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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 937 records · Page 52
All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

Numerical implementation, verification and validation of two-phase flow four-equation drift flux model with Jacobian-free Newton–Krylov method

This study presents a numerical investigation on using the Jacobian-free Newton–Krylov (JFNK) method to solve the two-phase flow four-equation drift flux model with realistic constitutive correlations (‘closure models’). The drift flux model is based on Isshi and his collaborators’ work. Additional constitutive correlations for vertical channel flow, such as two-phase flow pressure drop, flow regime map, wall boiling and interfacial heat transfer models, were taken from the RELAP5-3D Code Manual and included to complete the model. The staggered grid finite volume method and fully implicit backward Euler method was used for the spatial discretization and time integration schemes, respectively. The Jacobian-free Newton–Krylov method shows no difficulty in solving the two-phase flow drift flux model with a discrete flow regime map. In addition to the Jacobian-free approach, the preconditioning matrix is obtained by using the default finite differencing method provided in the PETSc package, and consequently the labor-intensive implementation of complex analytical Jacobian matrix is avoided. Extensive and successful numerical verification and validation have been performed to prove the correct implementation of the models and methods. Code-to-code comparison with RELAP5-3D has further demonstrated the successful implementation of the drift flux model.

42 ENGINEERING↗
NASA NTRS2009

Rover Slip Validation and Prediction Algorithm

A physical-based simulation has been developed for the Mars Exploration Rover (MER) mission that applies a slope-induced wheel-slippage to the rover location estimator. Using the digital elevation map from the stereo images, the computational method resolves the quasi-dynamic equations of motion that incorporate the actual wheel-terrain speed to estimate the gross velocity of the vehicle. Based on the empirical slippage measured by the Visual Odometry software of the rover, this algorithm computes two factors for the slip model by minimizing the distance of the predicted and actual vehicle location, and then uses the model to predict the next drives. This technique, which has been deployed to operate the MER rovers in the extended mission periods, can accurately predict the rover position and attitude, mitigating the risk and uncertainties in the path planning on high-slope areas.

Yen, Jeng↗
NASA NTRSDate not supplied

Cross-Validation of Computational and Experimental Distributed Surface Pressures on the Space Launch System

This paper presents a new workflow for comparing experimental pressure-sensitive paint (PSP) data to computational fluid dynamic (CFD) simulations by way of mapping data from corresponding grids utilizing interpolation methods. In addition to generating quantitative and qualitative point-to-point comparisons between PSP and CFD data, this workflow extracts sectional loading data from both grids and generates lineload comparison charts for corresponding PSP and CFD runs. Experimental PSP data presented in this paper were taken from a 2016 NASA Ames Research Center Unitary Plan Wind Tunnel 11- by 11-Foot Transonic WindTunnel Facility test of the NASA Space Launch System. CFD simulation data for comparison purposes were generated using the FUN3D code. Overall, interpolation onto PSP grids versus CFD grids yields comparable surface pressure fields. However, lineload comparisons are easier to make on the CFD grid-mapped data due to the grid topology and the current capabilities of the lineload analysis tools at NASA Langley Research Center. This workflow is written using contemporary software (Python, Tecplot, PyTecplot), is compatible with existing tools at NASA Langley, and is developed to be adaptable depending on the situation.

SLS↗
DOE OSTI2016

Surface water areas significantly impacted 2014 dengue outbreaks in Guangzhou, China

