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NASA NTRS1986

Computer code to interchange CDS and wave-drag geometry formats

A computer program has been developed on the PRIME minicomputer to provide an interface for the passage of aircraft configuration geometry data between the Rockwell Configuration Development System (CDS) and a wireframe geometry format used by aerodynamic design and analysis codes. The interface program allows aircraft geometry which has been developed in CDS to be directly converted to the wireframe geometry format for analysis. Geometry which has been modified in the analysis codes can be transformed back to a CDS geometry file and examined for physical viability. Previously created wireframe geometry files may also be converted into CDS geometry files. The program provides a useful link between a geometry creation and manipulation code and analysis codes by providing rapid and accurate geometry conversion.

Johnson, V. S.↗

NASA NTRS1994

The load separation technique in the elastic-plastic fracture analysis of two- and three-dimensional geometries

Load separation is the representation of the load in the test records of geometries containing cracks as a multiplication of two separate functions: a crack geometry function and a material deformation function. Load separation is demonstrated in the test records of several two-dimensional geometries such as compact tension geometry, single edge notched bend geometry, and center cracked tension geometry and three-dimensional geometries such as semi-elliptical surface crack. The role of load separation in the evaluation of the fracture parameter J-integral and the associated factor eta for two-dimensional geometries is discussed. The paper also discusses the theoretical basis and the procedure for using load separation as a simplified yet accurate approach for plastic J evaluation in semi-elliptical surface crack which is a three-dimensional geometry. The experimental evaluation of J, and particularly J(sub pl), for three-dimensional geometries is very challenging. A few approaches have been developed in this regard and they are either complex or very approximate. The paper also presents the load separation as a mean to identify the blunting and crack growth regions in the experimental test records of precracked specimens. Finally, load separation as a methodology in elastic-plastic fracture mechanics is presented.

Sharobeam, Monir H.↗

NASA NTRS2000

Convection in Slab and Spheroidal Geometries

Three-dimensional numerical simulations of compressible turbulent thermally driven convection, in both slab and spheroidal geometries, are reviewed and analyzed in terms of velocity spectra and mixing-length theory. The same ideal gas model is used in both geometries, and resulting flows are compared. The piecewise-parabolic method (PPM), with either thermal conductivity or photospheric boundary conditions, is used to solve the fluid equations of motion. Fluid motions in both geometries exhibit a Kolmogorov-like k(sup -5/3) range in their velocity spectra. The longest wavelength modes are energetically dominant in both geometries, typically leading to one convection cell dominating the flow. In spheroidal geometry, a dipolar flow dominates the largest scale convective motions. Downflows are intensely turbulent and up drafts are relatively laminar in both geometries. In slab geometry, correlations between temperature and velocity fluctuations, which lead to the enthalpy flux, are fairly independent of depth. In spheroidal geometry this same correlation increases linearly with radius over the inner 70 percent by radius, in which the local pressure scale heights are a sizable fraction of the radius. The effects from the impenetrable boundary conditions in the slab geometry models are confused with the effects from non-local convection. In spheroidal geometry nonlocal effects, due to coherent plumes, are seen as far as several pressure scale heights from the lower boundary and are clearly distinguishable from boundary effects.

