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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 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
NASA NTRS2012

Interval Management with Spacing to Parallel Dependent Runways (IMSPIDR) Experiment and Results

An area in aviation operations that may offer an increase in efficiency is the use of continuous descent arrivals (CDA), especially during dependent parallel runway operations. However, variations in aircraft descent angle and speed can cause inaccuracies in estimated time of arrival calculations, requiring an increase in the size of the buffer between aircraft. This in turn reduces airport throughput and limits the use of CDAs during high-density operations, particularly to dependent parallel runways. The Interval Management with Spacing to Parallel Dependent Runways (IMSPiDR) concept uses a trajectory-based spacing tool onboard the aircraft to achieve by the runway an air traffic control assigned spacing interval behind the previous aircraft. This paper describes the first ever experiment and results of this concept at NASA Langley. Pilots flew CDAs to the Dallas Fort-Worth airport using airspeed calculations from the spacing tool to achieve either a Required Time of Arrival (RTA) or Interval Management (IM) spacing interval at the runway threshold. Results indicate flight crews were able to land aircraft on the runway with a mean of 2 seconds and less than 4 seconds standard deviation of the air traffic control assigned time, even in the presence of forecast wind error and large time delay. Statistically significant differences in delivery precision and number of speed changes as a function of stream position were observed, however, there was no trend to the difference and the error did not increase during the operation. Two areas the flight crew indicated as not acceptable included the additional number of speed changes required during the wind shear event, and issuing an IM clearance via data link while at low altitude. A number of refinements and future spacing algorithm capabilities were also identified.

Baxley, Brian T.↗
DOE OSTI2019

Approximate Bayesian Model Inversion for PDEs with Heterogeneous and State-Dependent Coefficients

We present two approximate Bayesian inference methods for parameter estimation in partial differential equation (PDE) models with space-dependent and state-dependent parameters. We demonstrate that these methods provide accurate and cost-effective alternatives to Markov Chain Monte Carlo simulation. We assume a parameterized Gaussian prior on the unknown functions, and approximate the posterior density by a parameterized multivariate Gaussian density. The parameters of the prior and posterior are estimated from sparse observations of the PDE model's states and the unknown functions themselves by maximizing the evidence lower bound (ELBO), a lower bound on the log marginal likelihood of the observations. The first method, Laplace-EM, employs the expectation maximization algorithm to maximize the ELBO, with a Laplace approximation of the posterior on the E-step, and minimization of a Kullback-Leibler divergence on the M-step. The second method, DSVI-EB, employs the doubly stochastic variational inference (DSVI) algorithm, in which the ELBO is maximized via gradient-based stochastic optimization, with nosiy gradients computed via simple Monte Carlo sampling and Gaussian backpropagation. We apply these methods to identifying diffusion coefficients in linear and nonlinear diffusion equations, and we find that both methods provide accurate estimates of posterior densities and the hyperparameters of Gaussian priors. While the Laplace-EM method is more accurate, it requires computing Hessians of the physics model. The DSVI-EB method is found to be less accurate but only requires gradients of the physics model.

approximate Bayesian inference, model inversion, v↗
NASA NTRS2004

Hematopoietic Stem Cell Therapy as a Counter-Measure for Human Exploration of Deep Space

Human exploration of deep space depends, in part, on our ability to counter severe/invasive disorders that astronauts experience in space environments. The known symptoms include hematological/cardiac abnormalities,bone and muscle losses, immunodeficiency, neurological disorders, and cancer. Exploiting the extraordinary plasticity of hematopoietic stem cells (HSCs), which differentiate not only to all types of blood cells, but also to various tissues, we have advanced a hypothesis that ome of the space-caused disorders maybe amenable to hematopoietis stem cell therapy(HSCT) so as to maintain promote human exploration of deep space. Using mouse models of human anemia beta-thaiassemia) as well as spaceflight (hindlimb unloading system), we have obtained feasibility results of HSCT for space anemia, muscle loss, and immunodeficiency. For example, in the case of HSCT for muscle loss, the beta-galactosidese marked HSCs were detected in the hindlimbs of unloaded mouse following transplantation by -X-gal wholemaunt staining procedure. Histochemicaland physical analyses indicated structural contribution of HSCs to the muscle. HSCT for immunodeficiency was investigated ising beta-galactosidese gene-tagged Escherichia coli as the infectious agent. Results of the X-gal staining procedure indicated the rapeutic role of the HSCT. To facilitate the HSCT in space, growth of HSCs were optimized in the NASA Rotating Wall Vessel (RWV) culture systems, including Hydrodynamic Focusing Bioreactor (HFB).

