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Results for “Grid singularity”

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 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

A purely Lagrangian method for simulating the shallow water equations on a sphere using smooth particle hydrodynamics

It has long been suggested that a purely Lagrangian solution to global-scale atmospheric/oceanic flows can potentially outperform tradition Eulerian schemes. Meanwhile, a demonstration of a scalable and practical framework remains elusive. Motivated by recent progress in particle-based methods when applied to convection dominated flows, this work presents a fully Lagrangian method for solving the inviscid shallow water equations on a rotating sphere in a smooth particle hydrodynamics framework. To avoid singularities at the poles, the governing equations are solved in Cartesian coordinates, augmented with a Lagrange multiplier to ensure that fluid particles are constrained to the surface of the sphere. An underlying grid in spherical coordinates is used to facilitate efficient neighbor detection and parallelization. The method is applied to a suite of canonical test cases, and conservation, accuracy, and parallel performance are assessed..

Computer Science↗
DOE OSTI2019

Adaptive Grid Lens Modeling of the Cosmic Horseshoe Using Hubble Space Telescope Imaging

The Cosmic Horseshoe gravitational lensing system is an extraordinary example of strong gravitational lensing both due to the nearly complete Einstein ring formed in this system and due to the star-forming nature of the lensed $z$ = 2.38 Lyman-break galaxy. In this paper, we describe the development of a new lens modeling package and the lens models produced using the Hubble Space Telescope imaging. Our new lens modeling package uses adaptive grid methods, based especially on the algorithm described by Vegetti & Koopmans. The new lens modeling package introduces the K-means method to deal with multiple background sources. We utilize two parameterized models, the singular isothermal ellipsoid and the Navarro–Frenk–White model in order to optimize the Bayesian penalty function. Color–color diagrams show two distinct colors exist in the Einstein ring, which suggests that the Cosmic Horseshoe is formed from two background galaxies or from a highly irregular galaxy. We find that the best lens model includes two components and the total mass within the Einstein ring is $(5.43\pm 0.08)\times {10}^{12}\,{M}_{\odot }$. Furthermore, the background source reconstruction shows two peaks in the source plane and the most probable lens profile is consistent with the light profile of the foreground galaxy when comparing axis ratios and position angles.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2018

Steep Cliffs and Saturated Exponents in Three-Dimensional Scalar Turbulence

Herein the intermittency of a passive scalar advected by three-dimensional Navier-Stokes turbulence at a Taylor-scale Reynolds number of 650 is studied using direct numerical simulations on a 4096 3 grid; the Schmidt number is unity. By measuring scalar increment moments of high orders, while ensuring statistical convergence, we provide unambiguous evidence that the scaling exponents saturate to 1.2 for moment orders beyond about 12, indicating that scalar intermittency is dominated by the most singular shocklike cliffs in the scalar field. We show that the fractal dimension of the spatial support of steep cliffs is about 1.8, whose sum with the saturation exponent value of 1.2 adds up to the space dimension of 3, thus demonstrating a deep connection between the geometry and statistics in turbulent scalar mixing. The anomaly for the fourth and sixth order moments is comparable to that in the Kraichnan model for the roughness exponent of 4/3.

42 ENGINEERING↗
DOE OSTI2024

Powering Data Centers with Clean Energy: A Techno-Economic Case Study of Nuclear and Renewable Energy Dependability