Porter, David H.↗

NASA NTRS2010

Intelligent Patching of Conceptual Geometry for CFD Analysis

The iPatch computer code for intelligently patching surface grids was developed to convert conceptual geometry to computational fluid dynamics (CFD) geometry (see figure). It automatically uses bicubic B-splines to extrapolate (if necessary) each surface in a conceptual geometry so that all the independently defined geometric components (such as wing and fuselage) can be intersected to form a watertight CFD geometry. The software also computes the intersection curves of surface patches at any resolution (up to 10.4 accuracy) specified by the user, and it writes the B-spline surface patches, and the corresponding boundary points, for the watertight CFD geometry in the format that can be directly used by the grid generation tool VGRID. iPatch requires that input geometry be in PLOT3D format where each component surface is defined by a rectangular grid {(x(i,j), y(i,j), z(i,j)):1less than or equal to i less than or equal to m, 1 less than or equal to j less than or equal to n} that represents a smooth B-spline surface. All surfaces in the PLOT3D file conceptually represent a watertight geometry of components of an aircraft on the half-space y greater than or equal to 0. Overlapping surfaces are not allowed, but could be fixed by a utility code "fixp3d". The fixp3d utility code first finds the two grid lines on the two surface grids that are closest to each other in Hausdorff distance (a metric to measure the discrepancies of two sets); then uses one of the grid lines as the transition line, extending grid lines on one grid to the other grid to form a merged grid. Any two connecting surfaces shall have a "visually" common boundary curve, or can be described by an intersection relationship defined in a geometry specification file. The intersection of two surfaces can be at a conceptual level. However, the intersection is directional (along either i or j index direction), and each intersecting grid line (or its spine extrapolation) on the first surface should intersect the second surface. No two intersection relationships will result in a common intersection point of three surfaces. The output files of iPatch are IGES, d3m, and mapbc files that define the CFD geometry in VGRID format. The IGES file gives the NURBS definition of the outer mold line in the geometry. The d3m file defines how the outer mold line is broken into surface patches whose boundary curves are defined by points. The mapbc file specifies what the boundary condition is on each patch and the corresponding NURBS surface definition of each non-planar patch in the IGES file.

Li, Wu↗

NASA NTRS1980

An approach for management of geometry data

The strategies for managing Integrated Programs for Aerospace Design (IPAD) computer-based geometry are described. The computer model of geometry is the basis for communication, manipulation, and analysis of shape information. IPAD's data base system makes this information available to all authorized departments in a company. A discussion of the data structures and algorithms required to support geometry in IPIP (IPAD's data base management system) is presented. Through the use of IPIP's data definition language, the structure of the geometry components is defined. The data manipulation language is the vehicle by which a user defines an instance of the geometry. The manipulation language also allows a user to edit, query, and manage the geometry. The selection of canonical forms is a very important part of the IPAD geometry. IPAD has a canonical form for each entity and provides transformations to alternate forms; in particular, IPAD will provide a transformation to the ANSI standard. The DBMS schemas required to support IPAD geometry are explained.

Dube, R. P.↗

NASA NTRS2010

Parametric Geometry, Structured Grid Generation, and Initial Design Study for REST-Class Hypersonic Inlets

Computational design and analysis of three-dimensional hypersonic inlets with shape transition has been a significant challenge due to the complex geometry and grid required for three-dimensional viscous flow calculations. Currently, the design process utilizes an inviscid design tool to produce initial inlet shapes by streamline tracing through an axisymmetric compression field. However, the shape is defined by a large number of points rather than a continuous surface and lacks important features such as blunt leading edges. Therefore, a design system has been developed to parametrically construct true CAD geometry and link the topology of a structured grid to the geometry. The Adaptive Modeling Language (AML) constitutes the underlying framework that is used to build the geometry and grid topology. Parameterization of the CAD geometry allows the inlet shapes produced by the inviscid design tool to be generated, but also allows a great deal of flexibility to modify the shape to account for three-dimensional viscous effects. By linking the grid topology to the parametric geometry, the GridPro grid generation software can be used efficiently to produce a smooth hexahedral multiblock grid. To demonstrate the new capability, a matrix of inlets were designed by varying four geometry parameters in the inviscid design tool. The goals of the initial design study were to explore inviscid design tool geometry variations with a three-dimensional analysis approach, demonstrate a solution rate which would enable the use of high-fidelity viscous three-dimensional CFD in future design efforts, process the results for important performance parameters, and perform a sample optimization.

Ferlemann, Paul G.↗

NASA NTRS2017

Accounting for the Effects of Surface BRDF on Satellite Cloud and Trace-Gas Retrievals: A New Approach Based on Geometry-Dependent Lambertian-Equivalent Reflectivity Applied to OMI Algorithms