Dengue transmission in urban areas is strongly influenced by a range of biological and environmental factors, yet the key drivers still need further exploration. To better understand mechanisms of environment–mosquito–urban dengue transmission, we propose an empirical model parameterized and cross-validated from a unique dataset including viral gene sequences, vector dynamics and human dengue cases in Guangzhou, China, together with a 36-year urban environmental change maps investigated by spatiotemporal satellite image fusion. The dengue epidemics in Guangzhou are highly episodic and were not associated with annual rainfall over time. Our results indicate that urban environmental changes, especially variations in surface area covered by water in urban areas, can substantially alter the virus population and dengue transmission. The recent severe dengue outbreaks in Guangzhou may be due to the surge in an artificial lake construction, which could increase infection force between vector (mainly Aedes albopictus) and host when urban water area significantly increased. Impacts of urban environmental change on dengue dynamics may not have been thoroughly investigated in the past studies and more work needs to be done to better understand the consequences of urbanization processes in our changing world. - Highlights: • Urban dengue outbreak is associated with water area in Guangzhou, 1978–2014. • Surface water area can alter population size of dengue virus in urban area. • Urban dengue outbreak is not associated with annual rainfall in Guangzhou. • Spatiotemporal satellite image fusion can investigate urban environmental change. • Urban environmental change could induce virus, vector, and dengue epidemic change.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Tunable Atomic Layer Deposition into Ultra-High-Aspect-Ratio (>60000:1) Aerogel Monoliths Enabled by Transport Modeling

Atomic layer deposition (ALD) modification of ultra-high-aspect-ratio structures (>10,000:1) is a powerful platform with applications in catalysis, filtration, and energy conversion. However, the deposition of conformal and tunable ALD coatings at these aspect ratios remains challenging, resulting in empirical tradeoffs between precursor utilization and reaction time. Here, we demonstrate tunable control of the ALD infiltration depth into an aerogel monolith (AM) and develop a reaction-diffusion model to accurately describe the coating process. Specifically, we investigate the ALD exposure time and precursor dose needed to conformally coat a silica AM with pore sizes of ~20 nm, a monolith thickness of ~2.5 mm, and aspect ratios exceeding 60,000:1. We demonstrate complete infiltration into the AM, which is quantified by elemental mapping. A reaction-diffusion model is developed, which accounts for multiple doses and precursor depletion in the ALD chamber during an exposure step. The experimentally validated model enables the prediction and tuning of infiltration depth into a tortuous, high-aspect-ratio structure such as an AM, allowing for the synthesis of rationally designed material architectures. Additionally, the model allows for co-optimization of the total deposition time and percentage of unreacted precursor, which are important for the manufacturability and sustainability of ALD processing. Lastly, we demonstrate that ultra-thin ALD Al 2 O 3 coatings can be used to stabilize silica AMs against structural degradation under high-temperature annealing conditions (700-800 °C), by limiting changes in surface area and monolith volume. As a result, this improved high-temperature stability has implications for numerous aerogel applications, including catalysis and thermal insulation.

14 SOLAR ENERGY↗
DOE OSTI2025

Liquid Sorption-Enhanced Haber–Bosch Process

The use of a liquid sorbent in a traditional Haber-Bosch process enables significant improvements in energy efficiency and potential cost savings for arguably the most important chemical process on the planet. The approach presented in this report employs an incompressible liquid sorbent that absorbs and releases ammonia (NH 3 ) under specific conditions. To achieve this, we investigate reactions of ammonia and pure phosphoric acid (H 3 PO 4 , PA), which rapidly neutralize to form an equilibrated solution of monoammonium phosphate (MAP) and diammonium phosphate (DAP) that functions as a reversible and regenerable sorbent. Through intimate contact of the gas-phase Haber-Bosch reaction mixture with this liquid absorbent, complete equilibrium uptake may be achieved in an appropriately sized separator, and facile separation occurs through the use of independent liquid and gas phases. Following depressurization and release of the ammonia product, only the incompressible fluid needs to be repressurized and returned to the reactor. This study documents proof-of-concept absorption and desorption experiments carried out in 75 mL batch reactors, predominantly charged with precise MAP and DAP mixtures that equilibrate at process-relevant temperatures and pressures. We then assemble the first thermodynamic relationships that underlie this advantaged separation strategy, validated by reactive force field (ReaxFF) interatomic potential simulations, and benchmarked with traditional separation routes via process modeling and technoeconomic analysis. The scale of energy consumption in the century-old Haber-Bosch process is massive, and the elegant liquid sorption approach reported here offers opportunities to enhance its energy efficiency for the next frontier of ammonia synthesis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Fully synthetic platform to rapidly generate tetravalent bispecific nanobody–based immunoglobulins

