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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 847 records · Page 47
All sourcesNASA NTRSDOE OSTI
NASA NTRS1986

Using Hough harmonics to validate and assess nonlinear shallow-water models

The implementation of a technique for locating programming errors in shallow-water codes, establishing the correctness of the code, and assessing the performance of the numerical model under various flow conditions is described. The right-hand side of the differential equations is modified in such a way that the exact solution of the nonlinear initial-value problem is known, so that the truncation errors of the numerical scheme can be studied in detail. The exact solution is prescribed to be any linear combination of Hough harmonics which propagate in time according to their natural frequencies.

Dee, Dick P.↗
NASA NTRS1989

Far field beam pattern of one MW combined beam of laser diode array amplifiers for space power transmission

The far-field beam pattern and the power-collection efficiency are calculated for a multistage laser-diode-array amplifier consisting of about 200,000 5-W laser diode arrays with random distributions of phase and orientation errors and random diode failures. From the numerical calculation it is found that the far-field beam pattern is little affected by random failures of up to 20 percent of the laser diodes with reference of 80 percent receiving efficiency in the center spot. The random differences in phases among laser diodes due to probable manufacturing errors is allowed to about 0.2 times the wavelength. The maximum allowable orientation error is about 20 percent of the diffraction angle of a single laser diode aperture (about 1 cm). The preliminary results indicate that the amplifier could be used for space beam-power transmission with an efficiency of about 80 percent for a moderate-size (3-m-diameter) receiver placed at a distance of less than 50,000 km.

Kwon, Jin H.↗
DOE OSTI2025

Micrometer: Micromechanics transformer for predicting full field mechanical responses of heterogeneous materials

Predicting mechanical responses of heterogeneous materials across scales remains a significant challenge. Traditional computational methods often struggle with complex and multiscale nature of these materials, limiting their effectiveness in real-world applications. Here, in this paper, we introduce Micrometer, a vision transformer based deep learning model designed to predict full field mechanical responses of heterogeneous materials, bridging the gap between computer vision and solid mechanics problems. We show that Micrometer, trained on a large-scale high-resolution dataset of 2D fiber-reinforced composites, can achieve state-of-the-art performance in predicting microscale strain fields across a wide range of material properties and loading conditions. Our model demonstrates accuracy and computational efficiency in applications such as computational homogenization and multiscale modeling, reducing computational time by up to two orders of magnitude compared to conventional numerical solvers while maintaining less than 1 % errors in predicting macroscale stress fields. Furthermore, we showcase Micrometer’s adaptability through transfer learning experiments on new materials with limited data, highlighting its potential to tackle diverse scenarios in computational solid mechanics. These results represent a significant step towards AI-driven innovation in materials science, addressing the limitations of traditional numerical methods and paving the way for more efficient simulations of heterogeneous materials across various industrial applications.

Composite materials↗
DOE OSTI2020

Analysis and improvement of the hot disk transient plane source method for low thermal conductivity materials

The hot disk transient plane source (TPS) method is a widely used standard technique (ISO 22007-2) for the characterization of thermal properties of materials, especially the thermal conductivity, k. Despite its well-established reliability for a wide variety of common materials, the hot disk TPS method is also known to suffer from a substantial systematic errors when applied to low-k thermal insulation materials. Here, we present a combined numerical and experimental study on the influence of the geometry of hot disk sensor on measured value of low-k materials. We demonstrate that the error is strongly affected by the finite thickness and thermal mass of the sensor's insulation layer was well as the corresponding increase of the effective heater size beyond the radius of the embedded metal heater itself. We also numerically investigate the dependence of the error on the sample thermal properties, confirming that the errors are worse in low-k samples. A simple correction function is also provided, which converts the apparent (erroneous) result from a standard hot disk TPS measurement to a more accurate value. A standard polyimide sensor was also optimized using both wet and dry etching to provide more accurate measurement directly. Experimentally corrected value of k for Airloy x56 aerogel and a commercial silica aerogel using the numerical correction factor derived based on the standard TPS sensor is in excellent agreement with the directly measured value from the TPS sensor using the optimized polyimide sensor. Finally, both of these methods can reduce the errors to less than 4% as compared to around 40% error of overestimation from raw values measured with the pristine sensor. Such results show that both the numerical correction to a pristine senor or an optimized sensor are capable of providing highly accurate value of thermal conductivity for such materials.

