Search NASA⌕ Search

SEARCH · Search NASA

Results for “Numerical diffusion”

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 1,549 records · Page 86
All sourcesNASA NTRSDOE OSTI
NASA NTRS2016

Product of the SNPP VIIRS SD Screen Transmittance and the SD BRDF (RSB) From Both Yaw Maneuver and Regular On-Orbit Data

To assure data quality, the Earth-observing Visible Infrared Imaging Radiometer Suite (VIIRS) regularly performs on-orbit radiometric calibrations of its 22 spectral bands. The primary calibration radiance source for the reflective solar bands (RSBs) is a sunlit solar diffuser (SD). During the calibration process, sunlight goes through a perforated plate (the SD screen) and then strikes the SD. The SD scattered sunlight is used for the calibration, with the spectral radiance proportional to the product of the SD screen transmittance and the SD bidirectional reflectance distribution function (BRDF). The BRDF is decomposed to the product of its value at launch and a numerical factor quantifying its change since launch. Therefore, the RSB calibration requires accurate knowledge of the product of the SD screen transmittance and the BRDF (RSB; launch time). Previously, we calculated the product with yaw maneuver data and found that the product had improved accuracy over the prelaunch one. With both yaw maneuver and regular on orbit data, we were able to improve the accuracy of the SDSM screen transmittance and the product for the solar diffuser stability monitor SD view. In this study, we use both yaw maneuver and a small portion of regular on-orbit data to determine the product for the RSB SD view.

Lei, Ning↗
DOE OSTI2016

A comparison of Redlich-Kister polynomial and cubic spline representations of the chemical potential in phase field computations

Free energies play a central role in many descriptions of equilibrium and non-equilibrium properties of solids. Continuum partial differential equations (PDEs) of atomic transport, phase transformations and mechanics often rely on first and second derivatives of a free energy function. The stability, accuracy and robustness of numerical methods to solve these PDEs are sensitive to the particular functional representations of the free energy. In this communication we investigate the influence of different representations of thermodynamic data on phase field computations of diffusion and two-phase reactions in the solid state. First-principles statistical mechanics methods were used to generate realistic free energy data for HCP titanium with interstitially dissolved oxygen. While Redlich-Kister polynomials have formed the mainstay of thermodynamic descriptions of multi-component solids, they require high order terms to fit oscillations in chemical potentials around phase transitions. Here, we demonstrate that high fidelity fits to rapidly fluctuating free energy functions are obtained with spline functions. As a result, spline functions that are many degrees lower than Redlich-Kister polynomials provide equal or superior fits to chemical potential data and, when used in phase field computations, result in solution times approaching an order of magnitude speed up relative to the use of Redlich-Kister polynomials.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Quantifying local and global mass balance errors in physics-informed neural networks

Physics-informed neural networks (PINN) have recently become attractive for solving partial differential equations (PDEs) that describe physics laws. By including PDE-based loss functions, physics laws such as mass balance are enforced softly in PINN. This paper investigates how mass balance constraints are satisfied when PINN is used to solve the resulting PDEs. We investigate PINN’s ability to solve the 1D saturated groundwater flow equations (diffusion equations) for homogeneous and heterogeneous media and evaluate the local and global mass balance errors. We compare the obtained PINN’s solution and associated mass balance errors against a two-point finite volume numerical method and the corresponding analytical solution. We also evaluate the accuracy of PINN in solving the 1D saturated groundwater flow equation with and without incorporating hydraulic heads as training data. We demonstrate that PINN’s local and global mass balance errors are significant compared to the finite volume approach. Tuning the PINN’s hyperparameters, such as the number of collocation points, training data, hidden layers, nodes, epochs, and learning rate, did not improve the solution accuracy or the mass balance errors compared to the finite volume solution. Mass balance errors could considerably challenge the utility of PINN in applications where ensuring compliance with physical and mathematical properties is crucial.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Era of entropy: Synthesis, structure, properties, and applications of high-entropy materials