Rising data demands from artificial intelligence (AI) and large language models (LLMs) generating images, videos, and text have prompted increased need for larger and more robust data centers in the United States. Major companies interested in these larger data centers face the choice of linking them to existing regional grids, building stand-alone power supplies onsite, or a combination of both. The request, review, and approval process for new transmission lines to grids in the United States, however, has grown in recent years to times spans rivaling those of new construction for nuclear power plants. Building an islanded power supply for each data center is therefore becoming a prominent option. In this case study, several technologies are modeled in techno-economic simulations for long-term system costs subject to fixed electricity demand from a singular data center. A 250 MWe data center is assumed with additional 50 MWe for resiliency. Techno-economic simulations are conducted using the Holistic Energy Resource Optimization Network (HERON) software, which is a part of the Framework for Optimization of Resources and Economics (FORCE) tool suite. Technologies considered include solar, wind, lithium-ion batteries, and several types of nuclear reactors: large-scale reactors, small modular reactors, and microreactors. A low- and high-cost estimate for each technology is assumed to develop a range of expected economic performance. Low-cost estimates included several clean energy production tax credits. Different combinations of renewable energy generators with nuclear reactors are considered, ranging from a fully renewable-powered data center to a fully nuclear-powered data center. Historic time series of wind and solar availability from the Texas grid are used to train a reduced order model; this model then generates unique time series with similar characteristics of the training dataset. Multiple scenarios of weather and subsequent operations are simulated for each renewable-nuclear combination to determine total costs throughout the project lifetime. Fully renewable-powered configurations required large amounts of installed capacity (GW scale) in the simulations to meet the fixed demand of the data center. This is due to some scenarios in the historical dataset which captured low-wind and low-solar days, requiring over-building of these technologies as well as batteries to compensate for the low amounts of electricity generation. Fully nuclear-powered configurations outperformed the fully renewable and mixed renewable-nuclear configurations in terms of cost, with ranges between $1B and $10B in 2023 USDs compared to $40B+ for fully renewable configurations. Of the nuclear technologies, small modular reactors performed better economically than large-scale nuclear models due to lower projected capital costs, and both performed better than the microreactor models. These results demonstrate the applicability of firm, dispatchable electricity resources from baseload generators like nuclear power plants for operating facilities that run at constant power without daily variability.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

Conservative numerical schemes with optimal dispersive wave relations: Part I. Derivation and analysis

An energy-conserving and an energy-and-enstrophy conserving numerical schemes are derived by approximating the Hamiltonian formulation of the inviscid shallow water flows based on the vorticity-divergence variables. These schemes also conserve the first-order moments such as mass and vorticity, as usual. The conservative properties of the schemes stem from the skew-symmetry and singularities of the Poisson brackets, which are carefully retained in the discrete approximations. Here, the schemes operate on unstructured orthogonal dual meshes, over bounded or unbounded domains, and they are also shown to possess the same optimal dispersive wave relations as those of the Z-grid scheme, which is a consequence of the use of the vorticity and divergence variables.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2019

Coherency-Based Detection Algorithm for Synchrophasor Cyberattacks

The wide area monitoring system (WAMS) is critical for power system situational awareness, but represents a growing cybersecurity vulnerability. Malicious adversaries may seek to compromise one or more PMUs in order to effect control decisions that unnecessarily disrupt typical grid operations. One example of a particularly pernicious attack vector is the spoofing or replaying of a fault event using one or more compromised PMUs. This work documents the development and validation of a coherency-based cyberattack detection algorithm that integrates a sliding-window singular value decomposition (SVD) with physics-based partitioning analysis to achieve accurate classification of events. Special consideration is given to discerning a sophisticated fault-replay or fault spoofing attack from actual faults. A software-based cybersecurity testbed has been developed for rigorous testing of the algorithm. The algorithm is further validated using simulated synchrophasor datasets obtained from a MinniWECC 63-bus test system. Results show that the algorithm can successfully detect fault-replay attacks even when over half of the PMUs are compromised.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2024

Data-Driven Compression of Electron-Phonon Interactions

First-principles calculations of electron interactions in materials have seen rapid progress in recent years, with electron-phonon ( e − ph ) interactions being a prime example. However, these techniques use large matrices encoding the interactions on dense momentum grids, which reduces computational efficiency and obscures interpretability. For e − ph interactions, existing interpolation techniques leverage locality in real space, but the high dimensionality of the data remains a bottleneck to balance cost and accuracy. Here we show an efficient way to compress e − ph interactions based on singular value decomposition (SVD), a widely used matrix and image compression technique. Leveraging (un)constrained SVD methods, we accurately predict material properties related to e − ph interactions—including charge mobility, spin relaxation times, band renormalization, and superconducting critical temperature—while using only a small fraction (1%–2%) of the interaction data. These findings unveil the hidden low-dimensional nature of e − ph interactions. Furthermore, they accelerate state-of-the-art first-principles e − ph calculations by about 2 orders of magnitude without sacrificing accuracy. Our Pareto-optimal parametrization of e − ph interactions can be readily generalized to electron-electron and electron-defect interactions, as well as to other couplings, advancing quantitative studies of condensed matter. Published by the American Physical Society 2024

