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DOE OSTI2023

A Two-Step Time-Series Data Clustering Method for Building-Level Load Profile

Residential and commercial buildings have huge potential to contribute value to improve grid resilience by participating grid services. To reveal the significant value, it is critical to estimate the grid service capability from these buildings. Unlike the large-scale distributed energy resources such as wind and solar farms, those buildings need to participate grid services in aggregation, not by individual. Therefore, it is important to appropriately group buildings for aggregation. The load profiles in the same group will have similar characteristics at the same time step, so grid operators can send the grid service signal to the customer group with a higher chance to respond at that time step. In this paper, we develop a load profile clustering method to classify the building-level load profiles for grid service capability estimation and the results have proved the effectiveness of this method.

AMI↗

DOE OSTI2020

An analysis of the spatio-temporal resolution of the immersed boundary method with direct forcing

The immersed boundary method (IBM) with direct forcing is very popular in the simulation of rigid particulate flows. In the IBM, an interaction force is introduced at the interface between fluid and particle in order to approximate the no-slip boundary condition. The interaction force is calculated through dividing the velocity difference (or error) between fluid and particle at the interface by the time step. Here, a dynamic equation for the velocity difference is derived. Additionally, analyses on the dynamic equation provide a few new findings: (i) The interaction force is the solution of a least-squares error problem, with the direct implication that the Lagrangian marker distribution has no effect on the large scale flow structure once the distribution of Lagrangian markers become saturated along the interface (i.e., each marker remains properly correlated with all its neighbors); (ii) The Lagrangian volume-weight is a relaxation factor to control how fast the velocity error decays to the ideal value of zero; (iii) The optimal choice of the Lagrangian volume-weight is the largest value permissible by a stability condition. A comprehensive convergence analysis with regard to the spatial and temporal resolution is presented for the velocity error and also for the shear-stress and surface pressure. In three simple canonical problems, it is analytically and numerically shown that the IBM results converge to the theoretical solutions obtained with precise imposition of no-slip and no-penetration boundary conditions. It is observed that it is not necessary to match the Lagrangian marker volume-weight to that of the local Eulerian cell volume and in fact this matching leads to lower than optimal computational efficiency. However, it is found that extremely high Eulerian grid resolution and small time step have to be used to obtain high precision simulation results. Especially, the time step should be inversely proportional to the particle Reynolds number for low Reynolds number flows. For high frequency oscillation problems, the grid size needs to be reduced by a factor of the square root of the frequency, and the time step to be reduced by a factor of the frequency. The theoretical findings here can be used to alleviate the technical difficulties in simulating non-spherical particles by not requiring the Lagrangian marker distribution to match the Eulerian grids and also in the implementation of IBM on non-uniform Eulerian grids. The present work also provides simple practical guidance on the choice of temporal and spatial resolution so as to control the simulation error a priori.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2025

Asymptotic-preserving dynamical low-rank method for the stiff nonlinear Boltzmann equation

In kinetic theory, numerically solving the full Boltzmann equation is extremely expensive. This is because the Boltzmann collision operator involves a high-dimensional, nonlinear integral that must be evaluated at each spatial grid point and every time step. The challenge becomes even more pronounced in the fluid (strong collisionality) regime, where the collision operator exhibits strong stiffness, causing explicit time integrators to impose severe stability restrictions. In this paper, we propose addressing this problem through a dynamical low-rank (DLR) approximation. The resulting algorithm requires evaluating the Boltzmann collision operator only r 2 times, where r, the rank of the approximation, is much smaller than the number of spatial grid points. We propose a novel DLR integrator, called the XL integrator, which reduces the number of steps compared to the available alternatives (such as the projector splitting or basis update & Galerkin (BUG) integrator). For a class of problems including the Boltzmann collision operator which enjoys a separation property between physical and velocity space, we further propose a specialized version of the XL integrator, called the sXL integrator. This version requires solving only one differential equation to update the low-rank factors. Furthermore, the proposed low-rank schemes are asymptotic-preserving, meaning they can capture the asymptotic fluid limit in the case of strong collisionality. Our numerical experiments demonstrate the efficiency and accuracy of the proposed methods across a wide range of regimes, from non-stiff (kinetic) to stiff (fluid).