Nanobodies bind a target antigen with a kinetic profile similar to a conventional antibody, but exist as a single heavy chain domain that can be readily multimerized to engage antigen via multiple interactions. Presently, most nanobodies are produced by immunizing camelids; however, platforms for animal-free production are growing in popularity. Here, we describe the development of a fully synthetic nanobody library based on an engineered human V H 3-23 variable gene and a multispecific antibody-like format designed for biparatopic target engagement. To validate our library, we selected nanobodies against the SARS-CoV-2 receptor–binding domain and employed an on-yeast epitope binning strategy to rapidly map the specificities of the selected nanobodies. We then generated antibody-like molecules by replacing the V H and V L domains of a conventional antibody with two different nanobodies, designed as a molecular clamp to engage the receptor-binding domain biparatopically. The resulting bispecific tetra-nanobody immunoglobulins neutralized diverse SARS-CoV-2 variants with potencies similar to antibodies isolated from convalescent donors. Subsequent biochemical analyses confirmed the accuracy of the on-yeast epitope binning and structures of both individual nanobodies, and a tetra-nanobody immunoglobulin revealed that the intended mode of interaction had been achieved. This overall workflow is applicable to nearly any protein target and provides a blueprint for a modular workflow for the development of multispecific molecules.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2024

A Four-Layer Cyber-Physical Security Model for Electric Machine Drives Considering Control Information Flow

Despite the IEEE Power Electronics Society (PELS) establishing Technical Committee 10 on Design Methodologies with a focus on the cyber-physical security of power electronics systems, a holistic design methodology for addressing security vulnerabilities remains underdeveloped. This gap largely stems from the limited integration of computer science and power/control engineering studies in this interdisciplinary field. Addressing the inadequacy of unilateral cyber or control perspectives, this article presents a novel four-layer cyber-physical security model specifically designed for electric machine drives. Central to this model is the innovative control information flow (CIF) model, residing within the control layer, which serves as a pivotal link between the cyber layer's vulnerable resources and the physical layer's state-space models. By mapping vulnerable resources to control variable space and tracing attack propagation, the CIF model facilitates accurate impact predictions based on tainted control laws. The effectiveness and validity of this proposed model are demonstrated through hardware experiments involving two typical cyber-attack scenarios, underscoring its potential as a comprehensive framework for multidisciplinary security strategies.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Yet Another Discriminant Analysis (YADA): A Probabilistic Model for Machine Learning Applications

This paper presents a probabilistic model for various machine learning (ML) applications. While deep learning (DL) has produced state-of-the-art results in many domains, DL models are complex and over-parameterized, which leads to high uncertainty about what the model has learned, as well as its decision process. Further, DL models are not probabilistic, making reasoning about their output challenging. In contrast, the proposed model, referred to as Yet Another Discriminate Analysis(YADA), is less complex than other methods, is based on a mathematically rigorous foundation, and can be utilized for a wide variety of ML tasks including classification, explainability, and uncertainty quantification. YADA is thus competitive in most cases with many state-of-the-art DL models. Ideally, a probabilistic model would represent the full joint probability distribution of its features, but doing so is often computationally expensive and intractable. Hence, many probabilistic models assume that the features are either normally distributed, mutually independent, or both, which can severely limit their performance. YADA is an intermediate model that (1) captures the marginal distributions of each variable and the pairwise correlations between variables and (2) explicitly maps features to the space of multivariate Gaussian variables. Numerous mathematical properties of the YADA model can be derived, thereby improving the theoretic underpinnings of ML. Validation of the model can be statistically verified on new or held-out data using native properties of YADA. However, there are some engineering and practical challenges that we enumerate to make YADA more useful.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