The field of high-entropy materials (HEMs) has emerged as a dynamic area of scientific exploration, driven by the exceptional properties arising from their compositional complexity. Encompassing both high-entropy alloys (HEAs) and high-entropy ceramics (HECs), these materials have garnered significant attention across diverse research domains. From investigations into phase evolution and mechanical characteristics to studies of ionic, electronic, and magnetic behaviors, HEMs demonstrate remarkable potential for a wide array of applications. These range from catalysis and tribology to energy storage and superconductivity. Fundamental research has shed light on crucial phenomena such as configurational entropy, lattice distortion, and sluggish diffusion. These discoveries are paving the way for materials design strategies that enable new functional tunability and resistance to application-specific harsh environments. This burgeoning field promises to revolutionize material design and performance across numerous technological sectors. Here, this special collection between Applied Physics Letters and the Journal of Applied Physics provides a timely overview of the latest research in this area. It highlights the growing interest in understanding the impact of high compositional complexity on conventional structure–process–property–performance relationships in HEMs.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Generative unfolding with distribution mapping

Machine learning enables unbinned, highly-differential cross section measurements. A recent idea uses generative models to morph a starting simulation into the unfolded data. We show how to extend two morphing techniques, Schrödinger Bridges and Direct Diffusion, in order to ensure that the models learn the correct conditional probabilities. This brings distribution mapping (DM) to a similar level of accuracy as the state-of-the-art conditional generative unfolding methods. Numerical results are presented with a standard benchmark dataset of single jet substructure as well as for a new dataset describing a 22-dimensional phase space of Z+2 -jets.

Butter, Anja↗
NASA NTRS1974

Analysis of chromatograph systems using orthogonal collocation

Research is generating fundamental engineering design techniques and concepts for the chromatographic separator of a chemical analysis system for an unmanned, Martian roving vehicle. A chromatograph model is developed which incorporates previously neglected transport mechanisms. The numerical technique of orthogonal collocation is studied. To establish the utility of the method, three models of increasing complexity are considered, the latter two being limiting cases of the derived model: (1) a simple, diffusion-convection model; (2) a rate of adsorption limited, inter-intraparticle model; and (3) an inter-intraparticle model with negligible mass transfer resistance.

Woodrow, P. T.↗
NASA NTRS1974

Radiation from an array of gray circular fins of trapezoidal profile

A numerical method is developed to calculate the temperature distribution and radiation heat transfer for an annular fin and tube radiator, with fins having trapezoidal profiles. All surfaces are assumed gray and to emit and reflect diffusely. Radiative interactions between adjacent fins and between the fins and tube are included. The thermal conductivity of the fin material may vary linearly with temperature. Results of a parametric study of the special case of circular fins of triangular profile having constant thermal conductivity are presented and used to optimize a fin array with respect to minimum weight.

Schnurr, N. M.↗
NASA NTRS1979

Anomalous growth of single ice crystals in solution

It is shown that major discrepancies exist between experiments and theory for ice crystal growth from solution. Accurate data, taken in a microgravity environment, approximate analytical models, and exact (probably numerical) models all are needed to advance our understanding of ice crystal growth phenomena. A new approximate semi-empirical theory is presented which predicts that a relatively sharp transition from natural convection control to diffusion control for ice growth in pure water occurs at a subcooling of about 10 C (a reduced temperature difference of about 0.125). No reliable data exist to test this prediction. The theory also predicts qualitatively the growth of ice in NaCl solution in which maxima in the growth rates are observed at various levels of subcooling.

Gill, W. N.↗
NASA NTRS1984

Turbulent compressible convection in a deep atmosphere. II - Two-dimensional results for main-sequence A5 and F0 type envelopes

In the present two-dimensional numerical study of turbulent compressible convection in the A5 and F0 main-sequence envelope types, ionization effects are included in the equation of state of the gas, and radiative transfer is modeled in a diffusive process with tabulated gas opacities. It is noted that the thermal effects of ionization significantly affect the dynamics of the flows and that an inversion of the mean density can be created and sustained in a dynamical situation. The substantial differences in the flows of A5 and F0 indicate development trends in the transition from the radiative to the convective mode of energy transport. As convection becomes more effective, the flow becomes more turbulent and the scaling effects of local scale heights become more significant.

