictive model and uncertainty analysis. The numerical model results and uncertainty analysis are used for economic analysis. The dataset submitted here support the described study. Manuscript is submitted to Geothermics, will be linked once paper is accepted.

15 GEOTHERMAL ENERGY↗

DOE OSTI2026

Scalable foundation models for numerical simulations on HPC platforms

In recent years, foundation models (FMs) have begun to reshape numerical simulations on high-performance computing (HPC) platforms. These large, pre-trained AI models enable rapid predictions across a broad range of physical domains, including Earth system modeling, fluid dynamics, materials science, as well as complex multi-modal simulations in aerospace engineering and fusion research. By training on diverse datasets, FMs learn intricate relationships and underlying physical behavior while also enabling the quantification of uncertainty in their predictions. This capability allows simulations that once required days of numerical calculation to be completed in minutes (FM inference), supporting real-time design optimization, uncertainty-aware decision making, and more comprehensive exploration of complex scenarios.

AI↗

DOE OSTI2021

Practical CO2—WAG Field Operational Designs Using Hybrid Numerical-Machine-Learning Approaches

Machine-learning technologies have exhibited robust competences in solving many petroleum engineering problems. The accurate predictivity and fast computational speed enable a large volume of time-consuming engineering processes such as history-matching and field development optimization. The Southwest Regional Partnership on Carbon Sequestration (SWP) project desires rigorous history-matching and multi-objective optimization processes, which fits the superiorities of the machine-learning approaches. Although the machine-learning proxy models are trained and validated before imposing to solve practical problems, the error margin would essentially introduce uncertainties to the results. In this paper, a hybrid numerical machine-learning workflow solving various optimization problems is presented. By coupling the expert machine-learning proxies with a global optimizer, the workflow successfully solves the history-matching and CO2 water alternative gas (WAG) design problem with low computational overheads. The history-matching work considers the heterogeneities of multiphase relative characteristics, and the CO2-WAG injection design takes multiple techno-economic objective functions into accounts. This work trained an expert response surface, a support vector machine, and a multi-layer neural network as proxy models to effectively learn the high-dimensional nonlinear data structure. The proposed workflow suggests revisiting the high-fidelity numerical simulator for validation purposes. The experience gained from this work would provide valuable guiding insights to similar CO2 enhanced oil recovery (EOR) projects.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2023

Numerical Methods to Evaluate Hyperelastic Transducers: Hexagonal Distributed Embedded Energy Converters

Hexagonal distributed embedded energy converters, also known as hexDEECs, are centimeter-scale energy transducers that leverage variable capacitance to generate electricity when their hyperelastic structure is dynamically deformed. To better understand, characterize, and optimize hexDEEC designs, a series of numerical methods and techniques were developed to model the hyperelastic mechanics of hexDEECs, electrostatic properties, and electricity generation characteristics. The numerical methods developed for the hyperelastic structural analysis were corroborated by empirical results from another study, and the models and equations for capacitance, electrostatic forces, and electrical potential energy were derived from fundamental electrostatic equations. These methods and techniques were implemented within the STAR-CCM+ multiphysics software Version 2020.3 (15.06.008) environment. Results from this analysis revealed methodologies and techniques necessary to model the energy converters, which will enable future exploration and optimization of more specific designs and corresponding applications.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2024

Numerical coupling of aerosol emissions, dry removal, and turbulent mixing in the E3SM Atmosphere Model version 1 (EAMv1) – Part 1: Dust budget analyses and the impacts of a revised coupling scheme

Abstract. An earlier study evaluating dust life cycle in the Energy Exascale Earth System Model (E3SM) Atmosphere Model version 1 (EAMv1) has revealed that the simulated global mean dust lifetime is substantially shorter when higher vertical resolution is used, primarily due to significant strengthening of dust dry removal in source regions. This paper demonstrates that the sequential splitting of aerosol emissions, dry removal, and turbulent mixing in the model's time integration loop, especially the calculation of dry removal after surface emissions and before turbulent mixing, is the primary reason for the vertical resolution sensitivity reported in that earlier study. Based on this reasoning, we propose a revised numerical process coupling scheme that requires the least amount of code changes, in which the surface emissions are applied before turbulent mixing instead of before dry removal. The revised scheme allows newly emitted particles to be transported aloft by turbulence before being removed from the atmosphere, and hence better resembles the dust life cycle in the real world. Sensitivity experiments show that the revised process coupling substantially weakens dry removal and strengthens vertical mixing in dust source regions. It also strengthens the large-scale transport from source to non-source regions, strengthens dry removal outside the source regions, and strengthens wet removal and activation globally. In transient simulations of the years 2000–2009 conducted using 1∘ horizontal grid spacing, 72 vertical layers, and unchanged tuning parameters of emission strength, the revised process coupling leads to a 40 % increase in the global total dust burden and an increase of dust lifetime from 1.8 to 2.5 d in terms of 10-year averages. Weakened dry removal and increased mixing ratios are also seen for other aerosol species that have substantial surface emissions, although the changes in mixing ratio are considerably smaller for the submicron species than for dust and sea salt. Numerical experiments confirm that the revised coupling scheme significantly reduces the strong and non-physical sensitivities of model results to vertical resolution in the original EAMv1. This provides a motivation for adopting the revised scheme in EAM as well as for further improvements on the simple revision presented in this paper.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