ODIN: Characterizing the Three-dimensional Structure of Two Protocluster Complexes at z = 3.1

We present a detailed study of the 3D morphology of two extended associations of multiple protoclusters at z = 3.1. These protocluster "complexes," designated COSMOS-z3.1-A and COSMOS-z3.1-C, are the most prominent overdensities of z = 3.1 Lyα emitters (LAEs) identified in the COSMOS field by the One-hundred-deg$^{2}$ DECam Imaging in Narrowbands survey. These protocluster complexes have been followed up with extensive spectroscopy from Keck, Gemini, and DESI. Using a probabilistic method that combines photometrically selected and spectroscopically confirmed LAEs, we reconstruct the 3D structure of these complexes on scales of ≈50 cMpc. We validate our reconstruction method using the IllustrisTNG300-1 cosmological hydrodynamical simulation and show that it consistently outperforms approaches relying solely on spectroscopic data. The resulting 3D maps reveal that both complexes are irregular and elongated along a single axis, emphasizing the impact of sightline on our perception of structure morphology. The complexes consist of multiple density peaks, 10 in COSMOS-z3.1-A and 4 in COSMOS-z3.1-C. The former is confirmed to be a proto-supercluster, similar to Hyperion at z = 2.4 but observed at an even earlier epoch. Multiple "tails" connected to the cores of the density peaks are seen, likely representing cosmic filaments feeding into these extremely overdense regions. The 3D reconstructions further provide strong evidence that Lyα blobs preferentially reside in the outskirts of the highest density regions. Descendant mass estimates of the density peaks suggest that COSMOS-z3.1-A and COSMOS-z3.1-C will evolve to become ultramassive structures by z = 0, with total masses log ( M / M ,⊙ ,) ≳ 15.3 , exceeding that of Coma.

Ramakrishnan, Vandana [Purdue U., West Lafayette] ↗
NASA NTRS1987

Analysis and synthesis of abstract data types through generalization from examples

The discovery of general patterns of behavior from a set of input/output examples can be a useful technique in the automated analysis and synthesis of software systems. These generalized descriptions of the behavior form a set of assertions which can be used for validation, program synthesis, program testing, and run-time monitoring. Describing the behavior is characterized as a learning process in which the set of inputs is mapped into an appropriate transform space such that general patterns can be easily characterized. The learning algorithm must chose a transform function and define a subset of the transform space which is related to equivalence classes of behavior in the original domain. An algorithm for analyzing the behavior of abstract data types is presented and several examples are given. The use of the analysis for purposes of program synthesis is also discussed.

Wild, Christian↗
NASA NTRS2018

Dynamic Power Convertor Development for Radioisotope Power Systems at NASA Glenn Research Center