Most satellite nadir ultraviolet and visible cloud, aerosol, and trace-gas algorithms make use of climatological surface reflectivity databases. For example, cloud and NO2 retrievals for the Ozone Monitoring Instrument (OMI) use monthly gridded surface reflectivity climatologies that do not depend upon the observation geometry. In reality, reflection of incoming direct and diffuse solar light from land or ocean surfaces is sensitive to the sun-sensor geometry. This dependence is described by the bidirectional reflectance distribution function (BRDF). To account for the BRDF, we propose to use a new concept of geometry-dependent Lambertian equivalent reflectivity (LER). Implementation within the existing OMI cloud and NO2 retrieval infrastructure requires changes only to the input surface reflectivity database. The geometry-dependent LER is calculated using a vector radiative transfer model with high spatial resolution BRDF information from the Moderate Resolution Imaging Spectroradiometer (MODIS) over land and the Cox-Munk slope distribution over ocean with a contribution from water-leaving radiance. We compare the geometry-dependent and climatological LERs for two wavelengths, 354 and 466 nm, that are used in OMI cloud algorithms to derive cloud fractions. A detailed comparison of the cloud fractions and pressures derived with climatological and geometry-dependent LERs is carried out. Geometry-dependent LER and corresponding retrieved cloud products are then used as inputs to our OMI NO2 algorithm. We find that replacing the climatological OMI-based LERs with geometry-dependent LERs can increase NO2 vertical columns by up to 50% in highly polluted areas; the differences include both BRDF effects and biases between the MODIS and OMI-based surface reflectance data sets. Only minor changes to NO2 columns (within 5 %) are found over unpolluted and overcast areas.

Lambert-equivalent reflectivity↗

DOE OSTI2026

Two-phase flow numerical analysis of electrode geometry for alkaline water electrolyzers

Hydrogen is a promising component of a future energy-secure and efficient economy, but its competitiveness depends on reducing production costs. One strategy is to operate alkaline water electrolyzers at higher current densities to increase output. However, this intensifies performance losses due to gas bubble accumulation, which blocks transport pathways and deactivates electrochemically active surfaces. Enhancing bubble evacuation through electrode design is therefore essential. Previous studies have explored various approaches — such as modifying surface morphology, applying sonication or pressure modulation, and introducing surfactants — but these efforts have addressed a limited range of conditions due to the complexity of two-phase flow and electrode geometries. Experiments have also largely been focused on either cell level improvements, which lack the information necessary to isolate each contributing factor, or on modified geometries that are not relevant to practical cell operation. From a modeling perspective, conventional Eulerian multiphase models do not track the complex gas–liquid interfacial dynamics and often neglect surface tension and contact angle effects, reducing their predictive accuracy. To provide insights on the effects of different electrode geometries on the performance of alklaine water electrolyzers this work employs an immersed boundary volume-of-fluid method to simulate bubble behavior in 3D porous electrodes. Multiple base electrode geometries, typically used in practice, with varying porosity are evaluated under a constant surface gas generation rate. Simulation data is analyzed to quantify electrode gas coverage, bubble size dynamics and other relevant metrics. Results show that porosity strongly influences bubble accumulation on electrode surfaces, with higher porosity reducing gas coverage, and its not strictly dependent on the electrode geometry. However, the electrode’s base geometry significantly affects gas accumulation at the separator gap, independent of porosity. A foam electrode geometry resulted in the lowest gas coverage of all electrodes with a median volumetric gas coverage of 11%, but at the cost of a 70% reduction in active area compared with the largest surface area electrode, while gyroid electrodes showed the best trade-off between gas coverage, particularly at the separator surface, and electrochemically active area. In conclusion, the results highlight the need for holistic electrode design strategies.

Alkaline↗

DOE OSTI2025

Assessing the viability of a new subsize tensile specimen geometry for evaluation of structural nuclear and additively manufactured materials

