Search NASA⌕ Search

SEARCH · Search NASA

Results for “variable order”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 271 records · Page 15
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

On mass conservation and solvability of the discretized variable-density zero-Mach Navier-Stokes equations

This paper presents a study of a variable-density zero-Mach Navier-Stokes discretization and subtle difficulties associated with the pressure. A consistent compatibility condition between the temperature and velocity is first derived. It is shown that one can accurately and efficiently solve all primitive variables with the uniform order of accuracy of the specified discretization and time-marching schemes. It is shown that higher density ratios than those commonly reported are achievable, and it is, in part, traced to the solvability of the pressure Poisson equation. Numerical properties are assessed with the method of manufactured solutions, and several classical testing cases are carried out to validate the code, ranging from variable-density mixing problems to premixed flames with forcing.

42 ENGINEERING↗
NASA NTRS1992

Aerodynamic design and optimization in one shot

This paper describes an efficient numerical approach for the design and optimization of aerodynamic bodies. As in classical optimal control methods, the present approach introduces a cost function and a costate variable (Lagrange multiplier) in order to achieve a minimum. High efficiency is achieved by using a multigrid technique to solve for all the unknowns simultaneously, but restricting work on a design variable only to grids on which their changes produce nonsmooth perturbations. Thus, the effort required to evaluate design variables that have nonlocal effects on the solution is confined to the coarse grids. However, if a variable has a nonsmooth local effect on the solution in some neighborhood, it is relaxed in that neighborhood on finer grids. The cost of solving the optimal control problem is shown to be approximately two to three times the cost of the equivalent analysis problem. Examples are presented to illustrate the application of the method to aerodynamic design and constraint optimization.

Ta'asan, Shlomo↗
DOE OSTI2022

A high accuracy/resolution spectral element/Fourier–Galerkin method for the simulation of shoaling non-linear internal waves and turbulence in long domains with variable bathymetry

A high-order hybrid continuous-Galerkin numerical method, designed for the simulation of non-linear, non -hydrostatic internal waves and turbulence in long computational domains with complex bathymetry, is presented. The spatial discretization in the non-periodic wave-propagating directions, utilizes the nodal spectral element method. Such a high-order element-based discretization allows the highly accurate representation of complex domain geometry along with the flexibility of concentrating resolution in areas of interest. Under the assumption of the normal-to-isobath propagation of non-linear internal waves, a third periodic direction is incorporated via a Fourier-Galerkin discretization. The distinct non-hydrostatic nature of non-linear internal waves and, any instabilities and turbulence therein, necessitates the numerically challenging solution of the pressure Poisson problem. A defining feature of this work is the application of a domain decomposition approach, combined with block-Jacobi/deflation-based preconditioning to the pressure Poisson problem. Such a combined approach is particularly suitable for the long high aspect-ratio complex domains of interest and enables the efficient high-accuracy reproduction of the non-hydrostatic dynamics of non-linear internal waves. Implementation details are also described in the context of the stability of the solver and its parallelization strategy. A series of benchmarks of increasing complexity demonstrate the robustness of the flow solver. The benchmarks culminate with the three-dimensional simulation of a convectively breaking mode-one non-linear internal wave over a realistic South-China-Sea bathymetric transect and background current/stratification profiles.

Deflation↗
NASA NTRS2007

Variability in Global Top-of-Atmosphere Shortwave Radiation Between 2000 and 2005

Measurements from various instruments and analysis techniques are used to directly compare changes in Earth-atmosphere shortwave (SW) top-of-atmosphere (TOA) radiation between 2000 and 2005. Included in the comparison are estimates of TOA reflectance variability from published ground-based Earthshine observations and from new satellite-based CERES, MODIS and ISCCP results. The ground-based Earthshine data show an order-of-magnitude more variability in annual mean SW TOA flux than either CERES or ISCCP, while ISCCP and CERES SW TOA flux variability is consistent to 40%. Most of the variability in CERES TOA flux is shown to be dominated by variations global cloud fraction, as observed using coincident CERES and MODIS data. Idealized Earthshine simulations of TOA SW radiation variability for a lunar-based observer show far less variability than the ground-based Earthshine observations, but are still a factor of 4-5 times more variable than global CERES SW TOA flux results. Furthermore, while CERES global albedos exhibit a well-defined seasonal cycle each year, the seasonal cycle in the lunar Earthshine reflectance simulations is highly variable and out-of-phase from one year to the next. Radiative transfer model (RTM) approaches that use imager cloud and aerosol retrievals reproduce most of the change in SW TOA radiation observed in broadband CERES data. However, assumptions used to represent the spectral properties of the atmosphere, clouds, aerosols and surface in the RTM calculations can introduce significant uncertainties in annual mean changes in regional and global SW TOA flux.

