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NASA NTRS1990

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↗

NASA NTRS1999

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.↗

NASA NTRS1995

Algorithms for high aspect ratio oriented triangulations

Grid generation plays an integral part in the solution of computational fluid dynamics problems for aerodynamics applications. A major difficulty with standard structured grid generation, which produces quadrilateral (or hexahedral) elements with implicit connectivity, has been the requirement for a great deal of human intervention in developing grids around complex configurations. This has led to investigations into unstructured grids with explicit connectivities, which are primarily composed of triangular (or tetrahedral) elements, although other subdivisions of convex cells may be used. The existence of large gradients in the solution of aerodynamic problems may be exploited to reduce the computational effort by using high aspect ratio elements in high gradient regions. However, the heuristic approaches currently in use do not adequately address this need for high aspect ratio unstructured grids. High aspect ratio triangulations very often produce the large angles that are to be avoided. Point generation techniques based on contour or front generation are judged to be the most promising in terms of being able to handle complicated multiple body objects, with this technique lending itself well to adaptivity. The eventual goal encompasses several phases: first, a partitioning phase, in which the Voronoi diagram of a set of points and line segments (the input set) will be generated to partition the input domain; second, a contour generation phase in which body-conforming contours are used to subdivide the partition further as well as introduce the foundation for aspect ratio control, and; third, a Steiner triangulation phase in which points are added to the partition to enable triangulation while controlling angle bounds and aspect ratio. This provides a combination of the advancing front/contour techniques and refinement. By using a front, aspect ratio can be better controlled. By using refinement, bounds on angles can be maintained, while attempting to minimize the number of Steiner points.

Posenau, Mary-Anne K.↗

DOE OSTI2025

Ensuring electromagnetic compatibility in grid-connected power converters: Challenges, standards, and compliance strategies

In today's rapidly advancing world, electronic devices and systems are fundamental to a wide range of industries, including renewable energy and global telecommunications infrastructure. However, as these devices become more complex and widespread, the risk of electromagnetic interference (EMI) also increases, underscoring the importance of stringent Electromagnetic Compatibility (EMC) requirements for maintaining system integrity. This paper addresses the specific challenges associated with grid-connected power converters (GCPCs), which are critical in integrating renewable energy into existing power grids. It explores the complexities of EMI in the context of GCPCs, particularly given the recent emergence of tailored EMC standards for these systems. The paper also highlights the shortcomings of applying generic or unrelated standards to GCPCs, often leading to inadequate compliance and testing protocols. Through a detailed analysis of existing standards and recent advancements in product-specific EMC requirements, this paper provides a comprehensive overview of the current landscape, offering guidance to stakeholders on navigating the intricate EMC compliance landscape, with a focus on methodologies, testing procedures, and the evolving regulatory environment for GCPCs.

24 POWER TRANSMISSION AND DISTRIBUTION↗

NASA NTRS1993

Time-domain analysis of planar microstrip devices using a generalized Yee-algorithm based on unstructured grids

The generalized Yee-algorithm is presented for the temporal full-wave analysis of planar microstrip devices. This algorithm has the significant advantage over the traditional Yee-algorithm in that it is based on unstructured and irregular grids. The robustness of the generalized Yee-algorithm is that structures that contain curved conductors or complex three-dimensional geometries can be more accurately, and much more conveniently modeled using standard automatic grid generation techniques. This generalized Yee-algorithm is based on the the time-marching solution of the discrete form of Maxwell's equations in their integral form. To this end, the electric and magnetic fields are discretized over a dual, irregular, and unstructured grid. The primary grid is assumed to be composed of general fitted polyhedra distributed throughout the volume. The secondary grid (or dual grid) is built up of the closed polyhedra whose edges connect the centroid's of adjacent primary cells, penetrating shared faces. Faraday's law and Ampere's law are used to update the fields normal to the primary and secondary grid faces, respectively. Subsequently, a correction scheme is introduced to project the normal fields onto the grid edges. It is shown that this scheme is stable, maintains second-order accuracy, and preserves the divergenceless nature of the flux densities. Finally, for computational efficiency the algorithm is structured as a series of sparse matrix-vector multiplications. Based on this scheme, the generalized Yee-algorithm has been implemented on vector and parallel high performance computers in a highly efficient manner.

