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Transonic airfoil calculations using solution-adaptive grids

A new algorithm for generating solution-adaptive grids (SAG) about airfoil configurations embedded in transonic flow is presented. The present SAG approach uses only the airfoil surface solution to recluster grid points on the airfoil surface, i.e., the reclustering problem is one dimension smaller than the flow-field calculation problem. Special controls automatically built into the elliptic grid generation procedure are then used to obtain grids with suitable interior behavior. This concept of redistributing grid points greatly simplifies the idea of solution-adaptive grids. Numerical results indicate significant improvements in accuracy for SAG grids relative to standard grids using the same number of points.

Holst, T. L.

Topological grid structure - A data structure for earth science modeling

The automated analysis of land surface features is increasingly important to earth scientists. User-friendly algorithms for studying these features can be integrated into geographic information systems through the use of topological grid structure, which maintains the simplicity and transportability of standard grid structure while providing the essential capability to treat groups of contiguous, identically-classified pixels (corresponding to lakes, forests, fields, etc.) as distinct spatial entities.

Goldberg, M.

Untangling Sources of Error in the Density-Functional Many-Body Expansion

The many-body expansion provides a framework for data-driven applications of electronic structure theory, including parametrization of classical force fields and machine learning. In this article, we demonstrate that its use significantly amplifies quadrature grid errors when modern density-functional approximations are employed. Standard grids that work well in conventional density-functional calculations result in runaway error accumulation when used with the many-body expansion. At the same time, delocalization error is also exacerbated, leading to exaggerated estimates of nonadditive n-body interactions. This is illustrated for anion–water clusters using the SCAN, r2SCAN, ωB97X-V and ωB97M-V functionals. By employing dense quadrature grids, the inherent self-interaction error is exposed, which can then be mitigated using a variety of other strategies.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH

Grid Sensitivity Study for Slat Noise Simulations

The slat noise from the 30P/30N high-lift system is being investigated through computational fluid dynamics simulations in conjunction with a Ffowcs Williams-Hawkings acoustics solver. Many previous simulations have been performed for the configuration, and the case was introduced as a new category for the Second AIAA workshop on Benchmark problems for Airframe Noise Configurations (BANC-II). However, the cost of the simulations has restricted the study of grid resolution effects to a baseline grid and coarser meshes. In the present study, two different approaches are being used to investigate the effect of finer resolution of near-field unsteady structures. First, a standard grid refinement by a factor of two is used, and the calculations are performed by using the same CFL3D solver employed in the majority of the previous simulations. Second, the OVERFLOW code is applied to the baseline grid, but with a 5th-order upwind spatial discretization as compared with the second-order discretization used in the CFL3D simulations. In general, the fine grid CFL3D simulation and OVERFLOW calculation are in very good agreement and exhibit the lowest levels of both surface pressure fluctuations and radiated noise. Although the smaller scales resolved by these simulations increase the velocity fluctuation levels, they appear to mitigate the influence of the larger scales on the surface pressure. These new simulations are used to investigate the influence of the grid on unsteady high-lift simulations and to gain a better understanding of the physics responsible for the noise generation and radiation.

Lockard, David P.

Standard Library Grid-Forming Hybrid Control Inverter-Based Resource Model Specification (REGFM_C1)

This document describes a standard library grid-forming (GFM) hybrid control inverter-based resource (IBR) model. The GFM hybrid control approach implements both a typical GFM control and a typical grid-following (GFL) control inside one single inverter simultaneously, so that it can take advantage of both methods without comprising the benefits of a typical GFM. The initial version of model specification was jointly developed by Pacific Northwest National Laboratory (PNNL), Tesla Energy, and EPRI, and it was revised multiple times later to incorporate suggestions from WECC MVS members. Tesla Energy provided main control blocks to support the development of this model specification. This standard library model is developed to help the utility industry better understand the GFM technology. The model could be used to represent equipment for long-term planning studies where vendor-specific models are not available. As equipment matures and improves, standard library models will be updated to capture the new functionalities of GFMs. It is not intended that these models will always remain representative of all future GFM technologies.