Ohi, S.↗
NASA NTRS2012

Nuclear Propulsion through Direct Conversion of Fusion Energy: The Fusion Driven Rocket

The future of manned space exploration and development of space depends critically on the creation of a dramatically more proficient propulsion architecture for in-space transportation. A very persuasive reason for investigating the applicability of nuclear power in rockets is the vast energy density gain of nuclear fuel when compared to chemical combustion energy. Current nuclear fusion efforts have focused on the generation of electric grid power and are wholly inappropriate for space transportation as the application of a reactor based fusion-electric system creates a colossal mass and heat rejection problem for space application.

Propulsion↗
NASA NTRS2018

The Fusion Driven Rocket: Nuclear Propulsion through Direct Conversion of Fusion Energy

The future of manned space exploration and development of space depends critically on the creation of a dramatically more efficient propulsion architecture for in-space transportation. A very persuasive reason for investigating the applicability of nuclear power in rockets is the vast energy density gain of nuclear fuel when compared to chemical combustion energy. The Fusion Driven rocket (FDR) represents a revolutionary approach to fusion propulsion where the power source releases its energy directly into the propellant, not requiring conversion to electricity. It employs a solid lithium propellant that requires no significant tankage mass. The propellant is rapidly heated and accelerated to high exhaust velocity (> 30 km/s), while having no substantial physical interaction with the spacecraft thereby avoiding damage to the rocket and limiting both the thermal heat load and radiator mass. The key to achieving this stems from research at MSNW and the UW on the magnetically driven implosion of metal foils onto a magnetized plasma target to obtain fusion conditions. A logical extension of this work leads to a method that utilizes these metal shells (or liners) to not only achieve fusion conditions, but to serve as the propellant as well. Several low-mass, magnetically driven metal liners are inductively driven to converge radially and axially and form a thick blanket surrounding the target plasmoid and compress the plasmoid to fusion conditions. Virtually all of the radiant, neutron and particle energy from the plasma is absorbed by the encapsulating, thick metal blanket thereby isolating the spacecraft from the fusion. This energy, in addition to the intense Ohmic heating at peak magnetic field compression, is adequate to vaporize and ionize the metal blanket. The expansion of this hot, ionized metal propellant through a magnetically insulated nozzle produces high thrust at the optimal Isp. The energy from the fusion process, along with the waste heat, is thus utilized at very high efficiency. The basic scheme for FDR is illustrated and described in the report (see Fig. 2) The two most critical issues in meeting challenges introduced employing magneto-inertial fusion as the power source is driver efficiency and “stand-off” – the ability to isolate and protect fusion and thruster from the resultant fusion energy. By employing metal shells for compression, it is possible to produce the desired convergent motion inductively by inserting the metal sheets along the inner surface of cylindrical or conically tapered coils. Both stand-off and energy efficiency issues are solved by this arrangement. 3 This two year effort focused on achieving three key criteria for the Fusion Driven Rocket to move forward for technological development: (1) the physics of the FDR must be fully understood and validated, (2) the design and technology development for the FDR required for its implementation in space must be fully characterized, and (3) an in-depth analysis of the rocket design and spacecraft integration as well as mission architectures enabled by the FDR need to be performed. A subscale, laboratory liner compression test facility was assembled at the University of Washington Plasma Dynamics Laboratory with sufficient liner kinetic energy (~ 0.5 MJ) to reach conditions required for fusion breakeven conditions. Detailed experimental studies of the dynamic behavior of the driven liners as well as liner convergence and magnetic compression were performed. The development of both the 1D liner dynamics code and the full 3D ANSYS® liner calculations was achieved. The characterization of both the FDR and spacecraft as well as a design architecture analysis was conducted that included an examination of a wide range of mission architectures and destinations for which this fusion propulsion system would be enabling or critical. In particular a rapid, single launch manned Mars mission was developed.