The Thermal Energy Conversion Branch at NASA Glenn Research Center is supporting the development of high-efficiency power convertors for use in radioisotope power systems (RPS). Significant progress was made toward such a system that utilized Stirling conversion during the 2001 to 2015 timeframe. Flight development of the Advanced Stirling Radioisotope Generator (ASRG) was canceled in 2013 by the U.S. Department of Energy (DOE) and NASA Headquarters primarily due to budget constraints, and the Advanced Stirling Convertor (ASC) technology contract was subsequently concluded in 2015. A new chapter of technology development has recently been initiated by the NASA RPS Program. This effort is considering all dynamic power convertor options, such as Stirling and Brayton cycles. Four convertor development contracts supporting this effort were awarded in 2017. The awarded contracts include two free-piston Stirling, one thermoacoustic Stirling, and one turbo-Brayton design. The technology development contracts each consist of up to three phases: design, fabrication, and test. As of May 2018, all contracts have completed the design phase, and each underwent a design review with an independent review board. Three of the contracts are planned to execute the phase 2 option for fabrication. Convertors manifesting from these development efforts will then undergo independent validation and verification (IV and V) at NASA facilities, which will consist of convertor performance and RPS viability demonstrations. Example tests include launch vibration simulation, performance mapping over the environmental temperature range, and static acceleration exposure. In parallel with this renewed development effort, Glenn is still demonstrating free-piston Stirling convertor technology using assets from previous projects. The Stirling Research Laboratory (SRL) is still operating several convertors from previous development projects, which have similarities and relevance to current contract designs. Four of these are flexure-bearing based and another six are gas bearing based. One of the flexure-bearing convertors has accumulated over 110,000 h of operation and holds the current record for maintenance-free heat-engine run time. Another flexure-bearing convertor was recently manually shut down after 105,620 h of operation, then disassembled and inspected. This inspection produced a wealth of information about the effects of this amount of run time on the technology's components. One of the engineering unit flexure-bearing convertors recently underwent a launch simulation vibration test, a static acceleration exposure up to 20 g, and was then placed on extended operation. Among the gas-bearing convertors, the longest running unit has accumulated over 70,000 h of operation. Four high-fidelity gas-bearing convertors from the ASRG project are still operating continuously for which the longest run time has reached 28,000 h.

Oriti, Salvatore M.↗
NASA NTRS2014

Mapping Urban Expansion Across North America Using Multi-Temporal Landsat and Nighttime Lights Data

Urban expansion and the associated changes in land cover have important climatic, hydrologic, biophysical and ecologic and socio-economic impacts on the environment. Yet, despite todays abundance of remote sensing data, an automated characterization of large-scale historical changes in urban spatial extent remains a challenge due to the inherent complexity and variability of the urban environment, the lack of a spectral signature unique to urban land cover, and the absence of an unambiguous definition of what is urban versus non-urban.Here we present a consistent, robust, scalable, physically- based methodology for characterization of urban expansion using Landsat observations. We use atmospherically corrected Landsat Global Land Survey time series, Web-enabled Landsat data time series, DMSP-OLS and NPP-VIIRS nighttime lights, for mapping the built-up and vegetated components of urban settlements at 30m resolution through multi- temporal standardized spectral mixture analysis. The methodology is tested and validated over the North American continent where it provides a first quantification of urban expansion and vegetation abundance changes from 1990 to 2010.

Milesi, Cristina↗
NASA NTRS2017

The Evolution of the Orbiting Sample Container for a Future Mars Sample Return

Although NASA has no specific plans at this time to return samples from Mars, the Program Formulation Office of the Mars Exploration Program sponsors ongoing mission concept studies, systems analyses, and technology investments which explore different strategies for the potential return of samples from Mars, consistent with the charter of the program and stated priorities of the science community. A critical component of such a campaign would be an Orbiting Sample container (OS), which would contain the Mars samples to be returned to Earth. This paper discusses the most recent efforts by the JPL’s Mars Formulation Office to mature an OS design planned for use on a potential Mars Sample Return (MSR) mission. Similar to the “Decadal Study Architecture” [1], the current MSR architecture envisions as a three-mission campaign with each mission serving a critical role towards returning Martian rock and atmospheric samples back to Earth. An OS would be a central piece of hardware in the proposed MSR architecture due to its interfaces to all the three missions of the potential campaign. Additionally, numerous stakeholders and subsystems such as science and planetary protection impose challenging requirements on the OS’s functions and capabilities. As a result, designing an OS that meets all the requirements is challenging and quite complex. The story of the OS’s evolution from black box concept thru to the current-and-still-maturing baseline design is the focus of this paper. From the OS’s launch off Earth aboard a Sample Retrieval Lander (SRL) through to return to Earth, the design and functional requirements generated by and for each stage of the OS’s mission are discussed. Then, with an understanding of what the OS would be required to do, a mapping of the main requirements to the design features of the current OS concept is explained. Many tests and analyses have been conducted to support and validate the current OS design. Results from test and analysis in the areas of aerothermal, impact dynamics, optical tracking, and radio electromagnetics are presented.