Physics↗
DOE OSTI2025

The Verification and Validation of a Magnetic Plasma Fluid Model Utilizing the MOOSE (Multiphysics Object Oriented Simulation Environment) Framework

As the goal of achieving fusion power on the grid comes closer to fruition, fully coupled multiphysics models of fusion devices will be crucial. Currently, there are two main approaches to developing these platforms: (1) loosely coupled, where one couples existing codes and solvers together through input and output parameters and data, and (2) tightly coupled, where one develops the necessary models within a singular, integrated framework. This work focuses on the latter approach for magnetically confined fusion devices by developing a fluid-based plasma-edge model within the Multiphysics Object Oriented Simulation Environment (MOOSE) Framework. This effort is coordinated with other efforts to develop, test, demonstrate, and deploy fusion relevant multiphysics capabilities including electromagnetics, particle-in-cell plasma, tritium transport, and fusion blanket design. This new model is an expansion of the MOOSE-based plasma application, Zapdos, which was originally formulated to model low-temperature, non-magnetized plasma processes. Verification, benchmarking, and validation studies have been conducted. Verification studies involved utilizing the method of manufactured solutions and comparing the convergence slope of a known solution to the theoretical slope. Benchmarking consists of comparisons to existing edge codes, namely BOUT++ and SOLEDGE3X. Validation efforts focused on comparisons against open-source data from the TCV tokamak.

70 - PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2019

A New Multi-Scale State Estimation Framework for the Next Generation of Power Grid EMS

Accurate system state information under various operation conditions is a prerequisite for power grid monitoring and efficient control. To achieve that goal, a new multi-scale state estimation framework is proposed, paving the way for the development of next generation of energy management system (EMS). The developed framework consists of three key components, namely the static state estimation (SSE) module, the dynamic state estimation (DSE) module, the interfaces and switching logics between the two modules. Specifically, the singular spectrum analysis (SSA)-based change point detection approach is developed to monitor the system continuously. If no event is detected by the SSA, the robust SSE using both SCADA and PMU measurements is executed. Otherwise, the event is declared and the results from SSE are used to derive the initial condition for DSE. During the transient process, only PMU-based DSE is executed for system monitoring and it will be terminated when SSA does not detect any change point of the system. After that, the DSE results are forwarded for SSE initialization and bus voltage magnitude and angle estimations. Simulation results carried out on the IEEE 39-bus system demonstrate the effectiveness and benefits of the proposed framework.

Power system state estimation, energy management s↗
DOE OSTI2022

Grey Zone Test Range Social Model

The Grey Zone Test Range (GZTR) social model operates as a piece of the overall GZTR modeling effort. It works in conjunction with supply models for resources, an electric grid model for power availability, and a traffic model for road congestion, as well as a general controller framework that allows external system effects. The social model functions as an aggregate model where the entire population of the city is divided into groups based on the Transportation Analysis Zones (TAZs), a common geospatial boundary present in all GZTR models. These groups will act as a singular community; each time step the state of the system around them will be assessed and then community will come up with a general plan of action that they will attempt to follow for the day. Additionally, they will track values for their general emotional state and memory about negative impacts in the near past.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2018

The Effect of Transmission-Line Dynamics on a Globally Synchronizing Controller for Power Inverters

In this work, we analyze a dispatchable virtual oscillator control (dVOC) strategy for grid-forming power inverters that ensures almost global synchronization of inverterbased AC power systems when the dynamics of the transmission network are neglected, i.e., if an algebraic model of the transmission lines is used. While this approximation is often justified for conventional power systems, the dynamics of the transmission lines can compromise the stability of an inverterbased power system. Therefore, in this article, we use tools from singular perturbation theory to construct a Lyapunov function candidate and explicit bounds on the controller gains that guarantee global convergence to the set of steady-states for the full power-system with transmission line dynamics. Moreover, we show that the only undesirable steady-state is unstable.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2023