Energy↗
NASA NTRS2011

Miniature Sapphire Acoustic Resonator - MSAR

A room temperature sapphire acoustics resonator incorporated into an oscillator represents a possible opportunity to improve on quartz ultrastable oscillator (USO) performance, which has been a staple for NASA missions since the inception of spaceflight. Where quartz technology is very mature and shows a performance improvement of perhaps 1 dB/decade, these sapphire acoustic resonators when integrated with matured quartz electronics could achieve a frequency stability improvement of 10 dB or more. As quartz oscillators are an essential element of nearly all types of frequency standards and reference systems, the success of MSAR would advance the development of frequency standards and systems for both groundbased and flight-based projects. Current quartz oscillator technology is limited by quartz mechanical Q. With a possible improvement of more than x 10 Q with sapphire acoustic modes, the stability limit of current quartz oscillators may be improved tenfold, to 10(exp -14) at 1 second. The electromagnetic modes of sapphire that were previously developed at JPL require cryogenic temperatures to achieve the high Q levels needed to achieve this stability level. However sapphire fs acoustic modes, which have not been used before in a high-stability oscillator, indicate the required Q values (as high as Q = 10(exp 8)) may be achieved at room temperature in the kHz range. Even though sapphire is not piezoelectric, such a high Q should allow electrostatic excitation of the acoustic modes with a combination of DC and AC voltages across a small sapphire disk (approximately equal to l mm thick). The first evaluations under this task will test predictions of an estimated input impedance of 10 kilohms at Q = 10(exp 8), and explore the Q values that can be realized in a smaller resonator, which has not been previously tested for acoustic modes. This initial Q measurement and excitation demonstration can be viewed similar to a transducer converting electrical energy to mechanical energy and back. Such an electrostatic tweeter type excitation of a mechanical resonator will be tested at 5 MHz. Finite element calculation will be applied to resonator design for the desired resonator frequency and optimum configuration. The experiment consists of the sapphire resonator sandwiched between parallel electrodes. A DC+AC voltage can be applied to generate a force to act on a sapphire resonator. With the frequency of the AC voltage tuned to the sapphire resonator frequency, a resonant condition occurs and the sapphire Q can be measured with a high-frequency impedance analyzer. To achieve high Q values, many experimental factors such as vacuum seal, gas damping effects, charge buildup on the sapphire surface, heat dissipation, sapphire anchoring, and the sapphire mounting configuration will need attention. The effects of these parameters will be calculated and folded into the resonator design. It is envisioned that the initial test configuration would allow for movable electrodes to check gap spacing dependency and verify the input impedance prediction. Quartz oscillators are key components in nearly all ground- and space-based communication, tracking, and radio science applications. They play a key role as local oscillators for atomic frequency standards and serve as flywheel oscillators or to improve phase noise in high performance frequency and timing distribution systems. With ultra-stable performance from one to three seconds, an Earth-orbit or moon-based MSAR can enhance available performance options for spacecraft due to elimination of atmospheric path degradation.

Wang, Rabi T.↗
DOE OSTI2020

ABINIT: Overview and focus on selected capabilities

ABINIT is probably the first electronic-structure package to have been released under an open-source license about 20 years ago. It implements density functional theory, density-functional perturbation theory (DFPT), many-body perturbation theory (GW approximation and Bethe–Salpeter equation), and more specific or advanced formalisms, such as dynamical mean-field theory (DMFT) and the “temperature-dependent effective potential” approach for anharmonic effects. Relying on planewaves for the representation of wavefunctions, density, and other space-dependent quantities, with pseudopotentials or projector-augmented waves (PAWs), it is well suited for the study of periodic materials, although nanostructures and molecules can be treated with the supercell technique. The present article starts with a brief description of the project, a summary of the theories upon which ABINIT relies, and a list of the associated capabilities. It then focuses on selected capabilities that might not be present in the majority of electronic structure packages either among planewave codes or, in general, treatment of strongly correlated materials using DMFT; materials under finite electric fields; properties at nuclei (electric field gradient, Mössbauer shifts, and orbital magnetization); positron annihilation; Raman intensities and electro-optic effect; and DFPT calculations of response to strain perturbation (elastic constants and piezoelectricity), spatial dispersion (flexoelectricity), electronic mobility, temperature dependence of the gap, and spin-magnetic-field perturbation. The ABINIT DFPT implementation is very general, including systems with van der Waals interaction or with noncollinear magnetism. Community projects are also described: generation of pseudopotential and PAW datasets, high-throughput calculations (databases of phonon band structure, second-harmonic generation, and GW computations of bandgaps), and the library libpaw. ABINIT has strong links with many other software projects that are briefly mentioned.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Geometric Structure and Transversal Logic of Quantum Reed–Muller Codes