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Quantifying the Impact of Vertical Resolution on the Representation of Marine Boundary Layer Physics for Global-Scale Models

Abstract While GCM horizontal resolution has received the majority of scale improvements in recent years, ample evidence suggests that a model’s vertical resolution exerts a strong control on its ability to accurately simulate the physics of the marine boundary layer. Here we show that, regardless of parameter tuning, the ability of a single-column model (SCM) to simulate the subtropical marine boundary layer improves when its vertical resolution is improved. We introduce a novel objective tuning technique to optimize the parameters of an SCM against profiles of temperature and moisture and their turbulent fluxes, horizontal winds, cloud water, and rainwater from large-eddy simulations (LES). We use this method to identify optimal parameters for simulating marine stratocumulus and shallow cumulus. The novel tuning method utilizes an objective performance metric that accounts for the uncertainty in the LES output, including the covariability between model variables. Optimization is performed independently for different vertical grid spacings and value of time step, ranging from coarse scales often used in current global models (120 m, 180 s) to fine scales often used in parameterization development and large-eddy simulations (10 m, 15 s). Uncertainty-weighted disagreement between the SCM and LES decreases by a factor of ∼5 when vertical grid spacing is improved from 120 to 10 m, with time step reductions being of secondary importance. Model performance is shown to converge at a vertical grid spacing of 20 m, with further refinements to 10 m leading to little further improvement. Significance Statement In successive generations of computer models that simulate Earth’s atmosphere, improvements have been mainly accomplished by reducing the horizontal sizes of discretized grid boxes, while the vertical grid spacing has seen comparatively lesser refinements. Here we advocate for additional attention to be paid to the number of vertical layers in these models, especially in the model layers closest to Earth’s surface where climatologically important marine stratocumulus and shallow cumulus clouds reside. Our experiments show that the ability of a one-dimensional model to represent physical processes important to these clouds is strongly dependent on the model’s vertical grid spacing.

Meteorology & Atmospheric Sciences↗

NASA NTRS1984

Analysis of inviscid and viscous flows in cascades with an explicit multiple-grid algorithm

A rapid technique is used for calculating inviscid and viscous flows in turbomachinery cascades. The Euler and thin-layer Navier-Stokes equations are solved using the original explicit MacCormack algorithm. The Baldwin-Lomax eddy viscosity model is used for turbulent flows. Convergence to a steady state is accelerated by use of a variable time-step and a multiple-grid scheme. Computer time is reduced through vectorization. Details of the numerical method are presented along with computed results for two low-speed wind tunnel turning vanes, a space shuttle fuel pump turbine rotor, and a supersonic inflow compressor rotor. The method can predict subtle viscous flow phenomena in cascades and is fast enough to be used as a design tool.

Chima, R. V.↗

NASA NTRS1984

Analysis of inviscid and viscous flows in cascades with an explicit multiple-grid algorithm

Chima, R. V.↗

DOE OSTI2025

Addressing key physics problems in high-energy-density plasmas with a novel kinetic simulation capability

Many important physical processes in inertial confinement fusion (ICF) and dense Z-pinch (DZP) experiments require a kinetic (velocity-space-dependent) description. Conventional particle-in-cell (PIC) methods are poorly suited for high-energy-density (HED) plasmas, due to restrictive time-step constraints and the inability to conserve energy. In a previous LDRD (21-FS-048), we demonstrated that a fully implicit PIC formulation overcomes these limitations: it conserves energy even when coupled with Coulomb collision models and can be solved efficiently with large grid cells and large time steps. Thus, it is feasible to use this method to study kinetic effects in ICF and DZP plasmas on hydro-like time and spatial scales. In this follow-on LDRD, we advanced this methodology into a high-fidelity tool for production-scale simulations and used it to answer key questions relevant to ICF and DZP experiment.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2026

Mitigating Data Center Impact on Grid Stability: A Coordinated Control Strategy Using Verrus StabiliGrid Architecture

