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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 991 records · Page 55
All sourcesNASA NTRSDOE OSTI
NASA NTRS1986

A mechanism for tectonic deformation on Venus

In the absence of identifiable physiographic features directly associated with plate tectonics, alternate mechanisms are sought for the intense tectonic deformation observed in radar images of Venus. One possible mechanism is direct coupling into an elastic lithosphere of the stresses associated with convective flow in the interior. Spectral Green's function solutions have been obtained for stresses in an elastic lithosphere overlying a Newtonian interior with an exponential depth dependence of viscosity, and a specified surface-density distribution driving the flow. At long wavelengths and for a rigid elastic/fluid boundary condition, horizontal normal stresses in the elastic lid are controlled by the vertical shear stress gradient and are directly proportional to the depth of the density disturbance in the underlying fluid. The depth and strength of density anomalies in the Venusian interior inferred by analyses of long wavelength gravity data suggest that stresses in excess of 100 MPa would be generated in a 10 km thick elastic lid unless a low viscosity channel occurring beneath the lid or a positive viscosity gradient uncouples the flow stresses. The great apparent depth of compensation of topographic features argues against this, however, thus supporting the importance of the coupling mechanism. If there is no elastic lid, stresses will also be very high near the surface, providing also that the viscosity gradient is negative.

Phillips, Roger J.↗
NASA NTRS2006

Improving Thermomechanical Properties of SiC/SiC Composites

Today, a major thrust toward improving the thermomechanical properties of engine components lies in the development of fiber-reinforced silicon carbide matrix composite materials, including SiC-fiber/SiC-matrix composites. These materials are lighter in weight and capable of withstanding higher temperatures, relative to state-of-the-art metallic alloys and oxide-matrix composites for which maximum use temperatures are in the vicinity of 1,100 C. In addition, the toughness or damage tolerance of the SiC-matrix composites is significantly greater than that of unreinforced silicon-based monolithic ceramics. For successful application in advanced engine systems, the SiC-matrix composites should be able to withstand component service stresses and temperatures for the desired component lifetimes. Inasmuch as the high-temperature structural lives of ceramic materials are typically limited by creep-induced growth of flaws, a key property required of such composite materials is high resistance to creep under conditions of use. Also, the thermal conductivity of the materials should be as high as possible so as to minimize component thermal gradients and thermal stresses. A state-of-the-art SiC-matrix composite is typically fabricated in a three-step process: (1) fabrication of a component-shaped architectural preform reinforced by thermally stable high-performance fibers, (2) chemical-vapor infiltration (CVI) of a fiber-coating material such as boron nitride (BN) into the preform, and (3) infiltration of an SiC-based matrix into the remaining porosity in the preform. Generally, the matrices of the highest-performing composites are fabricated by initial use of a CVI SiC matrix component that is typically more thermally stable and denser than matrix components formed by processes other than CVI. As such, the initial SiC matrix component made by CVI provides better environmental protection to the coated fibers embedded within it. Also, the denser CVI SiC imparts to the composite better resistance to propagation of cracks, enhanced thermal conductivity, and higher creep resistance.

DiCarlo, James A.↗
DOE OSTI2022

A flexible and scalable scheme for mixing computed formation energies from different levels of theory

Abstract Computational materials discovery efforts are enabled by large databases of properties derived from high-throughput density functional theory (DFT), which now contain millions of calculations at the generalized gradient approximation (GGA) level of theory. It is now feasible to carry out high-throughput calculations using more accurate methods, such as meta-GGA DFT; however recomputing an entire database with a higher-fidelity method would not effectively leverage the enormous investment of computational resources embodied in existing (GGA) calculations. Instead, we propose here a general procedure by which higher-fidelity, low-coverage calculations (e.g., meta-GGA calculations for selected chemical systems) can be combined with lower-fidelity, high-coverage calculations (e.g., an existing database of GGA calculations) in a robust and scalable manner. We then use legacy PBE(+ U ) GGA calculations and new r 2 SCAN meta-GGA calculations from the Materials Project database to demonstrate that our scheme improves solid and aqueous phase stability predictions, and discuss practical considerations for its implementation.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Calcium Gradient-Doped LiNi 0.5 Mn 1.5 O 4 Cathode for Long Cycle Life Lithium-Ion Batteries