Sofia, S.↗
NASA NTRS1986

Measurement and prediction of flow through a replica segment of a mildly atherosclerotic coronary artery of man

Pressure distributions were measured along a hollow vascular axisymmetric replica of a segment of the left circumflex coronary artery of man with mildly atherosclerotic diffuse disease. A large range of physiological Reynolds numbers from about 60 to 500, including hyperemic response, was spanned in the flows investigation using a fluid simulating blood kinematic viscosity. Predicted pressure distributions from the numerical solution of the Navier-Stokes equations were similar in trend and magnitude to the measurements. Large variations in the predicted velocity profiles occurred along the lumen. The influence of the smaller scale multiple flow obstacles along the wall (lesion variations) led to sharp spikes in the predicted wall shear stresses. Reynolds number similarity was discussed, and estimates of what time averaged in vivo pressure drop and shear stress might be were given for a vessel segment.

Back, L. H.↗
NASA NTRS1986

Smoothing and the second law

The technique of obtaining second order, oscillation free, total variation diminishing (TVD), scalar difference schemes by adding a limited diffusion flux (smoothing) to a second order centered scheme is explored. It is shown that such schemes do not always converge to the correct physical answer. The approach presented here is to construct schemes that numerically satisfy the second law of thermodynamics on a cell by cell basis. Such schemes can only converge to the correct physical solution and in some cases can be shown to be TVD. An explicit scheme with this property and second order spatial accuracy was found to have an extremely restrictive time step limitation (Delta t less than Delta x squared). Switching to an implicit scheme removed the time step limitation.

Merriam, Marshal L.↗
NASA NTRS1987

Measurement of opaque film thickness

The theoretical and experimental framework for thickness measurements of thin metal films by low frequency thermal waves is described. Although it is assumed that the films are opaque and the substrates are comparatively poor thermal conductors, the theory is easily extended to other cases of technological interest. A brief description is given of the thermal waves and the experimental arrangement and parameters. The usefulness of the technique is illustrated for making absolute measurements of the thermal diffusivities of isotropic substrate materials. This measurement on pure elemental solids provides a check on the three dimensional theory in the limiting case of zero film thickness. The theoretical framework is then presented, along with numerical calculations and corresponding experimental results for the case of copper films on a glass substrate.

Thomas, R. L.↗
NASA NTRS1988

Element-by-element and implicit-explicit finite element formulations for computational fluid dynamics

Preconditioner algorithms to reduce the computational effort in FEM analyses of large-scale fluid-dynamics problems are presented. A general model problem is constructed on the basis of the convection-diffusion equation and the two-dimensional vorticity/stream-function formulation of the Navier-Stokes equations; this problem is then analyzed using element-by-element, implicit-explicit, and adaptive implicit-explicit approximation schemes. Numerical results for the two-dimensional advection and rigid-body rotation of a cosine hill, flow past a circular cylinder, and driven cavity flow are presented in extensive graphs and shown to be in good agreement with those obtained using implicit methods.

Tezduyar, T. E.↗
NASA NTRS1990

Linear tearing modes of a forced current-sheet equilibrium

Linear tearing modes are studied in a nearly singular forced current-sheet equilibrium, such as could result from global magnetic forces in the solar corona. Growth rates for the tearing modes, determined by solving the linearized reduced MHD (Strauss) equations numerically, were found to scale as (gamma)tau(d) = about S exp 4/5 k(y) exp 4/5, where S is the Lundquist number, k(y) is the wavenumber, and tau(d) is the classical resistive diffusion time. This scaling is in agreement with predictions from analytical theory. Because of the faster S scaling of these modes compared to the tearing modes of a diffuse current-sheet equilibrium, the modes have much higher growth rates (by a factor of about 10,000) for coronal values of S (about 10 to the 12th). For coronal parameters, the growth times of these new modes are estimated to be on the order of several hours to days, as compared to growth times of months to years for the tearing modes in a diffuse current-shear equilibrium. The growth times are comparable to reconnection times scales required in models of coronal heating by magnetic field dissipation.