Loebe, Norman G.↗
NASA NTRS2006

Verification of Software: The Textbook and Real Problems

The process of verification, or determining the order of accuracy of computational codes, can be problematic when working with large, legacy computational methods that have been used extensively in industry or government. Verification does not ensure that the computer program is producing a physically correct solution, it ensures merely that the observed order of accuracy of solutions are the same as the theoretical order of accuracy. The Method of Manufactured Solutions (MMS) is one of several ways for determining the order of accuracy. MMS is used to verify a series of computer codes progressing in sophistication from "textbook" to "real life" applications. The degree of numerical precision in the computations considerably influenced the range of mesh density to achieve the theoretical order of accuracy even for 1-D problems. The choice of manufactured solutions and mesh form shifted the observed order in specific areas but not in general. Solution residual (iterative) convergence was not always achieved for 2-D Euler manufactured solutions. L(sub 2,norm) convergence differed variable to variable therefore an observed order of accuracy could not be determined conclusively in all cases, the cause of which is currently under investigation.

Carlson, Jan-Renee↗
DOE OSTI2017

The two-dimensional kinetic ballooning theory for ion temperature gradient mode in tokamak

The two-dimensional (2D) kinetic ballooning theory is developed for the ion temperature gradient mode in an up-down symmetric equilibrium (illustrated via concentric circular magnetic surfaces). The ballooning transform converts the basic 2D linear gyro-kinetic equation into two equations: (1) the lowest order equation (ballooning equation) is an integral equation essentially the same as that reported by Dong et al., [Phys. Fluids B 4, 1867 (1992)] but has an undetermined Floquet phase variable, (2) the higher order equation for the rapid phase envelope is an ordinary differential equation in the same form as the 2D ballooning theory in a fluid model [Xie et al., Phys. Plasmas 23, 042514 (2016)]. The system is numerically solved by an iterative approach to obtain the (phase independent) eigen-value. The new results are compared here to the two earlier theories. We find a strongly modified up-down asymmetric mode structure, and non-trivial modifications to the eigen-value.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Symmetry-dependent ultrafast manipulation of nanoscale magnetic domains

Symmetry is a powerful concept in physics, but its applicability to far-from-equilibrium states is still being understood. Recent attention has focused on how far-from-equilibrium states lead to spontaneous symmetry breaking. Conversely, ultrafast optical pumping can be used to drastically change the energy landscape and quench the magnetic order parameter in magnetic systems. Here, we find a distinct symmetry-dependent ultrafast behaviour by use of ultrafast x-ray scattering from magnetic patterns with varying degrees of isotropic and anisotropic symmetry. After pumping with an optical laser, the scattered intensity reveals a radial shift exclusive to the isotropic component and exhibits a faster recovery time from quenching for the anisotropic component. These features arise even when both symmetry components are concurrently measured, suggesting a correspondence between the excitation and the magnetic order symmetry. Our results underline the importance of symmetry as a critical variable to manipulate the magnetic order in the ultrafast regime.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2018

Phase Field Dislocation Dynamics (PFDD)

Phase Field Dislocation Dynamics (PFDD) is a phase field approach for tracking the motion and interactions of individual dislocations in materials, mostly face-centered cubic (fcc) metals. The phase field approach relies on scalar order parameters or phase field variables to track a quantity of interest. In PFDD, these phase field variables represent the passage of perfect dislocations across each active slip system, with one order parameter defined in each slip system. Partial dislocations are represented with linear combinations of the order parameters. The system is evolved through minimization of the total system energy, which is directly dependent on the phase field variables. All of the physics is described by the total energy functional that is derived from a thermodynamic basis, and the system kinetics are evolved using a Ginzburg-Landau (GL) equation.