24 POWER TRANSMISSION AND DISTRIBUTION

Statistical Considerations of Data Processing in Giovanni Online Tool

The GES DISC Interactive Online Visualization and Analysis Infrastructure (Giovanni) is a web-based interface for the rapid visualization and analysis of gridded data from a number of remote sensing instruments. The GES DISC currently employs several Giovanni instances to analyze various products, such as Ocean-Giovanni for ocean products from SeaWiFS and MODIS-Aqua; TOMS & OM1 Giovanni for atmospheric chemical trace gases from TOMS and OMI, and MOVAS for aerosols from MODIS, etc. (http://giovanni.gsfc.nasa.gov) Foremost among the Giovanni statistical functions is data averaging. Two aspects of this function are addressed here. The first deals with the accuracy of averaging gridded mapped products vs. averaging from the ungridded Level 2 data. Some mapped products contain mean values only; others contain additional statistics, such as number of pixels (NP) for each grid, standard deviation, etc. Since NP varies spatially and temporally, averaging with or without weighting by NP will be different. In this paper, we address differences of various weighting algorithms for some datasets utilized in Giovanni. The second aspect is related to different averaging methods affecting data quality and interpretation for data with non-normal distribution. The present study demonstrates results of different spatial averaging methods using gridded SeaWiFS Level 3 mapped monthly chlorophyll a data. Spatial averages were calculated using three different methods: arithmetic mean (AVG), geometric mean (GEO), and maximum likelihood estimator (MLE). Biogeochemical data, such as chlorophyll a, are usually considered to have a log-normal distribution. The study determined that differences between methods tend to increase with increasing size of a selected coastal area, with no significant differences in most open oceans. The GEO method consistently produces values lower than AVG and MLE. The AVG method produces values larger than MLE in some cases, but smaller in other cases. Further studies indicated that significant differences between AVG and MLE methods occurred in coastal areas where data have large spatial variations and a log-bimodal distribution instead of log-normal distribution.

Suhung, Shen

A Survey of Open-Source Tools for Transmission and Distribution Systems Research

This work presents a review of open-source electric power transmission and distribution systems analysis tools suitable for use by industry professionals and academic researchers. Due to the high complexity of the electric grid, there exist numerous tools and extensive research pertaining to nearly every aspect of the design, operation, and control of transmission and distribution networks. In addition to the commercial tools, a wide range of free, open-source tools, models, and data usable by the scientific community for related research have been developed by different organizations, including both international and US universities and national laboratories. However, due to the absence of a catalog of available tools, models and data, researchers often lack a knowledge of existing capabilities and may develop duplicative software and tools. Increasing awareness of these available resources seeks to accelerate their broader use, leading to more efficient and standardized grid analysis. This review paper (which is part of a larger survey effort that studied over 400 tools in the transmission, distribution, buildings, and electric vehicles space) outlines selected open-source resources that have been developed in power transmission and distribution systems research. It is anticipated that this work can serve as a guide for industry and academic researchers alike, ensuring that research efforts are well-channeled.

24 POWER TRANSMISSION AND DISTRIBUTION

Grid Resolution Study over Operability Space for a Mach 1.7 Low Boom External Compression Inlet