36 MATERIALS SCIENCE↗
DOE OSTI2019

High Order Discontinuous Galerkin Method and Applications (Final Technical Report)

This project aims at the developments and improvements of high order accurate discontinuous Galerkin finite element methods for solving partial differential equations arising from DOE applications. Algorithm development, improvement, analysis, implementation and applications aspects are addressed. The partial differential equations under study involve solutions with shocks or other discontinuities, rapidly changing regions, or multiscale solutions. These include the so-called convection dominated cases, such as the hyperbolic equations (e.g. Euler equations of gas dynamics), parabolic equations with small viscosities (e.g. high Reynolds number Navier-Stokes equations), KdV type equations with small dispersion describing water waves (small third derivative terms), time-dependent bi-harmonic equations and equations with hyper-viscosity (small fourth or higher even derivative terms), problems with highly oscillatory coefficients, or problems for which the macro-scale PDE models may not be correct in localized regions and a micro-scale model must be used instead. Furthermore, we are interested in the long time solutions of such equations with waves traveling a long distance, such as the electromagnetic waves. The requirement on numerical methods is thus high order accuracy, low dissipation/dispersion errors over long time, and a clean and sharp discontinuity resolution. It would also be highly desirable to have the numerical methods to be flexible for complicated geometry and boundary conditions, and to be easy in an adaptive and massively parallel environment. The discontinuous Galerkin finite element method has this potential, however the design and analysis of the discontinuous Galerkin method for each specific class of partial differential equations would require detailed research.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2007

Global Distortion of GPS Networks Associated with Satellite Antenna Model Errors

Recent studies of the GPS satellite phase center offsets (PCOs) suggest that these have been in error by approx.1 m. Previous studies had shown that PCO errors are absorbed mainly by parameters representing satellite clock and the radial components of site position. On the basis of the assumption that the radial errors are equal, PCO errors will therefore introduce an error in network scale. However, PCO errors also introduce distortions, or apparent deformations, within the network, primarily in the radial (vertical) component of site position that cannot be corrected via a Helmert transformation. Using numerical simulations to quantify the effects of PC0 errors, we found that these PCO errors lead to a vertical network distortion of 6-12 mm per meter of PCO error. The network distortion depends on the minimum elevation angle used in the analysis of the GPS phase observables, becoming larger as the minimum elevation angle increases. The steady evolution of the GPS constellation as new satellites are launched, age, and are decommissioned, leads to the effects of PCO errors varying with time that introduce an apparent global-scale rate change. We demonstrate here that current estimates for PCO errors result in a geographically variable error in the vertical rate at the 1-2 mm/yr level, which will impact high-precision crustal deformation studies.

Cardellach, E.↗
DOE OSTI2021

Error estimates of finite difference methods for the Dirac equation in the massless and nonrelativistic regime

We present four frequently used finite difference methods and establish the error bounds for the discretization of the Dirac equation in the massless and nonrelativistic regime, involving a small dimensionless parameter 0 < ε &NestedLessLess; 1 inversely proportional to the speed of light. In the massless and nonrelativistic regime, the solution exhibits rapid motion in space and is highly oscillatory in time. Specifically, the wavelength of the propagating waves in time is at O(ε), while in space, it is at O(1) with the wave speed at O(ε -1 ). We adopt one leap-frog, two semi-implicit, and one conservative Crank-Nicolson finite difference methods to numerically discretize the Dirac equation in one dimension and establish rigorously the error estimates which depend explicitly on the time step τ, mesh size h, and the small parameter ε. The error bounds indicate that, to obtain the “correct” numerical solution in the massless and nonrelativistic regime, i.e., 0 < ε &NestedLessLess; 1, all these finite difference methods share the same ε-scalability as time step τ = O(ε 3/2 ) and mesh size h = O(ε 1/2 ). A large number of numerical results are reported to verify the error estimates.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1973

New mechanization equations for aided inertial navigation systems

Inertial navigation equations are developed which use area navigation (RNAV) waypoints and runway references as coodinate centers. The formulation is designed for aided inertial navigation systems and gives a high numerical accuracy through all phases of flight. A new formulation of the error equations for inertial navigation systems is also presented. This new formulation reduces numerical calculations in the use of Kalman filters for aided inertial navigation systems.

Schmidt, S. F.↗
NASA NTRS1988

Generation of a crowned pinion tooth surface by a plane

The topology of a crowned spur pinion tooth surface that reduces the level of transmission errors due to misalignment is described. The geometry of the modified pinion tooth surface and of the regular involute gear tooth surface is discussed. The tooth contact analysis between the meshing surfaces is also described. Generating a modified pinion tooth surface by a plane whose motion is controlled by a 5-degree-of-freedom system is investigated. The numerical results included indicate that the transmission error remains low as the gears are misaligned.

Litvin, F. L.↗
NASA NTRS1993

An end-to-end pointing budget approach to planetary observing systems with application to EOS

Previously published error budgets have focused on spacecraft error sources for pointing error and have tended to include only spacecraft pointing rather than the ultimate geolocation of each pixel of dam onto a well-defined spot on the surface of the Earth. A systematic approach to geolocation error budgeting, including all contributors in the geolocation process is presented. Its structure allows simultaneous expression of the needs of instrument teams as well as spacecraft design teams. It allows explicit acknowledgement of approximations made for on-board control as well as the ultimate geolocation accuracy achievable after ground processing and exploits the commonality inherent in the on-board and post-processing error budgets. It also includes the uncontrolled and unmeasured spacecraft jitter. This approach can be used to investigate the mission-wide benefit of a variety of design choices, (such as on-board sensing and ground correction of measurements contrasted with on-board correction of measurements). Additionally, in light of increasing accuracy requirements as sensor resolution improves, numerous non-spacecraft contributors to geolocation error are quantified.