High-voltage spinel LiNi 0.5 Mn 1.5 O 4 (LNMO) has attracted considerable attention as a cathode material for next-generation lithium-ion batteries due to its high operating voltage and intrinsically fast lithium-ion diffusion kinetics. However, the practical implementation of LNMO remains limited by its rapid capacity decay, primarily associated with bulk structural instability and parasitic interfacial reactions. To address these issues, we innovatively introduced calcium (Ca) as a dopant to enhance both the oxygen framework and surface stabilities of the LNMO crystal through gradient doping. Observations from the electronic microscopies, X-ray diffraction, and the elemental analysis confirmed that Ca is preferentially enriched at the particle surface, and a disordered crystal phase is preserved in the bulk in the gradient-doped LNMO cathodes. As cathodes in LIBs, the Ca gradient-doped (Ca gr) LNMO materials delivered formation capacities of ∼126−130 mAh/g and exhibited Coulombic efficiencies of 88−95%, which are consistently higher than those of the uniform-doped samples at the same doping level and undoped sample. Especially, the Ca gr 0.05 LNMO cathode demonstrated significantly improved rate capability with ∼113 mAh/g preserved at 10 C, while ∼92 mAh/g and ∼110 mAh/g for undoped and Ca uniform 0.05 LNMO, respectively, and excellent cycling stability, retaining ∼124.1 mAh/g (∼96.3% capacity retention) after 500 cycles. The analysis of cyclic voltammetry, differential capacity, and electrochemical impedance revealed that the excellent electrochemical performance is attributed to the structural and morphological advantages of gradient-doped LNMO cathodes with a disordered bulk structure for fast Li + diffusion and a Ca-enriched surface for minimizing the Mn dissolution.

25 ENERGY STORAGE↗
DOE OSTI2024

Gradient-based surface nuclear magnetic resonance for groundwater investigation

In medical magnetic resonance imaging, spatial localization (imaging) is based upon the application of controlled magnetic field gradients on top of the main magnetic field to spatially modulate the frequency and/or phase of the nuclear magnetic resonance (NMR) signal across the volume of investigation. In this work, we have applied similar physical principles to produce controlled magnetic field gradients during surface NMR-based groundwater investigations. In this approach, a gradient pulse of variable amplitude or duration is applied immediately after the excitation pulse to cause predictable phase encoding of the NMR signal as a function of depth. This approach is also applicable to emerging surface NMR detection methods that use a prepolarization field with fast nonadiabatic turn-off to generate detectable NMR signals from the shallow subsurface. In this case, the gradient pulse is applied after terminating the prepolarization field and provides a heretofore unavailable means of localizing the NMR response as a function of depth. The application of gradients can also be combined with tip-angle-based modulation to yield higher imaging resolution than can be achieved through either gradient- or tip-angle-based imaging alone. We implemented this new gradient-based capability into a surface NMR gradient generation accessory that is compatible with the GMR-Flex instrument and developed surface NMR-specific forward modeling and linear inverse models. We validated the accuracy of this novel gradient-based sNMR technology using computer simulations, experiments using a small pool filled with a discrete layer of bulk water, and field experiments at well-characterized groundwater test sites along Ebey Island, WA, and Larned, KS. The gradient-based sNMR imaging observations were compared with high-resolution direct push NMR results observed at these sites. The results of computer simulations and field experiments indicate improvements in both the detection (signal-to-noise ratio) and spatial resolution of shallow subsurface water content using gradient-based surface NMR, compared with traditional surface NMR imaging methods.

Geochemistry & Geophysics↗
NASA NTRS2013

Interpretation of CHAMP Magnetic Anomaly Data over the Pannonian Basin Region Using Lower Altitude Horizontal Gradient Data

The ESA SWARM mission will have three earth orbiting magnetometer bearing satellites one in a high orbit and two side-by-side in lower orbits. These latter satellites will record a horizontal magnetic gradient. In order to determine how we can use these gradient measurements for interpretation of large geologic units we used ten years of CHAMP data to compute a horizontal gradient map over a section of southeastern Europe with our goal to interpret these data over the Pannonian Basin of Hungary.