Large data centers, which now represent a significant and growing share of the total U.S. grid load, can inadvertently destabilize the electrical grid when they disconnect simultaneously during brief voltage disturbances. The July 10, 2024, Eastern Interconnection incident, in which a sub-100-millisecond transmission fault triggered the cascading loss of approximately 1,500 MW of data center load, illustrates this vulnerability. While commercial battery energy storage systems (BESS) deployed in data centers provide device-level fault ride-through per IEEE 1547, they lack coordination with facility protection logic and uninterruptible power supplies (UPS), limiting their effectiveness as grid-stabilizing assets. This report presents the Verrus StabiliGrid architecture, a coordinated control framework that integrates BESS, UPS, and point-of-interconnection (POI) protection settings to enable data centers to ride through both undervoltage and overvoltage grid contingencies without disconnecting. The four-step strategy encompasses: (1) high-resolution power quality monitoring to detect the grid state during events such as undervoltage, overvoltage, underfrequency, and overfrequency; (2) POI protection settings that allow for extended ride-through and grid-connected operation during grid contingencies; (3) grid state-driven autonomous dispatch of assets to improve grid resilience by reducing power draw during undervoltage or absorbing more power during overvoltage events; and (4) coordinated post-recovery dispatch of data center assets to restore firm load to pre-contingency levels. Validated through controller-hardware-in-the-loop (C-HIL) simulations at the National Laboratory of the Rockies, results show grid import restoration to pre-fault levels within 100 milliseconds of voltage recovery. This work advances the ability of data centers to transition from passive, disturbance-sensitive loads to active participants in grid stability, a capability increasingly required by emerging NERC and ERCOT regulatory frameworks.

24 POWER TRANSMISSION AND DISTRIBUTION↗

NASA NTRS1977

Implicit finite difference simulation of flow about arbitrary geometries with application to airfoils

Finite difference procedures are used to solve either the Euler equations or the 'thin layer' Navier-Stokes equations subject to arbitrary boundary conditions. An automatic grid generation program is employed, and because an implicit finite difference algorithm for the flow equations is used, time steps are not severely limited when grid points are finely distributed. Computational efficiency and compatibility to vectorized computer processors is maintained by use of approximate factorization techniques. Computed results for both inviscid and viscous flow about airfoils are described and compared to various known solutions.

Steger, J. L.↗

NASA NTRS1988

Grid embedding technique using Cartesian grids for Euler solutions

Grid-embedding techniques are presently applied to the solutions of the Euler equations on Cartesian grids for the NACA 0012 airfoil and the multielement SKF1.1 airfoil at transonic speeds. Based on comparisons with solutions on fine grids, it is shown that the present scheme, when used in conjunction with the Runge-Kutta time-stepping scheme as well as Cartesian grids, yields reduced memory requirements and a substantial reduction in computational time, without loss of accuracy.

Micheltree, R. A.↗

NASA NTRSDate not supplied

A Hybrid RANS-LES Perspective for the High Lift Common Research Model Using LAVA

An assessment of a Hybrid RANS/LES (HRLES) approach for𝐶𝐿,max prediction is presented for the NASA High-Lift Common Research Model (CRM-HL). Both the free air and the wind tunnel configuration of the CRM-HL are investigated and the results are compared to the QinetiQ wind tunnel experiments and to two other numerical approaches: Reynolds Averaged Navier-Stokes (RANS) and Wall-Modeled Large Eddy Simulations (WMLES). For the free-air configuration, HRLES was shown to address some of the known shortcomings in RANS methods and prevent inboard and outboard flow separation particularly in the region of𝐶𝐿,max and post-stall. To achieve these improvements over RANS, LES-appropriate grids and numerical discretizations are required. HRLES predicts a weak pitch break at the highest angle-of-attack due to onset of wing-root corner flow separation whereas the free-air corrected experiment values indicate an occurrence of a much stronger pitch break. The improvements of HRLES over a URANS approach has been objectively shown by computing a set of solutions with the same grid, same numerics and time-step size and comparing the solutions. It was also found that when applying HRLES to a RANS best practice grid and numerics that the HRLES method significantly under performed RANS. For the in tunnel configuration, HRLES showed good agreement with the loads, surface pressure and oil-flow photographs obtained in the experiment. HRLES was able to improve upon the RANS simulations, which showed a sharp loss of lift at the two highest angles-of-attack due to large scale inboard and outboard separation on the wing, by correctly predicting the corner flow separation and showing remarkably close agreement in the flow topologies with the experiment.