Hunter, Abigail↗
NASA NTRS1989

Optimal aeroassisted coplanar orbital transfer using an energy model

The atmospheric portion of the trajectories for the aeroassisted coplanar orbit transfer was investigated. The equations of motion for the problem are expressed using reduced order model and total vehicle energy, kinetic plus potential, as the independent variable rather than time. The order reduction is achieved analytically without an approximation of the vehicle dynamics. In this model, the problem of coplanar orbit transfer is seen as one in which a given amount of energy must be transferred from the vehicle to the atmosphere during the trajectory without overheating the vehicle. An optimal control problem is posed where a linear combination of the integrated square of the heating rate and the vehicle drag is the cost function to be minimized. The necessary conditions for optimality are obtained. These result in a 4th order two-point-boundary-value problem. A parametric study of the optimal guidance trajectory in which the proportion of the heating rate term versus the drag varies is made. Simulations of the guidance trajectories are presented.

Halyo, Nesim↗
NASA NTRS1993

Modeling the Arecibo nighttime F2 layer. I - Overhead properties

The paper extends the servo model of Rishbeth et al. (1978) and applies it to fit the height and plasma density of the nighttime F2 layer, as measured from the Arecibo Observatory during solar maximum by Burnside (1984). The model equations are integrated numerically to fit the observed peak height and density. The model adequately reproduces the observed behavior of the F2 layer. The additional terms in the extended servo-height equation affect the peak height computation by no more than 10 percent on average. The applied current is generally eastward though it becomes westward during the postmidnight collapse or descent of the layer. Differences between model and optically measured meridional wind speeds appear to be related to the presence of large vertical shears in the wind. The observed peak density can be reproduced to within 20 to 40 percent accuracy. Variable plasmaspheric fluxes of the order of 10 exp 13/sq m s contribute to the maintenance and variability of the nighttime peak density.

Melendez-Alvira, D. J.↗
NASA NTRS2009

A Multivariate Randomization Text of Association Applied to Cognitive Test Results

Randomization tests provide a conceptually simple, distribution-free way to implement significance testing. We have applied this method to the problem of evaluating the significance of the association among a number (k) of variables. The randomization method was the random re-ordering of k-1 of the variables. The criterion variable was the value of the largest eigenvalue of the correlation matrix.

Ahumada, Albert↗
NASA NTRS1981

Two-D results on human operator perception

The application of multidimensional scaling methodology in human factors engineering is presented. The nonorthogonality of internally perceived task variables is exhibited for first and second order plants with both dependent and independent task variables. Directions of operator preference are shown for actual performance, pilot opinion rating, and subjective measures of fatigue, adaptability, and system recognition. Improvement of performance in second order systems is exhibited by the use of bang-bang feedback information. Dissimilarity measures for system comparison are suggested in order to account for human operator rotations and subjective sense of time.

Siapkara, A. A.↗
NASA NTRS1998

Predicting Ecologically Important Vegetation Variables from Remotely Sensed Optical/Radar Data Using Neural Networks

A number of satellite sensor systems will collect large data sets of the Earth's surface during NASA's Earth Observing System (EOS) era. Efforts are being made to develop efficient algorithms that can incorporate a wide variety of spectral data and ancillary data in order to extract vegetation variables required for global and regional studies of ecosystem processes, biosphere-atmosphere interactions, and carbon dynamics. These variables are, for the most part, continuous (e.g. biomass, leaf area index, fraction of vegetation cover, vegetation height, vegetation age, spectral albedo, absorbed photosynthetic active radiation, photosynthetic efficiency, etc.) and estimates may be made using remotely sensed data (e.g. nadir and directional optical wavelengths, multifrequency radar backscatter) and any other readily available ancillary data (e.g., topography, sun angle, ground data, etc.). Using these types of data, neural networks can: 1) provide accurate initial models for extracting vegetation variables when an adequate amount of data is available; 2) provide a performance standard for evaluating existing physically-based models; 3) invert multivariate, physically based models; 4) in a variable selection process, identify those independent variables which best infer the vegetation variable(s) of interest; and 5) incorporate new data sources that would be difficult or impossible to use with conventional techniques. In addition, neural networks employ a more powerful and adaptive nonlinear equation form as compared to traditional linear, index transformations, and simple nonlinear analyses. These neural networks attributes are discussed in the context of the authors' investigations of extracting vegetation variables of ecological interest.