CHAMP↗
DOE OSTI2020

Uncertainty amplification due to density/refractive index gradients in background-oriented schlieren experiments

Here, we theoretically analyze the effect of density/refractive index gradients on the measurement precision of background-oriented schlieren (BOS) experiments by deriving the Cramer–Rao lower bound (CRLB) for the 2D centroid estimation process. A model is derived for the diffraction limited image of a dot viewed through a medium containing density gradients that includes the effect of the experimental parameters such as the magnification and f-number. It is shown using the model that nonlinearities in the density gradient field lead to blurring of the dot image. This blurring amplifies the effect of image noise on the centroid estimation process, leading to an increase in the CRLB and a decrease in the measurement precision. The ratio of position uncertainties of a dot in the reference and gradient images is shown to be a function of the ratio of the dot diameters and dot intensities. We termed this parameter the amplification ratio (A F ), and a methodology for reporting position uncertainties in tracking-based BOS measurements is proposed. The theoretical predictions of the dot position estimation variance from the CRLB are compared to ray tracing simulations, and agreement is obtained. The uncertainty amplification is also demonstrated on experimental BOS images of flow induced by a spark discharge, where it is seen that regions of high amplification ratio correspond to regions of density gradients. This analysis elucidates the dependence of the position uncertainty on density and refractive index gradient-induced distortion parameters, provides a methodology for accounting its effect on uncertainty quantification and provides a framework for optimizing experiment design.

42 ENGINEERING↗
DOE OSTI2023

Resolving intragranular stress fields in plastically deformed titanium using point-focused high-energy diffraction microscopy

Abstract The response of a polycrystalline material to a mechanical load depends not only on the response of each individual grain, but also on the interaction with its neighbors. These interactions lead to local, intragranular stress concentrations that often dictate the initiation of plastic deformation and consequently the macroscopic stress–strain behavior. However, very few experimental studies have quantified intragranular stresses across bulk, three-dimensional volumes. In this work, a synchrotron X-ray diffraction technique called point-focused high-energy diffraction microscopy (pf-HEDM) is used to characterize intragranular deformation across a bulk, plastically deformed, polycrystalline titanium specimen. The results reveal the heterogenous stress distributions within individual grains and across grain boundaries, a stress concentration between a low and high Schmid factor grain pair, and a stress gradient near an extension twinning boundary. This work demonstrates the potential for the future use of pf-HEDM for understanding the local deformation associated with networks of grains and informing mesoscale models. Graphical abstract

36 MATERIALS SCIENCE↗
NASA NTRS2017

Cause and Cure - Deterioration in Accuracy of CFD Simulations With Use of High-Aspect-Ratio Triangular Tetrahedral Grids

Traditionally high-aspect ratio triangular/tetrahedral meshes are avoided by CFD re-searchers in the vicinity of a solid wall, as it is known to reduce the accuracy of gradient computations in those regions and also cause numerical instability. Although for certain complex geometries, the use of high-aspect ratio triangular/tetrahedral elements in the vicinity of a solid wall can be replaced by quadrilateral/prismatic elements, ability to use triangular/tetrahedral elements in such regions without any degradation in accuracy can be beneficial from a mesh generation point of view. The benefits also carry over to numerical frameworks such as the space-time conservation element and solution element (CESE), where triangular/tetrahedral elements are the mandatory building blocks. With the requirement of the CESE method in mind, a rigorous mathematical framework that clearly identities the reason behind the difficulties in use of such high-aspect ratio triangular/tetrahedral elements is presented here. As will be shown, it turns out that the degree of accuracy deterioration of gradient computation involving a triangular element is hinged on the value of its shape factor Gamma def = sq sin Alpha1 + sq sin Alpha2 + sq sin Alpha3, where Alpha1; Alpha2 and Alpha3 are the internal angles of the element. In fact, it is shown that the degree of accuracy deterioration increases monotonically as the value of Gamma decreases monotonically from its maximal value 9/4 (attained by an equilateral triangle only) to a value much less than 1 (associated with a highly obtuse triangle). By taking advantage of the fact that a high-aspect ratio triangle is not necessarily highly obtuse, and in fact it can have a shape factor whose value is close to the maximal value 9/4, a potential solution to avoid accuracy deterioration of gradient computation associated with a high-aspect ratio triangular grid is given. Also a brief discussion on the extension of the current mathematical framework to the tetrahedral-grid case along with some of the practical results of this extension is also provided. Furthermore, through the use of numerical simulations of practical viscous problems involving high-Reynolds number flows, the effectiveness of the gradient evaluation procedures within the CESE framework (that have their basis on the analysis presented here) to produce accurate and stable results on such high-aspect ratio meshes is also showcased.