Spencer, David↗
DOE OSTI2012

A coupled neutronic/thermal-hydraulic scheme between COBAYA3 and SUBCHANFLOW within the NURESIM simulation platform

Multi-scale, multi-physics problems reveal significant challenges while dealing with coupled neutronic/thermal-hydraulic solutions. Current generation of codes applied to Light Water Reactors (LWR) are based on 3D neutronic nodal methods coupled with one or two phase flow thermal-hydraulic system or sub-channel codes. In addition, spatial meshing and temporal schemes are crucial for the proper description of the non-symmetrical core behavior in case of transient and accidents e.g. reactivity insertion accidents. This paper describes the coupling approach between the 3D neutron diffusion code COBAYA3 and the sub-channel code SUBCHANFLOW within SALOME. The coupling is done inside the SALOME open source platform that is characterized by a powerful pre- and post-processing capabilities and a novel functionality for mapping of the neutronic and thermal hydraulic domains. The peculiar functionalities of SALOME and the steps required for the code integration and coupling are presented. The validation of the coupled codes is done based on two benchmarks the PWR MOX/UO{sub 2} RIA and the TMI-1 MSLB benchmark. A discussion of the prediction capability of COBAYA3/SUBCHANFLOW compared to other coupled solutions will be provided too. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2018

Wildfire Mapping in Interior Alaska Using Deep Neural Networks on Imbalanced Datasets

Wildfires are the dominant disturbance impacting many regions in Alaska and is expected to intensify due to climate change. Accurate tracking and quantification of wildfires are important for climate modeling and ecological studies in this region. Remote sensing platforms (e.g., MODIS, Landsat) are an important tool for mapping wildfires in Alaska at varying spatial and temporal scales. Deep neural networks (DNN) have shown superior performance in many classification problems such as high-dimensional remote sensing data. Detection of wildfires is an imbalanced classification problem where one class contains a much smaller or larger sample size and DNNs performance can decline. We take a known weight-selection strategy during DNN training and apply them to MODIS variables (e.g., NDVI, surface reflectance) for a binary classification (i.e., wildfire or no-wildfire) across Alaska during the 2004 wildfire year, which is one of the largest on record. The method splits the input training data into sets, one for training the DNN to update weights and the other that splits into a validation set that is equally balanced between the wildfire and no-wildfire class. The performance is monitored on the validation set to select the weights based on the best validation-loss score. This approach was applied to two sampled datasets, such as where the no-wildfire class can significantly outweigh the wildfire class. The normal DNN training strategy was unable to map wildfires for the highly imbalanced dataset, however, the weight-selection strategy was able to map wildfires very accurately (0.96 recall score for 78,702 wildfire pixels (500×500 m)).

Langford, Zach↗
DOE OSTI2020

Validation of finite-element models using full-field experimental data: Levelling finite-element analysis data through a digital image correlation engine

Full-field data from digital image correlation (DIC) provide rich information for finite-element analysis (FEA) validation. However, there are several inherent inconsistencies between FEA and DIC data that must be rectified before meaningful, quantitative comparisons can be made, including strain formulations, coordinate systems, data locations, strain calculation algorithms, spatial resolutions and data filtering. As such, in this paper, we investigate two full-field validation approaches: (1) the direct interpolation approach, which addresses the first three inconsistencies by interpolating the quantity of interest from one mesh to the other, and (2) the proposed DIC-levelling approach, which addresses all six inconsistencies simultaneously by processing the FEA data through a stereo-DIC simulator to ‘level’ the FEA data to the DIC data in a regularisation sense. Synthetic ‘experimental’ DIC data were generated based on a reference FEA of an exemplar test specimen. The direct interpolation approach was applied, and significant strain errorswere computed, even though therewas no model form error, because the filtering effect of theDIC enginewas neglected. In contrast, the levelling approach provided accurate validation results, with no strain error when no model form error was present. Next, model form error was purposefully introduced via a mismatch of boundary conditions. With the direct interpolation approach, the mismatch in boundary conditions was completely obfuscated, while with the levelling approach, it was clearly observed. Finally, the ‘experimental’ DIC datawere purposefully misaligned slightly fromthe FEA data. Both validation techniques suffered from the misalignment, thus motivating continued efforts to develop a robust alignment process. In conclusion, direct interpolation is insufficient, and the proposed levelling approach is required to ensure that the FEA and the DIC data have the same spatial resolution and data filtering. Only after the FEA data have been ‘levelled’ to the DIC data can meaningful, quantitative error maps be computed.