The use of subsize specimens in nuclear materials testing has been a subject of ongoing interest due to radiation safety concerns and resource conservation needs. It is also of interest in additive manufacturing (AM), also known as 3D-printing, as subsize specimens can more accurately represent the behavior of the small, intricate geometries often produced using AM. A novel, extremely small geometry, called the Subsize Teeny (SST) was recently developed and is of interest for implementation. Given its extraordinarily small size and the complexities associated with subsize specimen testing, adequate vetting of this geometry is necessary to ensure data quality. Here, a variety of unirradiated nuclear structural materials were tested in the SST geometry and compared against the well-established SSJ3 geometry. In addition, two case studies implementing the SST as a screening geometry for AM materials were also conducted. The question of SST viability was found to be highly nuanced and will often be dependent on the context or application in question. It was determined, however, that the SST is a largely invalid geometry for exceptionally coarse-grained materials or in cases where the physical defect volume equals or exceeds 0.1 % or where the specimen machining parameters result in significant surface alterations. On the other hand, it was determined that the SST may be employed with confidence if the test material is nearly or totally free of physical defects, isotropic, demonstrates homogeneous plastic deformation, and possesses a fine-grained, nearly or totally homogeneous microstructure with at least twelve slip systems.

Additive manufacturing↗

DOE OSTI2026

The role of focusing geometry in MeV x-ray production from petawatt laser–solid interaction

Relativistic laser–plasma interactions provide a compact and flexible route to generating bright, ultrashort pulses of MeV x rays, with applications in high-energy density science, nuclear physics, and radiography. Despite extensive study of intensity scaling in laser-driven electron acceleration, the role of focusing geometry and focal-volume effects in MeV radiation production remains insufficiently understood. Here, we present experimental and kinetic simulation results from the Texas Petawatt Laser (120 J, 140 fs) in which the focusing geometry (f/3 or f/1.5) is varied, while the laser energy and pulse duration are fixed. Experimentally, the f/3 geometry produces approximately three times more MeV radiation than the f/1.5 geometry, despite its twofold lower nominal vacuum intensity. This result is based on the time-integrated radiation per unit solid angle, as measured along the diagnostic line of sight. Three-dimensional particle-in-cell simulations reproduce this trend when a modest (10s of μm) effective focal plane shift is introduced, demonstrating that relativistic laser–plasma coupling is highly sensitive to focal geometry in the presence of a preplasma. This behavior is consistent with differences in interaction length and effective intensity at the critical surface between the two configurations. The sensitivity of the tightly focused f/1.5 configuration ($z_R ≈$⁠ 5 μ m) reflects the combined influence of thermal lensing and an extended preplasma, while the f/3 geometry (⁠$z_R ≈$ 80 μ m) remains comparatively robust. These results demonstrate a breakdown of conventional intensity scaling and identify focusing geometry as a critical control parameter for MeV electron and x-ray generation at petawatt powers. Implications for laser–plasma-based radiographic facilities are also discussed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1981

Use of interactive graphics to analyze QUICK-geometry

The QUICK InterActive Graphics Analysis (QUIAGA) program and its advantages for displaying aircraft QUICK-geometry to aid in detection and analysis of errors are described. The QUICK-geometry system generates a completely analytical aircraft geometry description for use by finite-difference flow codes. The QUIAGA program was developed to exercise the QUICK-geometry subroutines to examine the analytic definition of a configuration by plotting cross sections and body lines on a graphics terminal. A number of options are available, including multiple cross-section views, hidden-line removal, and display of control point locations. Use of these options for the detection and analysis of errors in the QUICK-geometry definition can be of great assistance in speedily arriving at a correct analytical geometry description for flow-field computation. The QUIAGA program has been used in developing a QUICK-geometry model of the NASA Space Shuttle Orbiter, and examples from this experience are given to show some of the program's features. Details of program usage and an example session are given in the appendixes.

Townsend, J. C.↗

NASA NTRS1989

Detection of edges using local geometry

Researchers described a new representation, the local geometry, for early visual processing which is motivated by results from biological vision. This representation is richer than is often used in image processing. It extracts more of the local structure available at each pixel in the image by using receptive fields that can be continuously rotated and that go to third order spatial variation. Early visual processing algorithms such as edge detectors and ridge detectors can be written in terms of various local geometries and are computationally tractable. For example, Canny's edge detector has been implemented in terms of a local geometry of order two, and a ridge detector in terms of a local geometry of order three. The edge detector in local geometry was applied to synthetic and real images and it was shown using simple interpolation schemes that sufficient information is available to locate edges with sub-pixel accuracy (to a resolution increase of at least a factor of five). This is reasonable even for noisy images because the local geometry fits a smooth surface - the Taylor series - to the discrete image data. Only local processing was used in the implementation so it can readily be implemented on parallel mesh machines such as the MPP. Researchers expect that other early visual algorithms, such as region growing, inflection point detection, and segmentation can also be implemented in terms of the local geometry and will provide sufficiently rich and robust representations for subsequent visual processing.