CESE Method↗
NASA NTRS2011

Gradient Compression Stockings may Prevent Recovery after Bed Rest Deconditioning

Introduction: Astronauts continue to wear a compression garment during and immediately after landing to prevent orthostatic intolerance (OI). We recently developed a custom-fitted, 3-piece garment that consists of thigh-high stockings with biker-style shorts that provides continuous, gradient compression: 55 mmHg at the ankle that decreases to approximately 20 mmHg at the top of the leg and 15 mmHg over the abdomen. This garment has been shown to be effective in preventing symptoms of OI during a short stand test after Space Shuttle missions, but symptoms may persist for several days after a long-duration mission in some astronauts. The purpose of this study was to confirm the effectiveness of wearing these elastic, gradient compression garments during orthostatic testing after 2 weeks of 6 degree head-down tilt bed rest as a model of spaceflight and to determine whether they would impact recovery after bed rest. Methods: Eight (5 treatment, 3 control) of 16 subjects have completed this study to-date. All subjects wore the 3-piece garment from waking until tilt testing (~3 h) as a simulation of the timeline for astronauts on landing day (BR+0). Control subjects removed the garment after the tilt test. Treatment subjects wore the garment for the remainder of the day and wore lower compression thigh-high only garments on the day after bed rest (BR+1). Blood pressure, heart rate, and stroke volume responses to a 15-min 80 degree head-up tilt test were determined before 2 weeks of 6 degree head-down tilt, and on BR+0 and BR+1. Plasma volume (PV) was measured before each of these test sessions. Data are mean SE. Results: Compression garments prevented signs of OI on BR+0; all subjects in both groups completed the full 15-min test. Heart rate responses to tilt were lower on BR+0 than all other test days. Control subjects demonstrated a marginal PV decrease after bed rest, but showed typical recovery the day after bed rest (BR+0: 2.32 plus or minus 0.15 L to BR+1: 2.79 plus or minus 0.15 L). Treatment subjects did not recover PV the day after bed rest (BR+0: 2.61 plus or minus 0.23 L to BR+1: 2.61 plus or minus 0.23 L). Conclusion: Abdomen-high compression garments, which are effective in preventing post-bed rest orthostatic intolerance, may slow recovery of PV. Modified garments with reduced compression may be necessary to prevent prolonging recovery.

Stenger, Michael B.↗
NASA NTRS1992

Design of a high-temperature experiment for evaluating advanced structural materials

This report describes the design of an experiment for evaluating monolithic and composite material specimens in a high-temperature environment and subject to big thermal gradients. The material specimens will be exposed to aerothermal loads that correspond to thermally similar engine operating conditions. Materials evaluated in this study were monolithic nickel alloys and silicon carbide. In addition, composites such as tungsten/copper were evaluated. A facility to provide the test environment has been assembled in the Engine Research Building at the Lewis Research Center. The test section of the facility will permit both regular and Schlieren photography, thermal imaging, and laser Doppler anemometry. The test environment will be products of hydrogen-air combustion at temperatures from about 1200 F to as high as 4000 F. The test chamber pressure will vary up to 60 psia, and the free-stream flow velocity can reach Mach 0.9. The data collected will be used to validate thermal and stress analysis models of the specimen. This process of modeling, testing, and validation is expected to yield enhancements to existing analysis tools and techniques.

Mockler, Theodore T.↗
DOE OSTI2021

Rapid Identification of Synthetic Routes to Functional Metastable Phases Using X-ray Probed Laser Anneal Mapping (XPLAM) Time-Temperature Quench Maps

Many material systems have known or predicted functional phases that are metastable at standard temperature and pressure. While substantial advances have been made in the high-throughput and combinatorial synthesis of materials with a range of stoichiometries, investigation of thermal processing remains largely the domain of iterative uniform anneals or static gradients. Here we develop X-ray probed laser anneal mapping (XPLAM), a high throughput technique coupling spatially resolved X-ray diffraction with microsecond to millisecond laser gradient anneals to produce temperature–dwell–transformation (TDT) diagrams of the phase as a function of quench time and temperature. In addition to showing regimes where specific metastable phases form preferentially, TDT diagrams provide insight into the submillisecond kinetics of solid–solid phase transitions. This is a unique tool for mapping reaction pathways for metastable phases. As a first demonstration of XPLAM, we study Bi2O3, which has a rich set of polytypes, including the d-phase with an exceptionally high oxygen ion conductivity. We demonstrate the first annealing-driven synthesis of room temperature d-Bi2O3. We expect XPLAM to prove a powerful technique for rapid identification of synthetic routes to metastable phases and to generate the exhaustive data sets required for machine learning-guided exploration of materials processing.