Gedney, Stephen D.↗

NASA NTRS2012

Numerical Dissipation and Wrong Propagation Speed of Discontinuities for Stiff Source Terms

In compressible turbulent combustion/nonequilibrium flows, the constructions of numerical schemes for (a) stable and accurate simulation of turbulence with strong shocks, and (b) obtaining correct propagation speed of discontinuities for stiff reacting terms on coarse grids share one important ingredient - minimization of numerical dissipation while maintaining numerical stability. Here coarse grids means standard mesh density requirement for accurate simulation of typical non-reacting flows. This dual requirement to achieve both numerical stability and accuracy with zero or minimal use of numerical dissipation is most often conflicting for existing schemes that were designed for non-reacting flows. The goal of this paper is to relate numerical dissipations that are inherited in a selected set of high order shock-capturing schemes with the onset of wrong propagation speed of discontinuities as a function of stiffness of the source term and the grid spacing.

Yee, H. C.↗

DOE OSTI2026

DER Cybersecurity Standards: Assessment and Gap Analysis

The purpose of this report is to share the comprehensive gap analysis of existing cybersecurity standards applicable to Distributed Energy Resources (DERs) within the electric power sector. This analysis aims to identify critical deficiencies in current standards, assess their alignment with industry needs, and provide actionable recommendations for enhancing cybersecurity measures. The scope encompasses various DER technologies, including solar, wind, energy storage, and hydrogen fuel cells, and emphasizes the significance of establishing robust cybersecurity frameworks and standards to safeguard these increasingly integrated systems. The report provides valuable insights for stakeholders in the DER ecosystem, including manufacturers, utilities, and regulators. It underscores the importance of continued development and refinement of cybersecurity standards to keep up with the technical advances in DERs and associated cybersecurity challenges. The analysis evaluated IEC, IEEE, ISA, ISO, and UL standards relevant to DER cybersecurity. Standards were assessed on their coverage of key requirements including data availability, integrity, confidentiality, access control, authentication, encryption, and system hardening. For each standard, the analysis assessed its alignment with current industry practices, regulatory compliance, effectiveness in addressing known risks, coverage of emerging risks, and how it promotes interoperability. The evaluation also considered potential integration challenges and barriers to adoption.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

WINDPROF: Merged Best-Estimate Wind Profile Data – Nantucket (WFIP3 Campaign)

WINDPROF provides 10-minute wind and turbulence profiles that integrate scanning Doppler lidars, a profiling lidar, a 915 MHz radar wind profiler, and a sonic anemometer across Northeast U.S. coastal and offshore sites during the WFIP3 campaign. Variables include wind speed, wind direction, vertical velocity, turbulence intensity, and turbulent kinetic energy, each with per-instrument quality control and inter-instrument agreement validation. Profiles are mapped to a standardized height grid – a dedicated near-surface level at the sonic measurement height (5 m AGL), 20 m spacing to 100 m, and 30 m spacing above – and carry component and derived uncertainty estimates. Heights are reported above ground level; the site's ground elevation is stored separately. The Nantucket dataset covers 1 February 2024 – 8 September 2025.

17 WIND ENERGY↗

DOE OSTI2026

WINDPROF: Merged Best-Estimate Wind Profile Data – Block Island (WFIP3 Campaign)

WINDPROF provides 10-minute wind and turbulence profiles that integrate a scanning Doppler lidar, a profiling lidar, a 915 MHz radar wind profiler, and a surface met station across Northeast U.S. coastal and offshore sites during the WFIP3 campaign. Variables include wind speed, wind direction, vertical velocity, turbulence intensity, and turbulent kinetic energy, each with per-instrument quality control and inter-instrument agreement validation. Profiles are mapped to a standardized height grid – a dedicated near-surface level at the 10 m surface-wind height, 20 m spacing to 100 m, and 30 m spacing above – and carry component and derived uncertainty estimates. Heights are reported above ground level; the site's ground elevation is stored separately. The Block Island dataset covers 1 February 2024 – 8 September 2025.