42 ENGINEERING↗
DOE OSTI2017

Mapping of orthogonal 2D flux coordinates for two nearby magnetic X-points to logically rectangular domains

The behavior of plasmas in configurations with magnetic null points is of potential interest for a number of systems. Such nulls, sometimes referred to as X-points, a name strictly valid only for wellseparated nulls where magnetic separatrices cross at a right angle, may occur in only one component of the magnetic field, such as the poloidal field in a tokamak. Numerical simulations are often used to study and predict turbulence and transport in such systems. For cases with strong magnetic field such that the ion and electron gyro-frequencies are much larger that particle collision frequencies, there is a strong anisotropy in the plasma transport along the magnetic field compared to across the field. Because of the strong anisotropy, it is often advantageous for simulations to use a coordinate system based on magnetic flux surfaces together with a coordinate orthogonal to the flux surfaces. This report presents the topological considerations needed to construct the mapping on an orthogonal flux-surface mesh onto a logically rectangular domain often used in simulation codes of the divertor region of tokamaks having two nearby X-points, thus extending the mapping now common single-null or well-separated double nullpoint cases with one null located at the top and bottom of the device. This extension is especially relevant to study the capability of snowflake divertors in tokamaks for reducing the peak heat flux of exhaust plasma on the target plates [1-3]. The analysis presented here follows the analytic description of the poloidal magnetic field, B pol , near two closely-spaced X-points given by Ryutov [1-3]. This analysis is applicable to experimental devices where the two X-points are generated by distributed poloidal field coils and the plasma core current. This analytic description is used to identify topological features of an orthogonal mesh. A key parameter that specifies the various topology changes is the poloidal angle between the primary X-point and the second X-point, and the changes are associated with a set of critical angles. Understanding these changes leads to the final step in the mesh construction by identifying the locations of various regions or patches in configuration space and in a corresponding logically rectangular index space. UEDGE [4] and other 2-D fluid plasma simulation codes [5-7] describe the edge plasma of toroidally symmetric tokamak configurations with one or more X-points in a divertor region. The 2-D spatial mesh is usually based on a magnetic configuration produced by an MHD equilibrium code such as EFIT and written out as one or more “eqdsk” files. As illustrated in Fig. 1, the domain of the simulated plasma consists of several flux tubes bounded by poloidal magnetic flux surfaces. The number and spacing of the flux surfaces defines the “radial” resolution of the mesh. The “radial” direction is locally orthogonal to flux surfaces; the “poloidal” direction is locally parallel to flux surfaces. The “poloidal” resolution of the mesh is defined by the number of cells in the poloidal direction between adjacent flux surfaces. For boundary plasma transport codes used for tokamak configurations such as UEDGE it is convenient, though not necessary, to assume that all flux tubes have the same number of poloidal cells so the mesh is logically rectangular in index space, but does possess internal boundaries linking different sub-rectangles in the computational domain. The following sections of this report describe indexing schemes that map tokamak magnetic configurations with one or more x-points in the divertor region(s) onto a rectangular index space. Simulation results from the UEDGE code illustrate the schemes for a few configurations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