36 MATERIALS SCIENCE↗
DOE OSTI2021

An adaptive Hessian approximated stochastic gradient MCMC method

Bayesian approaches have been successfully integrated into training deep neural networks. One popular family is stochastic gradient Markov chain Monte Carlo methods (SG-MCMC), which have gained increasing interest due to their ability to handle large datasets and the potential to avoid overfitting. Although standard SG-MCMC methods have shown great performance in a variety of problems, they may be inefficient when the random variables in the target posterior densities have scale differences or are highly correlated. Here, we present an adaptive Hessian approximated stochastic gradient MCMC method to incorporate local geometric information while sampling from the posterior. The idea is to apply stochastic approximation (SA) to sequentially update a preconditioning matrix at each iteration. The preconditioner possesses second-order information and can guide the random walk of a sampler efficiently. Instead of computing and saving the full Hessian of the log posterior, we use limited memory of the samples and their stochastic gradients to approximate the inverse Hessian-vector multiplication in the updating formula. Moreover, by smoothly optimizing the preconditioning matrix via SA, our proposed algorithm can asymptotically converge to the target distribution with a controllable bias under mild conditions. To reduce the training and testing computational burden, we adopt a magnitude-based weight pruning method to enforce the sparsity of the network. Our method is user-friendly and demonstrates better learning results compared to standard SG-MCMC updating rules. The approximation of inverse Hessian alleviates storage and computational complexities for large dimensional models. Numerical experiments are performed on several problems, including sampling from 2D correlated distribution, synthetic regression problems, and learning the numerical solutions of heterogeneous elliptic PDE. The numerical results demonstrate great improvement in both the convergence rate and accuracy.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Fast multiscale contrast independent preconditioners for linear elastic topology optimization problems

The goal of this work is to present a fast and viable approach for the numerical solution of the high-contrast state problems arising in topology optimization. The optimization process is iterative, and the gradients are obtained by an adjoint analysis, which requires the numerical solution of large high-contrast linear elastic problems with features spanning several length scales. The size of the discretized problems forces the utilization of iterative linear solvers with solution time dependent on the quality of the preconditioner. The lack of clear separation between the scales, as well as the high-contrast, imposes severe challenges on the standard preconditioning techniques. Thus, here we propose new methods for the high-contrast elasticity equation with performance independent of the high-contrast and the multi-scale structure of the elasticity problem. The solvers are based on two-levels domain decomposition techniques with a carefully constructed coarse level to deal with the high-contrast and multi-scale nature of the problem. The construction utilizes spectral equivalence between scalar diffusion and each displacement block of the elasticity problems and, in contrast to previous solutions proposed in the literature, is able to select the appropriate dimension of the coarse space automatically. The new methods inherit the advantages of domain decomposition techniques, such as easy parallelization and scalability. Finally, the presented numerical experiments demonstrate the excellent performance of the proposed methods.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1983

Chlorophyll and carotenoid pigments of prochloron (prochlorophyta)

High-performance liquid chromatography (HPLC) with a gradient-elution technique was utilized to separate and quantify chlorophylls a and b as well as major carotenoid pigments present in freeze-dried preprations of prochloron-didemnid associations and in Prochloron cells separated from host colonies. Results confirm earlier spectrophotometric evidence for both chlorophylls a and b in this prokaryote. Chlorophyll a:b ratios range from 4.14 to 19.71; generally good agreement was found between ratios determined in isolated cell preprations and in symbiotic colonies (in hospite). These values are 1.5 to 5-fold higher than ratios determined in a variety of eukaryotic green plants. The carotenoids in Prochloron are quantitatively and qualitatively similar to those found in various freshwater and marine blue-green algae (cyanopbytes) from high-light environments. However, Prochloron differs from cyanophytes by the absence of myxoxanthophyll and related glycosidic carotenoids. It pigment characteristics are considered sufficiently different from those of cyanophytes to justify its assignment to a separate algal division.