This paper presents a statistical methodology whereby the probability limits associated with CFD grid resolution of inlet flow analysis can be determined which provide quantitative information on the distribution of that error over the specified operability range. The objectives of this investigation is to quantify the effects of both random (accuracy) and systemic (biasing) errors associated with grid resolution in the analysis of the Lockheed Martin Company (LMCO) N+2 Low Boom external compression supersonic inlet. The study covers the entire operability space as defined previously by the High Speed Civil Transport (HSCT) High Speed Research (HSR) program goals. The probability limits in terms of a 95.0% confidence interval on the analysis data were evaluated for four ARP1420 inlet metrics, namely (1) total pressure recovery (PFAIP), (2) radial hub distortion (DPH/P), (3) ) radial tip distortion (DPT/P), and (4) ) circumferential distortion (DPC/P). In general, the resulting +/-0.95 delta Y interval was unacceptably large in comparison to the stated goals of the HSCT program. Therefore, the conclusion was reached that the "standard grid" size was insufficient for this type of analysis. However, in examining the statistical data, it was determined that the CFD analysis results at the outer fringes of the operability space were the determining factor in the measure of statistical uncertainty. Adequate grids are grids that are free of biasing (systemic) errors and exhibit low random (precision) errors in comparison to their operability goals. In order to be 100% certain that the operability goals have indeed been achieved for each of the inlet metrics, the Y+/-0.95 delta Y limit must fall inside the stated operability goals. For example, if the operability goal for DPC/P circumferential distortion is ≤0.06, then the forecast Y for DPC/P plus the 95% confidence interval on DPC/P, i.e. +/-0.95 delta Y, must all be less than or equal to 0.06.

Grid

Region-based modeling algorithms for remotely-sensed data

Five algorithms being developed for performing region-based modeling operations on classified remotely-sensed images are described. The first algorithm converts images from standard grid structure into topological grid structure, while the remaining algorithms act upon topologically grid-structured images to perform region-based relabelling, overlaying, distance searching, and neighborhood scanning operations. The use of precomputed topological information, through the use of topological grid structure, makes region-based algorithms highly accessible to earth scientists.

Goldberg, M.

Seasonal and temporal changes in the vertical profiles of polar stratospheric ozone: 1978-1986

The long-term changes in stratospheric ozone in both Antarctic and Arctic regions during the period November 1978 to October 1986 exhibit significant interhemispheric differences in terms of time of onset, altitude, latitude, longitude, and phase. The 8-year data set of stratospheric ozone derived from observations with the Nimbus 7 Solar Backscatter Ultraviolet (SBUV) spectrometer instrument were deseasonalized by subtracting monthly deviations from 6-year monthly means for 10 degree bands centered at latitudes 80 S-80 N and the 64x64 standard NMC grid at standard pressure levels in the atmosphere. Linear trends are derived from the linear regression of monthly deviations from long term monthly means in terms of annual and monthly trends for the latitude region 55 to 81 degrees in both hemispheres. An assessment has been made of the SBUV instrument drift from analyses of annual deviations from long term annual means of stratospheric ozone in north temperate regions from 25 N-55 N with corresponding Umkehr observations from 5 stations at latitudes from 36 N-52 N which have been corrected for stratospheric aerosols derived from 5 lidar stations (DeLuisi and Mateer, 1988).

Heath, Donald F.

Goddard Latent Heating Retrieval Algorithm for TRMM and GPM

The Goddard Convective-Stratiform Heating (CSH) algorithm has been used to retrieve latent heating (LH) associated with clouds and cloud systems in support of the Tropical Rainfall Measuring Mission (TRMM) and Global Precipitation Measurement (GPM) mission. The CSH algorithm requires the use of a cloud-resolving model (CRM) to simulate LH profiles to build look-up tables (LUTs). In this paper we describe the current V6 CSH and its differences/similarities versus the previous V5 CSH. Long-term CRM simulations are conducted to identify the impact of CRM resolution and the convective-stratiform separation method on LH structure/profiles. The TRMM and GPM Combined algorithm derived surface rainfall rates and their associated precipitation properties are the input to the CSH algorithm. Since there is no direct measurement of LH structure, the performance of the CSH V6 algorithm is examined by comparing its vertically-integrated heating (or equivalent surface rainfall rate) against the surface rainfall rate derived from the TRMM/GPM Combined algorithm. The results suggest the CSH three-month and zonal mean equivalent surface rain rates are in good agreement with the Combined rates over the ITCZ region; the agreement is best over ocean. CSH three-month and zonal mean equivalent surface rain rates are larger than the Combined rates over land in both the tropics and sub-tropics. CSH three-month mean equivalent surface rainfall rates also have local differences with the Combined rates that can be smoothed by area averaging to larger horizontal resolutions (from the CSH standard grid of 0.25° × 0.25° to 0.5° × 0.5° or 1.0° × 1.0°). CSH equivalent surface rainfall rates have more light rain rates but less larger rain rates compared to the GPM Combined surface rain rates.