17 WIND ENERGY↗

DOE OSTI2026

WINDPROF: Merged Best-Estimate Wind Profile Data – Cape Cod (WFIP3 Campaign)

WINDPROF provides 10-minute wind and turbulence profiles that integrate a scanning Doppler lidar, a profiling Doppler lidar, and two sonic anemometers across Northeast U.S. coastal and offshore sites during the WFIP3 campaign. Variables include wind speed, wind direction, vertical velocity, turbulence intensity, and turbulent kinetic energy, each with per-instrument quality control and inter-instrument agreement validation. Profiles are mapped to a standardized height grid – dedicated near-surface levels at the sonic measurement heights (4 m and 10 m AGL), 20 m spacing to 100 m, and 30 m spacing above – and carry component and derived uncertainty estimates. Heights are reported above ground level; the site's ground elevation is stored separately. The Cape Cod dataset covers 1 February 2024 – 6 September 2025.

17 WIND ENERGY↗

DOE OSTI2026

WINDPROF: Merged Best-Estimate Wind Profile Data – Rhode Island (WFIP3 Campaign)

WINDPROF provides 10-minute wind and turbulence profiles that integrate a scanning Doppler lidar, a continuous-wave profiling lidar, and a sonic anemometer across Northeast U.S. coastal and offshore sites during the WFIP3 campaign. Variables include wind speed, wind direction, vertical velocity, turbulence intensity, and turbulent kinetic energy, each with per-instrument quality control and inter-instrument agreement validation. Profiles are mapped to a standardized height grid – a dedicated near-surface level at the sonic measurement height (4 m AGL), 20 m spacing to 100 m, and 30 m spacing above – and carry component and derived uncertainty estimates. Heights are reported above ground level; the site's ground elevation is stored separately. The Rhode Island dataset covers 7 February 2024 – 4 September 2025.

17 WIND ENERGY↗

NASA NTRS1984

A method for modeling finite-core vortices in wake-flow calculations

A numerical method for computing nonplanar vortex wakes represented by finite-core vortices is presented. The approach solves for the velocity on an Eulerian grid, using standard finite-difference techniques; the vortex wake is tracked by Lagrangian methods. In this method, the distribution of continuous vorticity in the wake is replaced by a group of discrete vortices. An axially symmetric distribution of vorticity about the center of each discrete vortex is used to represent the finite-core model. Two distributions of vorticity, or core models, are investigated: a finite distribution of vorticity represented by a third-order polynomial, and a continuous distribution of vorticity throughout the wake. The method provides for a vortex-core model that is insensitive to the mesh spacing. Results for a simplified case are presented. Computed results for the roll-up of a vortex wake generated by wings with different spanwise load distributions are presented; contour plots of the flow-field velocities are included; and comparisons are made of the computed flow-field velocities with experimentally measured velocities.

Stremel, P. M.↗

NASA NTRS1992

Grid management

A computational environment that allows many Computational Fluid Dynamics (CFD) engineers to work on the same project exists in the Special Project Office (SPO). This environment enables several users to carry out the task of grid generation. The grid management system, used by the engineers, is described in a brief overview. The topics will include the grid file naming system, the grid-generation procedure, grid storage, and the grid format standard.