Paerl, H. W.↗
NASA NTRSDate not supplied

Self-Aligned Focusing Schlieren at the 0.3-M Transonic Cryogenic Tunnel and the National Transonic Facility

The implementation of a self-aligned focusing schlieren (SAFS) system at two cryogenic wind tunnels at NASA Langley Research Center is discussed. Risk-reduction testing of the SAFS system was first performed at the 0.3-M Transonic Cryogenic Tunnel to evaluate the system’s operation in a small-scale characteristic cryogenic facility. Testing was conducted with three models: a three-quarter span 25.4-mm-diameter cylinder, a semi-span 65A006 tapered unswept airfoil, and a full-span SC(3)-0712 airfoil. Testing with the cylinder and semi-span airfoil revealed a highly dynamic shock environment, whereas the shock on the full-span airfoil was stationary, solidifying the usage of this model for a pre-/post-shock particle tracking velocimetry measurement. Temperature-induced polarization-altering window stresses were encountered during low-temperature testing and were mitigated using a “non-ideal” quartz/quartz Rochon prism that had largely been neglected since the SAFS system’s first introduction in favor of the more favorable “ideal” glass/quartz Rochon prism. The size of the SAFS system was then decreased in order to fit inside an environmentally controlled camera can enclosure at the National Transonic Facility (NTF) for testing of a sting-mounted aircraft model. The SAFS system was demonstrated to be effective at filtering out the large density gradient flow in the0.3-M plenum, and the thick, high density turbulent boundary layers on the wind tunnel walls at the NTF. Results of the testing campaigns and improvements to future systems are discussed.

Joshua M Weisberger↗
NASA NTRS1996

Global, Collisional Model of High-Energy Photoelectrons

A previously-developed colissional, interhemispheric flux tube model for photoelectrons (PE) has been extended to three dimensions by including transport due to vector E x vector B and magnetic gradient-curvature drifts. Using this model, initial calculations of the high-energy (greater then 50 eV) PE distribution as a function of time, energy, pitch angle, and spatial location in the equatorial plane, are reported for conditions of low geomagnetic activity. To explore both the dynamic and steady behaviors of the model, the simulation starts with the abrupt onset of photoelectron excitation, and is followed to steady state conditions. The results illustrate several features of the interaction of photoelectrons with typical magnetospheric plasmas and fields, including collisional diffusion of photoelectrons in pitch angle with flux tube filling, diurnal intensity and pitch angle asymmetries introduced by directional sunlight, and energization of the photoelectron distribution in the evening sector. Cross-field drift is shown to have a long time scale, taking 12 to 24 hours to reach a steady state distribution. Future applications of the model are briefly outlined.

Khazanov, G. V.↗
DOE OSTI2025

Angular-spatial hp -adaptivity for radiative transfer with discontinuous Galerkin spectral element methods

Radiative transfer is important for many science and engineering applications, and numerical simulations of radiative transfer can be challenging. For instance, the radiation field is seven-dimensional – three spatial, two angular, one wavelength, and one temporal – and often features steep gradients. Therefore, memory usage is a key issue. To reduce memory, some past work has investigated the use of adaptive mesh refinement (AMR), typically for either the spatial or angular coordinate, and typically for only h -adaptivity. Here, we propose the use of AMR for the spatial and angular coordinates together, and the use of h - and p -adaptivity together as hp -AMR for the potential for further memory savings. We implemented the proposed method for several test cases in two spatial and one angular dimension, with the discontinuous Galerkin spectral element method. These test cases featured highly anisotropic angular radiation, with or without steep spatial gradients. Our primary findings from these test cases were: (1) Angular hp -adaptivity can deliver the radiation solution with the same accuracy as, and with much less computational memory than, uniform angular h - or p -refinements, or angular h -adaptivity alone. This is most obvious when the incoming radiation is highly anisotropic, in which case the savings can be orders of magnitude. (2) Full spatial-angular hp -adaptivity is more efficient in solution representation, compared to solely spatial or solely angular -adaptivity. This is most evident when steep gradients are present in both the spatial and angular distribution. These results suggest that adaptive spatial- hp angular-refinement may perform well in large-scale seven-dimensional applications.

Adaptive refinement↗