Kimes, Daniel S.↗
DOE OSTI2019

Approach to qualification using E-PBF in-situ process monitoring in Ti-6Al-4V

Traditional design and qualification methodologies for parts manufactured by traditional methods are being applied to Additive Manufacturing (AM) without understanding the nuances of the machines. While mapping process variables and tracking build data is helpful, some variables such as build geometry, support structure, and part melt order have not been researched in depth. Changing these variables can result in significant variations in material properties and defect structure such that the process appears to be unreliable compared to traditional manufacturing. Hence, this research focuses on the need to understand the effects of overlooked variables such as melt order and nested geometry on the distribution of defects and bulk material properties in Ti-6Al-4 V alloy builds manufactured using the Arcam AB ® electron beam powder bed fusion process 1 . This work collected and analyzed process log data and near infrared (NIR) images for every layer to correlate trends in porosity formation and mechanical performance. The location of pores, while naturally stochastic, is greatly influenced by the cross-sectional area as detected by NIR images and correlates with the failure sites from uniaxial testing.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Machine-learning-based investigation of the variables affecting summertime lightning occurrence over the Southern Great Plains

Lightning is affected by many factors, many of which are not routinely measured, well understood, or accounted for in physical models. Several commonly used machine learning (ML) models have been applied to analyze the relationship between Atmospheric Radiation Measurement (ARM) data and lightning data from the Earth Networks Total Lightning Network (ENTLN) in order to identify important variables affecting lightning occurrence in the vicinity of the Southern Great Plains (SGP) ARM site during the summer months (June, July, August and September) of 2012 to 2020. Testing various ML models, we found that the random forest model is the best predictor among common classifiers. When convective clouds were detected, it predicts lightning occurrence with an accuracy of 76.9 % and an area under the curve (AUC) of 0.850. Using this model, we further ranked the variables in terms of their effectiveness in nowcasting lightning and identified geometric cloud thickness, rain rate and convective available potential energy (CAPE) as the most effective predictors. The contrast in meteorological variables between no-lightning and frequent-lightning periods was examined for hours with CAPE values conducive to thunderstorm formation. Besides the variables considered for the ML models, surface variables and mid-altitude variables (e.g., equivalent potential temperature and minimum equivalent potential temperature, respectively) have statistically significant contrasts between no-lightning and frequent-lightning hours. For example, the minimum equivalent potential temperature from 700 to 500 hPa is significantly lower during frequent-lightning hours compared with no-lightning hours. Finally, a notable positive relationship between the intracloud (IC) flash fraction and the square root of CAPE ($\sqrt{CAPE}$) was found, suggesting that stronger updrafts increase the height of the electrification zone, resulting in fewer flashes reaching the surface and consequently a greater IC flash fraction.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1983

Modular design attitude control system

The problem of applying modular attitude control to a rigid body - flexible suspension model of a flexible spacecraft with some state variables inaccessible was addressed by developing a sequence of single axis models and generating a series of reduced state linear observers of minimum order to reconstruct those scalar variables that were inaccessible. The specific single axis models treated consisted of two, three and four rigid bodies, respectively, interconnected by a flexible shaft passing through the mass centers of the bodies. Reduced state linear observers of all orders up to one less than the total number of scalar state variables were generated for each of the three single axis models cited.

Chichester, F. D.↗
DOE OSTI2023

Verification and validation of the open-source plasma fluid code: Zapdos

Zapdos is an open-source finite element plasma fluid solver based on the MOOSE multiphysics framework. This paper outlines Zapdos verification, benchmarking, and validation efforts for 1D and 2D RF capacitively coupled plasma discharge models for mid-range pressures (0.1 - 1 Torr). The verification process involved using the method of manufactured solutions to assess Zapdos spatial and temporal error convergence. L2 errors ranged from 10 -2 to 10 -4 , while the convergence’s slope were in agreement with the predicted slopes for the tested variable and time integration orders. The benchmarking process involved comparisons to previously results from the validated finite element code, LSODI. These works included 1D and 2D simulations for a range of plasma parameters (densities, temperatures, voltage, etc.). For the 1D cases, Zapdos and LSODI results were in very good agreement. In the 2D cases, variable behaviors matched, with slight discrepancies in peak values. The validation process involved comparisons to experimental works including electron density measurements by microwave interferometry and metastable density measurements by planar laser-induced fluorescence imaging. Results shown reasonable agreement at higher pressure, with results starting to diverge at low pressures. Furthermore, probable causes for this diverges are the limitation of the fluid assumption for plasmas at low pressure, or the need for more robust boundary conditions. Overall, Zapdos shown reasonable results for the verification, benchmarking, and validation efforts, and Zapdos can be downloaded at https://github.com/shannon-lab/zapdos.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