Unified analysis of finite-size error for periodic Hartree-Fock and second order Møller-Plesset perturbation theory

Despite decades of practice, finite-size errors in many widely used electronic structure theories for periodic systems remain poorly understood. For periodic systems using a general Monkhorst-Pack grid, there has been no comprehensive and rigorous analysis of the finite-size error in the Hartree-Fock theory (HF) and the second order Møller-Plesset perturbation theory (MP2), which are the simplest wavefunction based method, and the simplest post-Hartree-Fock method, respectively. Such calculations can be viewed as a multi-dimensional integral discretized with certain trapezoidal rules. Due to the Coulomb singularity, the integrand has many points of discontinuity in general, and standard error analysis based on the Euler-Maclaurin formula gives overly pessimistic results. The lack of analytic understanding of finite-size errors also impedes the development of effective finite-size correction schemes. We propose a unified analysis to obtain sharp convergence rates of finite-size errors for the periodic HF and MP2 theories. Our main technical advancement is a generalization of the result of Lyness [Math. Comp. 30 (1976), pp. 1–23] for obtaining sharp convergence rates of the trapezoidal rule for a class of non-smooth integrands. Our result is applicable to three-dimensional bulk systems as well as low dimensional systems (such as nanowires and 2D materials). Our unified analysis also allows us to prove the effectiveness of the Madelung-constant correction to the Fock exchange energy, and the effectiveness of a recently proposed staggered mesh method for periodic MP2 calculations (see X. Xing, X. Li, and L. Lin [J. Chem. Theory Comput. 17 (2021), pp. 4733–4745]). In conclusion, our analysis connects the effectiveness of the staggered mesh method with integrands with removable singularities, and suggests a new staggered mesh method for reducing finite-size errors of periodic HF calculations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

TuckerMPI: A Parallel C++/MPI Software Package for Large-scale Data Compression via the Tucker Tensor Decomposition

With this study, our goal is compression of massive-scale grid-structured data, such as the multi-terabyte output of a high-fidelity computational simulation. For such data sets, we have developed a new software package called TuckerMPI, a parallel C++/MPI software package for compressing distributed data. The approach is based on treating the data as a tensor, i.e., a multidimensional array, and computing its truncated Tucker decomposition, a higher-order analogue to the truncated singular value decomposition of a matrix. The result is a low-rank approximation of the original tensor-structured data. Compression efficiency is achieved by detecting latent global structure within the data, which we contrast to most compression methods that are focused on local structure. In this work, we describe TuckerMPI, our implementation of the truncated Tucker decomposition, including details of the data distribution and in-memory layouts, the parallel and serial implementations of the key kernels, and analysis of the storage, communication, and computational costs. We test the software on 4.5 and 6.7 terabyte data sets distributed across 100 s of nodes (1,000 s of MPI processes), achieving compression ratios between 100 and 200,000×, which equates to 99--99.999% compression (depending on the desired accuracy) in substantially less time than it would take to even read the same dataset from a parallel file system. Moreover, we show that our method also allows for reconstruction of partial or down-sampled data on a single node, without a parallel computer so long as the reconstructed portion is small enough to fit on a single machine, e.g., in the instance of reconstructing/visualizing a single down-sampled time step or computing summary statistics. The code is available at https://gitlab.com/tensors/TuckerMPI.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Verification of a Fluid-Based Plasma-Edge Model Within the Multiphysics Object-Oriented Simulation Environment (MOOSE) Framework