Throckmorton, A.↗
NASA NTRS1985

Double symbol error rates for differential detection of narrow-band FM

This paper evaluates the double symbol error rate (average probability of two consecutive symbol errors) in differentially detected narrow-band FM. Numerical results are presented for the special case of MSK with a Gaussian IF receive filter. It is shown that, not unlike similar results previously obtained for the single error probability of such systems, large inaccuracies in predicted performance can occur when intersymbol interference is ignored.

Simon, M. K.↗
DOE OSTI2017

Application of Backward Differentiation Formulas to Neutron Kinetics Problems

The neutron kinetics equations belong to the class of stiff equations for numerical time integration schemes. In this work, the accuracy and speed of algorithms based on backward differentiation formulas (BDFs) are studied with regard to point and spatial neutron kinetics problems. Using a BDF algorithm with the automatic selection of time step and order, solutions to a number of model problems with both a positive and negative reactivity insertion are analyzed. Plots of numerical cost dependences on local and global errors are presented. The results indicate that algorithms based on BDFs are highly efficient and that their application to nuclear reactor simulation is justified.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS2003

Analytic Method for Computing Instrument Pointing Jitter

A new method of calculating the root-mean-square (rms) pointing jitter of a scientific instrument (e.g., a camera, radar antenna, or telescope) is introduced based on a state-space concept. In comparison with the prior method of calculating the rms pointing jitter, the present method involves significantly less computation. The rms pointing jitter of an instrument (the square root of the jitter variance shown in the figure) is an important physical quantity which impacts the design of the instrument, its actuators, controls, sensory components, and sensor- output-sampling circuitry. Using the Sirlin, San Martin, and Lucke definition of pointing jitter, the prior method of computing the rms pointing jitter involves a frequency-domain integral of a rational polynomial multiplied by a transcendental weighting function, necessitating the use of numerical-integration techniques. In practice, numerical integration complicates the problem of calculating the rms pointing error. In contrast, the state-space method provides exact analytic expressions that can be evaluated without numerical integration.

Bayard, David↗
NASA NTRS1987

Optical communication with semiconductor laser diodes

A 25 megabit/sec direct detection optical communication system that used Q=4 PPM signalling was constructed and its performance measured under laboratory conditions. The system used a single-mode AlGaAs laser diode transmitter and low noise silicon avalanche photodiode (APD) photodetector. Comparison of measured performance with the theoretical revealed that modeling the APD output as a Gaussian process under conditions of negligible background radiation and low (less than 10 to the -12 power A) APD bulk leakage currents leads to substantial underestimates of optimal APD gain to use and overestimates of system bit error probability. A procedure is given to numerically compute system performance which uses the more accurate Webb's Approximation of the exact Conradi distribution for the APD ouput signal that does not require excessive amounts of computer time (a few minutes of VAX 8600 CPU time per system operating point). Examples are given which illustrate the breakdown of the Gaussian approximation in assessing system performance. This system achieved a bit error probability of 10 to the -6 power at a received signal energy corresponding to an average of 60 absorbed photons/bit and optimal APD gain of 700.

Davidson, F.↗
NASA NTRS1995

A well-posed numerical method to track isolated conformal map singularities in Hele-Shaw flow

We present a new numerical method for calculating an evolving 2D Hele-Shaw interface when surface tension effects are neglected. In the case where the flow is directed from the less viscous fluid into the more viscous fluid, the motion of the interface is ill-posed; small deviations in the initial condition will produce significant changes in the ensuing motion. This situation is disastrous for numerical computation, as small round-off errors can quickly lead to large inaccuracies in the computed solution. Our method of computation is most easily formulated using a conformal map from the fluid domain into a unit disk. The method relies on analytically continuing the initial data and equations of motion into the region exterior to the disk, where the evolution problem becomes well-posed. The equations are then numerically solved in the extended domain. The presence of singularities in the conformal map outside of the disk introduces specific structures along the fluid interface. Our method can explicitly track the location of isolated pole and branch point singularities, allowing us to draw connections between the development of interfacial patterns and the motion of singularities as they approach the unit disk. In particular, we are able to relate physical features such as finger shape, side-branch formation, and competition between fingers to the nature and location of the singularities. The usefulness of this method in studying the formation of topological singularities (self-intersections of the interface) is also pointed out.

Baker, Gregory↗
NASA NTRS1993

Solution of elastic-plastic stress analysis problems by the p-version of the finite element method

The solution of small strain elastic-plastic stress analysis problems by the p-version of the finite element method is discussed. The formulation is based on the deformation theory of plasticity and the displacement method. Practical realization of controlling discretization errors for elastic-plastic problems is the main focus. Numerical examples which include comparisons between the deformation and incremental theories of plasticity under tight control of discretization errors are presented.

Szabo, Barna A.↗