Designing efficient and noise-tolerant quantum computation protocols generally begins with an understanding of quantum error-correcting codes and their native logical operations. The simplest class of native operations are transversal gates, which are naturally fault-tolerant. Here, in this paper, we aim to characterize the transversal gates of quantum Reed–Muller (RM) codes by exploiting the well-studied properties of their classical counterparts. We start our work by establishing a new geometric characterization of quantum RM codes via the Boolean hypercube and its associated subcube complex. More specifically, a set of stabilizer generators for a quantum RM code can be described via transversal X and Z operators acting on subcubes of particular dimensions. This characterization leads us to define subcube operators composed of single-qubit π/2 k Z -rotations that act on subcubes of given dimensions. We first characterize the action of subcube operators on the code space: depending on the dimension of the subcube, these operators either (1) act as a logical identity on the code space, (2) implement non-trivial logic, or (3) rotate a state away from the code space. Second, and more remarkably, we uncover that the logic implemented by these operators corresponds to circuits of multi-controlled-Z gates that have an explicit and simple combinatorial description. Overall, this suite of results yields a comprehensive understanding of a class of natural transversal operators for quantum RM codes.

Reed–Muller (RM) codes↗
NASA NTRS1991

STS-40 Spacelab Life Sciences 1 (SLS-1): The first dedicated spacelab life sciences mission

Successful exploration of space depends on the health and well-being of people who travel and work there. For this reason, the National Aeronautics and Space Administration (NASA) has dedicated several Space Shuttle missions to examine how living and working in space affects the human body. Spacelab Life Sciences 1 (SLS-1) is the first of these missions. The main purpose of the SLS-1 mission is to study the mechanisms, magnitudes, and time courses of certain physiological changes that occur during space flight and to investigate the consequences of the body's adaptation to microgravity and readjustment to gravity upon return to Earth. How does space flight influence the heart and circulatory system, metabolic processes, the muscles and bones, and the cells? If responses to weightlessness are undesirable, how can they be prevented or controlled? Will the human body maintain its physical and chemical equilibrium during months aboard a space station and years-long missions to Mars? When crews return to Earth, what can they expect to experience as their bodies readjust to Earth's gravity? With the SLS-1 experiments, NASA is addressing some of these questions. Various aspects of the SLS-1 are discussed.

Source record↗
NASA NTRS1988

Automatic calibration of space based manipulators and mechanisms

Four tasks in manipulator kinematic calibration are summarized. Calibration of a seven degree of freedom manipulator was simulated. A calibration model is presented that can be applied on a closed-loop robot. It is an expansion of open-loop kinematic calibration algorithms subject to constraints. A closed-loop robot with a five-bar linkage transmission was tested. Results show that the algorithm converges within a few iterations. The concept of model differences is formalized. Differences are categorized as structural and numerical, with emphasis on the structural. The work demonstrates that geometric manipulators can be visualized as points in a vector space with the dimension of the space depending solely on the number and type of manipulator joint. Visualizing parameters in a kinematic model as the coordinates locating the manipulator in vector space enables a standard evaluation of the models. Key results include a derivation of the maximum number of parameters necessary for models, a formal discussion on the inclusion of extra parameters, and a method to predetermine a minimum model structure for a kinematic manipulator. A technique is presented that enables single point sensors to gather sufficient information to complete a calibration.