As the goal of achieving fusion power on the grid comes closer to fruition, fully coupled multiphysics models of fusion devices will be crucial. These models must incorporate the interconnected phenomena of these devices, including plasma physics, neutronics, first wall interactions, and tritium transport. Currently, there are two main approaches to developing these platforms: (1) loosely coupled, where one couples existing codes and solvers together through input and output parameters and data, and (2) tightly coupled, where one develops the necessary models within a singular, integrated framework. This work focuses on the latter approach for magnetically confined fusion devices by developing a fluid-based plasma-edge model within the Multiphysics Object Oriented Simulation Environment (MOOSE) Framework. This effort is coordinated with other efforts to develop, test, demonstrate, and deploy fusion relevant multiphysics capabilities including electromagnetics, particle-in-cell plasma, tritium transport, and fusion blanket design. This new model is an expansion of the MOOSE-based plasma application, Zapdos, which was originally formulated to model low-temperature, non-magnetized plasma processes. Verification studies have been conducted using newly developed magnetic plasma capabilities. These involved convergence analyses utilizing the method of manufactured solutions to verify new operators and case studies. A modular approach was taken here to demonstrate increasingly complicated simulation scenarios, which included a singular fluid with uniform magnetic field case, a singular fluid with spatially varying magnetic field case, and a coupled multifluid case.

70 - PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Cardinality-Regularized Hawkes-Granger Model

We propose a new sparse Granger-causal learning framework for temporal event data. We focus on a specific class of point processes called the Hawkes process. We begin by pointing out that most of the existing sparse causal learning algorithms for the Hawkes process suffer from a singularity in maximum likelihood estimation. As a result, their sparse solutions can appear only as numerical artifacts. In this paper, we propose a mathematically well-defined sparse causal learning framework based on a cardinality-regularized Hawkes process, which remedies the pathological issues of existing approaches. We leverage the proposed algorithm for the task of instance-wise causal event analysis, where sparsity plays a critical role. We validate the proposed framework with two real use-cases, one from the power grid and the other from the cloud data center management domain.

Ide, Tsuyoshi↗
DOE OSTI2018

A conservative scheme for electromagnetic simulation of magnetized plasmas with kinetic electrons

A conservative scheme has been formulated and confirmed for gyrokinetic particle simulations of electromagnetic waves and instabilities in magnetized plasmas. An electron continuity equation derived from the drift kinetic equation is used to time advance the electron density perturbation by using the perturbed mechanical flow calculated from the parallel vector potential, and the parallel vector potential is solved by using the perturbed canonical flow from the perturbed distribution function. In gyrokinetic particle simulations using this new scheme, the shear Alfvén wave dispersion relation in the shearless slab and continuum damping in the sheared cylinder have been recovered. The new scheme overcomes the stringent requirement in the conventional perturbative simulation method that perpendicular grid size needs to be as small as electron collisionless skin depth even for the long wavelength Alfvén waves. The new scheme also circumvents the problem in the typical approach that an unphysically large parallel electric field arises due to the inconsistency between electrostatic potential calculated from the perturbed density and vector potential calculated from the perturbed canonical flow. Lastly, the gyrokinetic particle simulations of the Alfvén waves in sheared cylinder have superior numerical properties compared with the fluid simulations, which suffer from numerical difficulties associated with singular mode structures.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

A learned closure method applied to phase mixing in a turbulent gradient-driven gyrokinetic system in simple geometry

We present a new method for formulating closures that learn from kinetic simulation data. We apply this method to phase mixing in a simple gyrokinetic turbulent system – temperature-gradient-driven turbulence in an unsheared slab. The closure, called the learned multi-mode (LMM) closure, is constructed by, first, extracting an optimal basis from a nonlinear kinetic simulation using singular value decomposition. Subsequent nonlinear fluid simulations are projected onto this basis and the results are used to formulate the closure. We compare the closure with other closures schemes over a broad range of the relevant two-dimensional parameter space (collisionality and gradient drive). We find that the turbulent kinetic system produces phase-mixing rates much lower than the linear expectations, which the LMM closure is capable of capturing. We also compare radial heat fluxes. A Hammett–Perkins closure, generalized to include collisional effects, is quite successful throughout the parameter space, producing ${\sim }14\,\%$ root-mean-square (r.m.s.) error. The LMM closure is also very effective: when trained at three (two) points (in a 35 point parameter grid), the LMM closure produces $8\,\%$ ( $12\,\%$ ) r.m.s. errors. The LMM procedure can be readily generalized to other closure problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