TTT↗

DOE OSTI2024

Grid Planning for Building Electrification: A Report by the Energy Systems Integration Group’s Grid Planning for Building Electrification Task Force

The increased electrification of buildings across the United States is being driven by technical advancements, cost reductions for some building technologies, consumer preferences, and policy goals for decarbonization. However, the effects of this load growth on the electric distribution system are often only a minor consideration in policymaking and long-term planning studies. The long lead time and useful life of power system equipment means that the decisions taken today are expected to support our society well into the 2060s and beyond. Distribution planning stakeholders can take steps today to establish a grid foundation that captures the new challenges presented by building electrification. This report focuses on building electrification for the residential and commercial sectors, focusing most heavily on space heating, as this end use stands to most strongly impact demand.1 Across all end uses, building electrification could require somewhere between 10% and 70% more electricity generation capacity than exists today depending on technology adoption and energy efficiency.

24 POWER TRANSMISSION AND DISTRIBUTION↗

NASA NTRS2015

Unstructured Grids for Sonic Boom Analysis and Design

An evaluation of two methods for improving the process for generating unstructured CFD grids for sonic boom analysis and design has been conducted. The process involves two steps: the generation of an inner core grid using a conventional unstructured grid generator such as VGRID, followed by the extrusion of a sheared and stretched collar grid through the outer boundary of the core grid. The first method evaluated, known as COB, automatically creates a cylindrical outer boundary definition for use in VGRID that makes the extrusion process more robust. The second method, BG, generates the collar grid by extrusion in a very efficient manner. Parametric studies have been carried out and new options evaluated for each of these codes with the goal of establishing guidelines for best practices for maintaining boom signature accuracy with as small a grid as possible. In addition, a preliminary investigation examining the use of the CDISC design method for reducing sonic boom utilizing these grids was conducted, with initial results confirming the feasibility of a new remote design approach.

Campbell, Richard L.↗

DOE OSTI2024

Project Title: Adaptive Vertical Grid Enhancement for E3SM (Final Technical Report)

During the first phase of the project (2018/05-2021/05), we proved the hypothesis that, without tuning, high vertical resolution improves the representation of unresolved, parameterized low altitude clouds such as stratocumulus clouds in global climate models. We evaluated the effectiveness of the newly developed computational framework, Framework for Improvement by Vertical Enhancement (FIVE) by implementing it into E3SM. FIVE aims to improve representation of the target cloud, low level cloud for this project, with use of a locally high vertical resolution for computation of selected processes. FIVE was assessed via direct comparison among E3SM, E3SM-FIVE, and satellite data as well as a newly developed ensemble artificial neural network methodology. We demonstrated that E3SM-FIVE remarkably improves marine stratocumulus representation. To advance the FIVE methodology, we took a first step toward the adaptive vertical grid in the FIVE method by modifying the E3SM single column model. For future application of FIVE to the global storm resolving model with a few km horizontal grid resolution, we developed the vertical-meridional two-dimensional (2D) Hadley circulation model, which allows one to run simulations with much higher vertical resolution and significantly longer duration than current three-dimensional global storm resolving model. During the second phase of the project (2021/05-2023/11; period for this technical report), we sought a way to appropriately transform FIVE to a regionalized version of FIVE, which allows one to select locations with/without FIVE. In parallel, we demonstrated that E3SM-FIVE with a 25-km mesh significantly reduced the bias associated with coastal stratocumulus. Furthermore, we showed that the same improvement was able to be obtained with the use of both the Regional Refined Model (RRM) targeted to one of the stratocumulus regions with 25-km resolution and FIVE. We explored a new implementation strategy of FIVE with our 2D Hadley circulation model. In parallel we applied the 2D Hadley circulation model to study the double intertropical convergence zone bias with storm resolving model resolution and aerosol-cloud interactions within the Hadley circulation with near large eddy simulation resolution. Last, we have been investigating Arctic mixed-phase stratocumulus clouds with large eddy simulations in order to improve their representation in global models. During the course of the entire project, 6 journal articles were published, and 3 manuscripts are currently in preparation. We gave a total of 30 presentations at various domestic and international conferences. In addition we gave 6 seminar talks at universities and a national laboratory. E3SM- FIVE is available as a branch of E3SM.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS2013