Everett, Louis J.↗
DOE OSTI2018

Simulating Electron Dynamics of Complex Molecules with Time-Dependent Complete Active Space Configuration Interaction

In this paper, time-dependent electronic structure methods are growing in popularity as tools for modeling ultrafast and/or nonlinear processes, for computing spectra, and as the electronic structure component of mean-field molecular dynamics simulations. Time-dependent configuration interaction (TD-CI) offers several advantages over the widely used real-time time-dependent density functional theory: namely, that it correctly models Rabi oscillations; it offers a spin-pure description of open-shell systems; and a hierarchy of TD-CI methods can be defined that systematically approach the exact solution of the time-dependent Schrodinger equation (TDSE). In this work, we present a novel TD-CI approach that extends TD-CI to large complete active-space configuration expansions. Such extension is enabled by use of a direct configuration interaction approach that eliminates the need to explicitly build, store, or diagonalize the Hamiltonian matrix. Graphics processing unit (GPU) acceleration enables fast solution of the TDSE even for large active spaces—up to 12 electrons in 12 orbitals (853776 determinants) in this work. A symplectic split operator propagator yields long-time norm conservation. We demonstrate the applicability of our approach by computing the response of a large molecule with a strongly correlated ground state, decacene (C 42 H 24 ), to various pulses (δ-function, transform limited, chirped). Our simulations predict that chirped pulses can be used to induce dipole-forbidden transitions. Simulations of decacene using the 6-31G(d) basis set and a 12 electrons/12 orbitals active space took 20.1 h to propagate for 100 fs with a 1 attosecond time step on a single NVIDIA K40 GPU. Convergence with respect to time step is found to depend on the property being computed and the chosen active space.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Bilevel parameter optimization for learning nonlocal image denoising models

We propose a bilevel optimization approach for the estimation of parameters in nonlocal image denoising models. The parameters we consider are both the space-dependent fidelity weight and weights within the kernel of the nonlocal operator. In both cases we investigate the differentiability of the solution operator in function spaces and derive a first order optimality system that characterizes local minima. For the numerical solution of the problems, we propose a second-order trust-region algorithm in combination with a finite element discretization of the nonlocal denoising models and we introduce a computational strategy for the solution of the resulting dense linear systems. Several experiments illustrate the applicability and effectiveness of our approach.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Reimagining full wave rf quasilinear theory in a tokamak

The velocity dependent resonant interaction of particles with applied radiofrequency (rf) waves during heating and current drive in the presence of pitch angle scattering collisions gives rise to narrow collisional velocity space boundary layers that dramatically enhance the role of collisions as recently shown by Catto ( J. Plasma Phys. , vol. 86, 2020, 815860302). The behaviour is a generalization of the narrow collisional boundary layer that forms during Landau damping as found by Johnston ( Phys. Fluids , vol. 14, 1971, pp. 2719–2726) and Auerbach ( Phys. Fluids , vol. 20, 1977, pp. 1836–1844). For a wave of parallel wave number ${k_{||}}$ interacting with weakly collisional plasma species of collision frequency $\nu$ and thermal speed ${v_{\textrm{th}}}$ , the effective collision frequency becomes of order $\nu {({k_{||}}{v_{th}}/\nu )^{2/3}} \gg \nu $ . The narrow boundary layers that arise because of the diffusive nature of the collisions allow a physically meaningful wave–particle interaction time to be defined that is the inverse of this effective collision frequency. The collisionality implied by the narrow boundary layer results in changes in the standard quasilinear treatment of applied rf fields in tokamaks while remaining consistent with causality. These changes occur because successive poloidal interactions with the rf are correlated in tokamak geometry and because the resonant velocity space dependent interactions are controlled by the spatial and temporal behaviour of the perturbed full wave fields rather than just the spatially local Landau and Doppler shifted cyclotron wave–particle resonance condition associated with unperturbed motion of the particles. The correlation of successive poloidal circuits of the tokamak leads to the appearance in the quasilinear operator of transit averaged resonance conditions localized in velocity space boundary layers that maintain negative definite entropy production.