Numerical coupling of aerosol emissions, dry removal, and turbulent mixing in the E3SM Atmosphere Model version 1 (EAMv1) – Part 2: A semi-discrete error analysis framework for assessing coupling schemes

Abstract. Part 1 (Wan et al., 2024) of this study discusses the motivation and empirical evaluation of a revision to the aerosol-related numerical process coupling in the atmosphere component of the Energy Exascale Earth System Model version 1 (EAMv1) to address the previously reported issue of strong sensitivity of the simulated dust aerosol lifetime and dry removal rate to the model's vertical resolution. This paper complements that empirical justification of the revised scheme with a mathematical justification leveraging a semi-discrete analysis framework for assessing the splitting error of process coupling methods. The framework distinguishes the error due to numerical splitting from the error due to the time integration method(s) used for each individual process. Such a distinction results in a framework that provides an intuitive understanding of the causes of the splitting error. The application of this framework to the dust life cycle in EAMv1 confirms (i) that the original EAMv1 scheme artificially strengthens the effect of dry removal processes and (ii) that the revised splitting reduces that artificial strengthening. While the error analysis framework is presented in the context of the dust life cycle in EAMv1, the framework can be broadly leveraged to evaluate process coupling schemes, both in other physical problems and for any number of processes. This framework will be particularly powerful when the various process implementations support a variety of time integration approaches. Whereas traditional local truncation error approaches require separate consideration of each combination of time integration methods, this framework enables evaluation of coupling schemes independent of particular time integration approaches for each process while still allowing for the incorporation of these specific time integration errors if so desired. The framework also explains how the splitting error terms result from (i) the integration of individual processes in isolation from other processes and (ii) the choices of input state and time step size for the isolated integration of processes. Such a perspective has the potential for the rapid development of alternative coupling approaches that utilize knowledge both about the desired accuracy and about the computational costs of individual processes.

58 GEOSCIENCES↗

NASA NTRS1966

Numerical Studies of the Non-linear Vlasov Equation

The subject of this dissertation is the numerical integration of the initial-value problem for the non-linear Vlasov equation. The Vlasov equation is used to describe the dynamics of a "collisionless", one-dimensional, classical electron gas confined between two perfectly reflecting boundaries. Only the long-range Coulomb interactions of the electrons are considered; effects associated with the discrete structure are neglected. The numerical results obtained for non-linear Landau damping compare well with similar results obtained by Knorr. A general statement of the results on stable initial conditions is: As the degree of non-linearity of the initial conditions is increased, the deviation from linear Landau damping appears sooner and is more severe. In some cases damping was observed to cease. Curves showing the time dependence of the damping decrement are derived and compared with predictions of non-linear theories. New results obtained in this study include the observation that for strongly non-linear cases, the damping of the electric field causes an initially Maxwellian fo (v, O) to develop a peak in the neighborhood of the phase velocity; strong growth of the second harmonic is seen after fo (v, t) develops such a peak. Also new in this study is the interpretation of the development of a certain class of strongly unstable initial conditions as approaching an inhomogeneous equilibrium.

NUMERICAL INTEGRATION↗

NASA NTRS2001

Noninvasive assessment of mitral inertness: clinical results with numerical model validation

Inertial forces (Mdv/dt) are a significant component of transmitral flow, but cannot be measured with Doppler echo. We validated a method of estimating Mdv/dt. Ten patients had a dual sensor transmitral (TM) catheter placed during cardiac surgery. Doppler and 2D echo was performed while acquiring LA and LV pressures. Mdv/dt was determined from the Bernoulli equation using Doppler velocities and TM gradients. Results were compared with numerical modeling. TM gradients (range: 1.04-14.24 mmHg) consisted of 74.0 +/- 11.0% inertial forcers (range: 0.6-12.9 mmHg). Multivariate analysis predicted Mdv/dt = -4.171(S/D (RATIO)) + 0.063(LAvolume-max) + 5. Using this equation, a strong relationship was obtained for the clinical dataset (y=0.98x - 0.045, r=0.90) and the results of numerical modeling (y=0.96x - 0.16, r=0.84). TM gradients are mainly inertial and, as validated by modeling, can be estimated with echocardiography.

NASA Discipline Cardiopulmonary↗