Understanding the Impact of Field-Emitter Characteristics on Electron Beam Focusing in the VAPoR Time-of-Fight Mass Spectrometer

Simulations of field emission of electrons from an electron gun are used to determine the angular distribution of the emitted electron beam and the percentage of charge transmitted through the grid. The simulations are a first step towards understanding the spherical aberration present after focusing the electron beam. The effect of offset of the cathode with respect to the grid and the separation between cathode and grid on the angular distributions of emitted electrons and transmission of the grid are explored.

electron gun↗

NASA NTRS1990

An adaptive grid algorithm for one-dimensional nonlinear equations

Richards' equation, which models the flow of liquid through unsaturated porous media, is highly nonlinear and difficult to solve. Step gradients in the field variables require the use of fine grids and small time step sizes. The numerical instabilities caused by the nonlinearities often require the use of iterative methods such as Picard or Newton interation. These difficulties result in large CPU requirements in solving Richards equation. With this in mind, adaptive and multigrid methods are investigated for use with nonlinear equations such as Richards' equation. Attention is focused on one-dimensional transient problems. To investigate the use of multigrid and adaptive grid methods, a series of problems are studied. First, a multigrid program is developed and used to solve an ordinary differential equation, demonstrating the efficiency with which low and high frequency errors are smoothed out. The multigrid algorithm and an adaptive grid algorithm is used to solve one-dimensional transient partial differential equations, such as the diffusive and convective-diffusion equations. The performance of these programs are compared to that of the Gauss-Seidel and tridiagonal methods. The adaptive and multigrid schemes outperformed the Gauss-Seidel algorithm, but were not as fast as the tridiagonal method. The adaptive grid scheme solved the problems slightly faster than the multigrid method. To solve nonlinear problems, Picard iterations are introduced into the adaptive grid and tridiagonal methods. Burgers' equation is used as a test problem for the two algorithms. Both methods obtain solutions of comparable accuracy for similar time increments. For the Burgers' equation, the adaptive grid method finds the solution approximately three times faster than the tridiagonal method. Finally, both schemes are used to solve the water content formulation of the Richards' equation. For this problem, the adaptive grid method obtains a more accurate solution in fewer work units and less computation time than required by the tridiagonal method. The performance of the adaptive grid method tends to degrade as the solution process proceeds in time, but still remains faster than the tridiagonal scheme.

Gutierrez, William E.↗

NASA NTRS1986

Implicit, vectorizable schemes for the flux-difference split, three-dimensional Navier-Stokes equations

Two hybrid upwind models are defined for solving the Euler equations. The algorithms both employ approximate factorization (AF) in crossplane and symmetric block Gauss-Seidel relaxation in the third direction. One approach adds an additional factorization step to lower the number of required grid point operations for inversion of the block tridiagonal matrices; however, the move permits only one third of the operations to be vectorized. Finite difference solutions are calculated on a C-H-type grid, in this case enveloping a slender, sharp-edged delta wing. Sample data are provided for the calculated vortex flow for Re of 10,000, at a 20.5 deg angle of attack, represented in a crossflow velocity vector plot and in a spanwise pressure coefficient distribution. The AF scheme, without additional factorization, when used with a grid covering 51 x 51 x 72 points provides a convergent solution with no time step lasting longer than 0.00001 sec.

Liu, C. H.↗

NASA NTRS1982

Multiple-grid acceleration of Lax-Wendroff algorithms

A technique for accelerating the convergence of a one-step Lax-Wendroff method to a steady-state solution is discussed and its applicability extended to the more general class of two-step Lax-Wendroff methods. Several two-step methods which lead to quite efficient multiple grid algorithms are discussed. Computational results are presented using the full two dimensional Euler equations for both subcritical and shocked supercritical flows. Extensions and generalizations are mentioned.

Johnson, G. M.↗