Physics↗
DOE OSTI2016

On the nature of high field charge transport in reinforced silicone dielectrics: Experiment and simulation

The high field charge injection and transport properties in reinforced silicone dielectrics were investigated by measuring the time-dependent space charge distribution and the current under dc conditions up to the breakdown field and were compared with the properties of other dielectric polymers. It is argued that the energy and spatial distribution of localized electronic states are crucial in determining these properties for polymer dielectrics. Tunneling to localized states likely dominates the charge injection process. A transient transport regime arises due to the relaxation of charge carriers into deep traps at the energy band tails and is successfully verified by a Monte Carlo simulation using the multiple-hopping model. The charge carrier mobility is found to be highly heterogeneous due to the non-uniform trapping. The slow moving electron packet exhibits a negative field dependent drift velocity possibly due to the spatial disorder of traps.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Reimagining full wave rf quasilinear theory in a tokamak

The velocity dependent resonant interaction of particles with applied radio frequency (rf) waves during heating and current drive in the presence of pitch angle scattering collisions gives rise to narrow collisional velocity space boundary layers that dramatically enhance the role of collisions as recently shown by Catto (J. Plasma Phys., vol. 86, 815860302, 2020). The behavior is a generalization of the narrow collisional boundary layer that forms during Landau damping as found by Johnston (Phys. Fluids, vol. 14, 1971, pp. 2719-2726) and Auerbach (Phys. Fluids, vol. 20, 1977, pp. 1836-1844). For a wave of parallel wave number k|| interacting with weakly collisional plasma species of collision frequency ν and thermal speed vth , the effective collision frequency becomes of order ν(k_||v_th /ν)^2/3>> ν . The narrow boundary layers that arise because of the diffusive nature of the collisions allows a physically meaningful wave-particle interaction time to be defined that is the inverse of this effective collision frequency. The collisionality implied by the narrow boundary layer results in changes in the standard quasilinear treatment of applied rf fields in tokamaks while remaining consistent with causality. These changes occur because successive poloidal interactions with the rf are correlated in tokamak geometry and because the resonant velocity space dependent interactions are controlled by the spatial and temporal behavior of the perturbed full wave fields rather than just the spatially local Landau and Doppler shifted cyclotron wave-particle resonance condition associated with unperturbed motion of the particles. The correlation of successive poloidal circuits of the tokamak leads to the appearance in the quasilinear operator of transit averaged resonance conditions localized in velocity space boundary layers that maintain negative definite entropy production.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Neural refinement of sample weights

Monte Carlo simulations are an essential tool in particle physics data analysis. Events are typically generated alongside weights that redistribute the cross section of the simulated process across the phase space. These weights can be negative, and several post hoc methods have been developed to eliminate or mitigate the negative values. All of these methods share the common strategy of approximating the average weight as a function of phase space. We introduce an alternative approach, which, instead of reweighting to the average, refines the initial weights with a scaling transformation, utilizing a phase space-dependent factor. Since this new refinement method does not need to model the full weight distribution, it can be more accurate. High-dimensional and unbinned phase space is processed using neural networks for the refinement method. In addition to the refinement method, we introduce a new resampling protocol, which can be used in conjunction with any weight transformation to not only preserve the average weight but also the statistical uncertainties of the initial distribution. Using both realistic and synthetic examples, we show that the new neural refinement method is able to match or exceed the accuracy of similar weight transformations and that the new resampling protocol is simpler in implementation than previous methods while exhibiting equivalent statistical properties.

Artificial neural networks↗
DOE OSTI2022

Sensitivity Analysis for Solutions to Heterogeneous Nonlocal Systems. Theoretical and Numerical Studies

The paper presents a collection of results on continuous dependence for solutions to nonlocal problems under perturbations of data and system parameters. The integral operators appearing in the systems capture interactions via heterogeneous kernels that exhibit different types of weak singularities, space dependence, even regions of zero-interaction. Here, the stability results showcase explicit bounds involving the measure of the domain and of the interaction collar size, nonlocal Poincaré constant, and other parameters. In the nonlinear setting, the bounds quantify in different L p norms the sensitivity of solutions under different nonlinearity profiles. The results are validated by numerical simulations showcasing discontinuous solutions, varying horizons of interactions, and symmetric and heterogeneous kernels.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1988

Generating Coordinates For Aerodynamical Calculations

Elliptic method generates composite grids about three-dimensional aircraft body. Grid lines on surface of wing and body vary in spacing, depending on level of detail needed to model airflow accurately in region. Grid intervals for zone might be unchanged in one direction, halved in second orthogonal direction, and reduced to much finer spacing in third direction. Computer generates grids with little or no human intervention.

Sorenson, Reese L.↗