Latent heating retrieval

Baroclinic instability in vertically discrete systems

The Charney-Phillips (1953) standard vertical grid for quasi-geostrophic models is compared with the Lorenz (1960) vertical grid (which departs from the standard grid by carrying horizontal velocity and potential temperature at same levels) in the framework of the quasi-geostrophic potential vorticity equation and baroclinic instability. It is demonstrated that the Charney-Phillips grid makes it possible to maintain important dynamical constraints on quasi-geostrophic flow, such as the conservation of quasi-geostrophic potential vorticity through horizontal advection and resulting integral constraints. The Lorenz grid, on the other hand, is not straightforward even to define quasi-geostrophic potential vorticity. Moreover, due to an extra degree of freedom in potential temperature, the Lorenz grid can falsely satisfy the necessary condition for baroclinic instability near the lower and the upper boundaries.

Arakawa, Akio

Fibonacci Grids

Recent years have seen a resurgence of interest in a variety of non-standard computational grids for global numerical prediction. The motivation has been to reduce problems associated with the converging meridians and the polar singularities of conventional regular latitude-longitude grids. A further impetus has come from the adoption of massively parallel computers, for which it is necessary to distribute work equitably across the processors; this is more practicable for some non-standard grids. Desirable attributes of a grid for high-order spatial finite differencing are: (i) geometrical regularity; (ii) a homogeneous and approximately isotropic spatial resolution; (iii) a low proportion of the grid points where the numerical procedures require special customization (such as near coordinate singularities or grid edges). One family of grid arrangements which, to our knowledge, has never before been applied to numerical weather prediction, but which appears to offer several technical advantages, are what we shall refer to as "Fibonacci grids". They can be thought of as mathematically ideal generalizations of the patterns occurring naturally in the spiral arrangements of seeds and fruit found in sunflower heads and pineapples (to give two of the many botanical examples). These grids possess virtually uniform and highly isotropic resolution, with an equal area for each grid point. There are only two compact singular regions on a sphere that require customized numerics. We demonstrate the practicality of these grids in shallow water simulations, and discuss the prospects for efficiently using these frameworks in three-dimensional semi-implicit and semi-Lagrangian weather prediction or climate models.

Swinbank, Richard

An automated system for mosaicking spaceborne SAR imagery

An automated system has been developed for mosaicking spaceborne synthetic aperture radar (SAR) imagery. The system is capable of producing multiframe mosaics for large-scale mapping by combining images in both the along-track direction and adjacent cross-track swaths from ascending and descending passes. The system requires no operator interaction and is capable of achieving high registration accuracy. The output product is a geocoded mosaic on a standard map grid such as UTM or polar stereographic. The procedure described in detail in this paper consists essentially of remapping the individual image frames into these standard grids, frame-to-frame image registration and radiometric smoothing of the seams. These procedures are directly applicable to both the Magellan Venus Mapper and a scanning SAR design such as Radarsat, Eos SAR in addition to merging image frames from traditional SAR systems such as SEASAT and SIR-B. With minor modifications, it may also be applied to spaceborne optical sensor data to generate large-scale mosaics efficiently and with a high degree of accuracy. The system has been tested with SEASAT, SIR-B and Landsat TM data. Examples presented in this paper include a 38-frame mosaic of the Yukon River basin in central Alaska, a 33-frame mosaic of southern California and a three-frame terrain-corrected geocoded mosaic of the Wind River basin in Wyoming.