Gualtieri, J. A.↗

NASA NTRS1993

Unit cell geometry of multiaxial preforms for structural composites

The objective of this study is to investigate the yarn geometry of multiaxial preforms. The importance of multiaxial preforms for structural composites is well recognized by the industry but, to exploit their full potential, engineering design rules must be established. This study is a step in that direction. In this work the preform geometry for knitted and braided preforms was studied by making a range of well designed samples and studying them by photo microscopy. The structural geometry of the preforms is related to the processing parameters. Based on solid modeling and B-spline methodology a software package is developed. This computer code enables real time structural representations of complex fiber architecture based on the rule of preform manufacturing. The code has the capability of zooming and section plotting. These capabilities provide a powerful means to study the effect of processing variables on the preform geometry. the code also can be extended to an auto mesh generator for downstream structural analysis using finite element method. This report is organized into six sections. In the first section the scope and background of this work is elaborated. In section two the unit cell geometries of braided and multi-axial warp knitted preforms is discussed. The theoretical frame work of yarn path modeling and solid modeling is presented in section three. The thin section microscopy carried out to observe the structural geometry of the preforms is the subject in section four. The structural geometry is related to the processing parameters in section five. Section six documents the implementation of the modeling techniques into the computer code MP-CAD. A user manual for the software is also presented here. The source codes and published papers are listed in the Appendices.

Ko, Frank↗

NASA NTRS2018

Summary of the 1st AIAA Geometry and Mesh Generation Workshop (GMGW-1) and Future Plans

The 1st AIAA Geometry and Mesh Generation Workshop (GMGW-1) was held in conjunction with the AIAA Aviation Forum and Exposition 2017 and in collaboration with the 3rd AIAA Computational Fluid Dynamics (CFD) High Lift Prediction Workshop (HiLiftPW-3). As the first AIAA workshop on these topics, GMGW-1's broad objectives were to assess the current state-of-the art in geometry preprocessing and mesh generation technology as well as software as applied to aircraft and spacecraft systems. The workshop was intended to identify and develop understanding of areas of needed improvement in terms of performance, accuracy, and applicability. It was also to provide a foundation for documenting best practices for geometry preprocessing and mesh generation. The genesis of GMGW-1 is found in the indictments levied against geometry preprocessing and mesh generation - not undeservedly - by the NASA CFD Vision 2030 Study. In order to create a reference against which future progress in geometry preprocessing and mesh generation can be measured, the organizers of GMGW-1, with the assistance of the organizers of HiLiftPW- 3, focused GMGW-1 on generation of meshes of the NASA High Lift Common Research Model (HL-CRM). Some of the generated meshes were provided for use by the participants in HiLiftPW-3. All meshes and the processes by which they were generated were analyzed by GMGW-1 as a first assessment of state of the art practices. The results of GMGW-1 added quantitative detail to known problem areas including geometry modeling, data interoperability, and amount of human intervention. They do provide a clear path toward a vision of geometry preprocessing and mesh generation in the year 2030. The next milepost along this path will be a second workshop.

Chawner, John R.↗

DOE OSTI2025

An efficient second-order adaptive procedure for inserting CAD geometries into hexahedral meshes using volume fractions

Here, this paper is concerned with inserting three-dimensional computer-aided design (CAD) geometries into meshes composed of hexahedral elements using a volume fraction representation. An adaptive procedure for doing so is presented. The procedure consists of two steps. The first step performs spatial acceleration using a k-d tree. The second step involves subdividing individual hexahedra in an adaptive mesh refinement (AMR)-like fashion and approximating the CAD geometry linearly (as a plane) at the finest subdivision. The procedure requires only two geometric queries from a CAD kernel: determining whether or not a queried spatial coordinate is inside or outside the CAD geometry and determining the closest point on the CAD geometry’s surface from a given spatial coordinate. We prove that the procedure is second-order accurate for sufficiently smooth geometries and sufficiently refined background meshes. We demonstrate the expected order of accuracy is achieved with several verification tests and illustrate the procedure’s effectiveness for several exemplar CAD geometries.