Liewer, Paulett C.↗
NASA NTRS1993

Correcting for diffraction in the far-infrared reflectance measurement of rough surfaces

The manner in which diffraction can increase the reflectance measured from very rough surfaces is shown by observations of diffracted light within the instrument profile of a far-IR reflectometer system. A correction to the calibration signal based on numerical integration of the diffracted part of the instrument profile is described. Diffraction correction factors as large as 2.94 have been found with small optics at long wavelength (630 microns). The effect of diffraction on diffuse reflectance measurements of a very rough perfect reflector is shown at wavelengths from 56 to 200 microns.

Smith, Sheldon M.↗
NASA NTRS1994

Tectonic and climatic significance of a late Eocene low-relief, high-level geomorphic surface, Colorado

New paleobotanical data suggest that in the late Eocene the erosion surface which capped the Front Range, Colorado was 2.2-2.3 km in elevation, which is similar to the 2.5-km present elevation of surface remnants. This estimated elevation casts doubt on the conventional belief that the low-relief geomorphic surface was formed by lateral planation of streams to a base level not much higher than sea level and that the present deeply incised canyons must represent Neogene uplift of Colorado. Description of the surface, calculations of sediment volume, and isostatic balance and fluvial landsculpting models demonstrate that while the high elevation of the erosion surface was due to tectonic forces, its smoothness was mostly a result of climatic factors. A sediment balance calculated for the Front Range suggests that from 2 to 4 km of material were eroded by the late Eocene, consistent with fission track ages. This amount of erosion would remove a significant portionof the 7 km of Laramide upper crustal thickening. Isostatic modeling implies that the 2.2-3.3 km elevation was most likely created by lower crustal thickening during the Laramide. A numerical model of fluvial erosion and deposition suggests a way that a late Eocene surface could have formed at this high elevation without incision. A humid climate with a preponderance of small storm events will diffusively smooth topography and is a possible mechanism for formation oflow-relief, high-level surfaces. Paleoclimate models suggest a lack of large strom events in the late Eocene because of cool sea surface temperatures in the equatorial region. Return to a drier but stormier climate post-Eocene could have caused the incision of the surface by young canyons. By this interpretation, regional erosion surfaces may represent regional climatic rather than tectonic conditions.

Gregory, Kathryn M.↗
NASA NTRS1993

Partially Coherent Scattering in Stellar Chromospheres: Analytic Wing Approximations - Part 4

Simple analytic expressions are derived to understand resonance-line wings in stellar chromospheres and similar astrophysical plasmas. The results are approximate, but compare well with accurate numerical simulations. The redistribution is modeled using an extension of the partially coherent scattering approximation (PCS) which we term the comoving-frame partially coherent scattering approximation (CPCS). The distinction is made here because Doppler diffusion is included in the coherent/noncoherent decomposition, in a form slightly improved from the earlier papers in this series.

Gayley, K. G.↗
NASA NTRS1998

The Oxidation of AlN in Dry and Wet Oxygen

The oxidation kinetics of AlN containing 3.5 wt% Y2O3 were studied by thermogravimetric analysis in dry oxygen and 10% H2O/balance oxygen at temperatures between 1000 and 1200 C for times between 48 and 100 h. The oxidation kinetics for AlN in dry oxygen were parabolic and of approximately the same magnitude and temperature dependence as other alumina forming materials. In this case, diffusion of oxygen and/or aluminum through the alumina scale is the rate limiting mechanism. The oxidation kinetics for AlN in wet oxygen were nearly linear and much more rapid than rates observed in dry oxygen. Numerous micropores were observed in the alumina formed on AIN in wet oxygen. These pores provide a fast path for oxygen transport. The linear kinetics observed in this case suggest that the interface reaction rate of AlN with wet oxygen is the oxidation rate limiting step.

Opila, Elizabeth↗