Kwok, Ronald

Evaluation of IEC 62443 Standard Gaps for Electric Grid Substation Model Use Case

This report presents an evaluation of the IEC 62443 standards in the context of electric grid substations, as part of a collaborative effort among Sandia National Laboratories (SNL), Idaho National Laboratory (INL), and the National Renewable Energy Laboratory (NREL). The primary objective is to assess the applicability of these standards to enhance cybersecurity measures for industrial automation and control systems (IACS) within the energy sector. The evaluation identifies strengths, such as the scalability of security levels and the structured lifecycle guidance provided by IEC 62443. However, it also highlights significant gaps, including limited integration of physical security, insufficient guidance for legacy systems, and challenges in addressing emerging threats like supply chain vulnerabilities. Recommendations for refining the standards are proposed, including the need for tailored guidance for securing legacy systems, integrating physical security with cybersecurity frameworks, and enhancing interoperability across multi-vendor environments. By addressing these gaps, the IEC 62443 standards can be strengthened to ensure comprehensive cybersecurity for electric grid substations, thereby supporting the resilience and reliability of critical energy infrastructure.

24 POWER TRANSMISSION AND DISTRIBUTION

Multigrid with Overlapping Patches

Solving boundary value problems with optimal efficiency requires adaptivity and multilevel techniques. Previously, an implementation of the AFACx algorithm is presented that is based on rectangular Cartesian grids. This implementation does not allow for the over]ap of grids that lie on the same level of refinement. We investigate the case in which these grids overlap. A standard technique for overlapping grids is the Schwarz algorithm. Some ways of using the Schwarz algorithm in a standard multigrid scheme are presented. Also, a problem that arises in some situations with non-aligned, overlapping grids is described. This situation comes up in a natural way when the Schwarz algorithm is used as a relaxation scheme within a multilevel algorithm. We identify the reason for the bad convergence and show that by more sophisticated interpolation the difficulties can be overcome. Then we present a multiplicative Schwarz algorithm for a large number of grids that has a high potential for parallelization. Finally we give some numerical results for the FACx algorithm with overlapping grids on each refinement level. The implementation of the described codes uses C++ and the array class libraries A++ and P++. Using the A++/P++ programming environment, it was possible to move from a serial code to a parallel code within a few days.

Berndt, Markus

The evolution of horizontal-branch stars - Theoretical sequences

A new grid of standard (i.e., solar CNO/Fe, no core rotation, and including semiconvection) horizontal-branch evolutionary sequences are presented which extend the grid of Sweigart both by including the final phase of core helium exhaustion and by using a finer grid of compositions. These sequences were constructed specifically for the studies of the Sandage period-shift effect and the second parameter phenomenon among the Galactic globular clusters. The numerical results for the observable characteristics of the sequences are tabulated which can be directly used to synthesize the observed horizontal-branch distributions. The present computations suggest that the observed difference in period change of RR Lyrae stars in the globular clusters M3 and M15 could be attributed, at least in the mean, to stellar evolution.

Lee, Young-Wook

Plane Smoothers for Multiblock Grids: Computational Aspects

Standard multigrid methods are not well suited for problems with anisotropic discrete operators, which can occur, for example, on grids that are stretched in order to resolve a boundary layer. One of the most efficient approaches to yield robust methods is the combination of standard coarsening with alternating-direction plane relaxation in the three dimensions. However, this approach may be difficult to implement in codes with multiblock structured grids because there may be no natural definition of global lines or planes. This inherent obstacle limits the range of an implicit smoother to only the portion of the computational domain in the current block. This report studies in detail, both numerically and analytically, the behavior of blockwise plane smoothers in order to provide guidance to engineers who use block-structured grids. The results obtained so far show alternating-direction plane smoothers to be very robust, even on multiblock grids. In common computational fluid dynamics multiblock simulations, where the number of subdomains crossed by the line of a strong anisotropy is low (up to four), textbook multigrid convergence rates can be obtained with a small overlap of cells between neighboring blocks.

Llorente, Ignacio M.