Adaptive↗

DOE OSTI2024

Enabling the broader adoption of fusion simulation on complex geometry

This project addressed a key barrier to advanced fusion and nuclear simulation: the difficulty of performing high-fidelity Monte Carlo neutronics directly on complex, real-world CAD geometry. Traditional workflows require engineers to rebuild CAD models as simplified constructive solid geometry, a time-consuming and error-prone process that limits design iteration and broader adoption of simulation tools. The goal of this Phase I SBIR was to make CAD-based neutronics practical, accessible, and robust for industrial and research users. During the project, Coreform significantly enhanced the Direct Accelerated Geometry Monte Carlo (DAGMC) workflow and fully integrated it into Coreform Cubit as a first-class capability. Major achievements include optimized material assignment and surface meshing workflows, substantial performance improvements to geometry imprinting and preparation, native export of DAGMC models, and new visualization tools to support OpenMC source definition and lost-particle debugging. Coreform also expanded Cubit’s capabilities as a full OpenMC preprocessor, including the ability to convert OpenMC constructive solid geometry models back into CAD for visualization, multiphysics coupling, and debugging. In collaboration with Argonne National Laboratory, the project delivered comprehensive new DAGMC documentation and training materials, transforming DAGMC from a research-oriented tool into a production-ready workflow. Results were disseminated through tutorials, conference training, and multiple well-attended webinars demonstrating integrated CAD-based neutronics and multiphysics workflows. Overall, this project demonstrated that high-fidelity Monte Carlo simulations can be performed directly on complex CAD geometry, reducing setup time, improving usability, and enabling faster, more informed design decisions for fusion and nuclear energy systems.

42 ENGINEERING↗

DOE OSTI2025

Geometry-aware framework for deep energy method: An application to structural mechanics with hyperelastic materials

Here, in this work, we introduce a novel physics-informed framework named the Geometry-Aware Deep Energy Method (GADEM) for solving structural mechanics problems on different geometries. As the weak form of the physical system equation (or the energy-based approach) has demonstrated clear advantages compared to the strong form for solving solid mechanics problems, GADEM employs the weak form and aims to infer the solution on multiple shapes of geometries. Integrating a geometry-aware framework into an energy-based method results in an effective physics-informed deep learning model in terms of accuracy and computational cost. Different ways to represent the geometric information and to encode the geometric latent vectors are investigated in this work. We introduce a loss function of GADEM which is minimized based on the potential energy of all considered geometries. An adaptive learning method is also employed for the sampling of collocation points to enhance the performance of GADEM. We present some applications of GADEM to solve solid mechanics problems, including a loading simulation of a toy tire involving contact mechanics and large deformation hyperelasticity. The numerical results of this work demonstrate the remarkable capability of GADEM to infer the solution on various and new shapes of geometries using only one trained model.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Numerical simulation of asteroid geometry variance on airburst threat

For an atmospheric airburst the primary source of concern when assessing uncertainty is the size and velocity. Determining these properties provides the basis for threat assessment, as the total energy of the asteroid may then be estimated, and the threat investigated thoroughly. Even with clarity as to how much energy an asteroid may deposit, a great deal of uncertainty still exists for the actual energy deposition process. One such source of uncertainty is the geometry of the incoming asteroid. The geometry of an asteroid will alter the stress distribution during entry, which adds uncertainty to when fracture will occur. Here, in this study, we use Smoothed Particle Hydrodynamics to model the atmospheric airburst of Tunguska-scale asteroids with varying geometric profiles, including a sphere, ellipsoid, binary and superellipsoid. Each asteroid is modeled as a homogenous structure with strength. We assess uncertainty through a series of planar 2D simulation cases for each geometry, comparing the source of stochasticity across geometries. A single 3D airburst simulation for each geometry is also analyzed. Additionally, the 3D cases are compared to the highly uncertain Tunguska event, predicting variance in burst height across geometries, but all bounded by theoretical burst heights proposed for Tunguska.

Airburst↗