Hwang, Danny↗

NASA NTRS1993

CFD analysis of turbopump volutes

An effort is underway to develop a procedure for the regular use of CFD analysis in the design of turbopump volutes. Airflow data to be taken at NASA Marshall will be used to validate the CFD code and overall procedure. Initial focus has been on preprocessing (geometry creation, translation, and grid generation). Volute geometries have been acquired electronically and imported into the CATIA CAD system and RAGGS (Rockwell Automated Grid Generation System) via the IGES standard. An initial grid topology has been identified and grids have been constructed for turbine inlet and discharge volutes. For CFD analysis of volutes to be used regularly, a procedure must be defined to meet engineering design needs in a timely manner. Thus, a compromise must be established between making geometric approximations, the selection of grid topologies, and possible CFD code enhancements. While the initial grid developed approximated the volute tongue with a zero thickness, final computations should more accurately account for the geometry in this region. Additionally, grid topologies will be explored to minimize skewness and high aspect ratio cells that can affect solution accuracy and slow code convergence. Finally, as appropriate, code modifications will be made to allow for new grid topologies in an effort to expedite the overall CFD analysis process.

Ascoli, Edward P.↗

NASA NTRS2011

Numerical Dissipation and Wrong Propagation Speed of Discontinuities for Stiff Source Terms

In compressible turbulent combustion/nonequilibrium flows, the constructions of numerical schemes for (a) stable and accurate simulation of turbulence with strong shocks, and (b) obtaining correct propagation speed of discontinuities for stiff reacting terms on coarse grids share one important ingredient - minimization of numerical dissipation while maintaining numerical stability. Here coarse grids means standard mesh density requirement for accurate simulation of typical non-reacting flows. This dual requirement to achieve both numerical stability and accuracy with zero or minimal use of numerical dissipation is most often conflicting for existing schemes that were designed for non-reacting flows. The goal of this paper is to relate numerical dissipations that are inherited in a selected set of high order shock-capturing schemes with the onset of wrong propagation speed of discontinuities for two representative stiff detonation wave problems.

Yee, H. C.↗

NASA NTRS2013

On Spurious Numerics in Solving Reactive Equations

The objective of this study is to gain a deeper understanding of the behavior of high order shock-capturing schemes for problems with stiff source terms and discontinuities and on corresponding numerical prediction strategies. The studies by Yee et al. (2012) and Wang et al. (2012) focus only on solving the reactive system by the fractional step method using the Strang splitting (Strang 1968). It is a common practice by developers in computational physics and engineering simulations to include a cut off safeguard if densities are outside the permissible range. Here we compare the spurious behavior of the same schemes by solving the fully coupled reactive system without the Strang splitting vs. using the Strang splitting. Comparison between the two procedures and the effects of a cut off safeguard is the focus the present study. The comparison of the performance of these schemes is largely based on the degree to which each method captures the correct location of the reaction front for coarse grids. Here "coarse grids" means standard mesh density requirement for accurate simulation of typical non-reacting flows of similar problem setup. It is remarked that, in order to resolve the sharp reaction front, local refinement beyond standard mesh density is still needed.

Numerics↗

NASA NTRS2002

Grids for Dummies: Featuring Earth Science Data Mining Application

This viewgraph presentation discusses the concept and advantages of linking computers together into data grids, an emerging technology for managing information across institutions, and potential users of data grids. The logistics of access to a grid, including the use of the World Wide Web to access grids, and security concerns are also discussed. The potential usefulness of data grids to the earth science community is also discussed, as well as the Global Grid Forum, and other efforts to establish standards for data grids.

Hinke, Thomas H.↗

NASA NTRS1996

3D Structured Grid Adaptation

Grid adaptation for structured meshes is the art of using information from an existing, but poorly resolved, solution to automatically redistribute the grid points in such a way as to improve the resolution in regions of high error, and thus the quality of the solution. This involves: (1) generate a grid vis some standard algorithm, (2) calculate a solution on this grid, (3) adapt the grid to this solution, (4) recalculate the solution on this adapted grid, and (5) repeat steps 3 and 4 to satisfaction. Steps 3 and 4 can be repeated until some 'optimal' grid is converged to but typically this is not worth the effort and just two or three repeat calculations are necessary. They also may be repeated every 5-10 time steps for unsteady calculations.

Banks, D. W.↗