Search NASA⌕ Search

SEARCH · Search NASA

Results for “Approximation methods”

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 361 records · Page 20
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

A Low-Rank Solver for the Navier--Stokes Equations with Uncertain Viscosity

In this work, we study an iterative low-rank approximation method for the solution of the steady-state stochastic Navier--Stokes equations with uncertain viscosity. The method is based on linearization schemes using Picard and Newton iterations and stochastic finite element discretizations of the linearized problems. For computing the low-rank approximate solution, we adapt the nonlinear iterations to an inexact and low-rank variant, where the solution of the linear system at each nonlinear step is approximated by a quantity of low rank. This is achieved by using a tensor variant of the GMRES method as a solver for the linear systems. We explore the inexact low-rank nonlinear iteration with a set of benchmark problems, using a model of flow over an obstacle, under various configurations characterizing the statistical features of the uncertain viscosity, and we demonstrate its effectiveness by extensive numerical experiments.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

A simple method of measuring the effective SRS coefficient in single-mode optical fibres and its applicability limits

This paper describes techniques for measuring the SRS coefficient in a wide spectral range, including the region of small Stokes shifts. A simple, approximate method is proposed for evaluating the SRS coefficient near a gain peak. Spectral dependences of the SRS coefficient are presented for various telecom fibres. (nonlinear optical phenomena)

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
NASA NTRS1990

Reduced size first-order subsonic and supersonic aeroelastic modeling

Various aeroelastic, aeroservoelastic, dynamic-response, and sensitivity analyses are based on a time-domain first-order (state-space) formulation of the equations of motion. The formulation of this paper is based on the minimum-state (MS) aerodynamic approximation method, which yields a low number of aerodynamic augmenting states. Modifications of the MS and the physical weighting procedures make the modeling method even more attractive. The flexibility of constraint selection is increased without increasing the approximation problem size; the accuracy of dynamic residualization of high-frequency modes is improved; and the resulting model is less sensitive to parametric changes in subsequent analyses. Applications to subsonic and supersonic cases demonstrate the generality, flexibility, accuracy, and efficiency of the method.

Karpel, Mordechay↗
DOE OSTI2018

SolarPILOT: A power tower solar field layout and characterization tool

This paper develops and demonstrates a new SolarPower tower Integrated Layout and Optimization Tool (SolarPILOT). The tool uses the analytical flux image Hermite series approximation originally implemented in the DELSOL3 software developed by Sandia National Laboratory in the early 1980s. By applying the analytical model to individual heliostat images rather than large groups or zones of heliostats, SolarPILOT can characterize a wide variety of heliostat field layouts. The individual heliostat modeling approach increases computational expense in comparison with DELSOL3, so SolarPILOT implements a number of improvements to the analytical approximation method to improve model accuracy and computational efficiency. This paper discusses several of these methods, including dynamic heliostat grouping to reduce the expense of intercept factor evaluation, approximation of annual productivity with a subset of time steps throughout the year, polygon clipping to accurately calculate inter-heliostat shadowing and blocking, receiver and tower geometry optimization, and a trigonometric image transformation technique that ensures model accuracy for small heliostats. SolarPILOT also integrates a Monte-Carlo ray tracing engine (SolTrace), providing improved receiver optical modeling capability, a user-friendly front end for geometry definition, and side-by-side validation of the analytical algorithms.

14 SOLAR ENERGY↗
DOE OSTI2016

Exact analytical solution of shear-induced flexural vibration of functionally graded piezoelectric beam

The priority of this paper is to obtain the exact analytical solution for free flexural vibration of FGPM beam actuated using the d{sub 15} effect. In piezoelectric actuators, the potential use of d{sub 15} effect has been of particular interest for engineering applications since shear piezoelectric coefficient d15 is much higher than the other piezoelectric coupling constants d{sub 31} and d{sub 33}. The applications of shear actuators are to induce and control the flexural vibrations of beams and plates. In this study, a modified Timoshenko beam theory is used where electric potential is assumed to vary sinusoidaly along the thickness direction. The material properties are assumed to be graded across the thickness in accordance with power law distribution. Hamilton's principle is employed to obtain the equations of motion along with the associated boundary conditions for FGPM beams. Exact analytical solution is derived thus obtained equations of motion. Results for clamped-clamped and clamped-free boundary conditions are presented. The presented result and method shell serve as benchmark for comparing the results obtained from the other approximate methods.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Efficient prediction of time- and angle-resolved photoemission spectroscopy measurements on a nonequilibrium BCS superconductor

We study how time- and angle-resolved photoemission (tr-ARPES) reveals the dynamics of BCS-type, s -wave superconducting systems with time-varying order parameters. Approximate methods are discussed, based on previous approaches to either optical conductivity or quantum dot transport, to enable computationally efficient prediction of photoemission spectra. One use of such predictions is to enable extraction of the underlying order parameter dynamics from experimental data, which is topical given the rapidly growing use of tr-ARPES in studying unconventional superconductivity. The methods considered model the two-time lesser Green's functions with an approximated lesser self-energy that describes relaxation by coupling of the system to two types of baths. The approach primarily used here also takes into consideration the relaxation of the excited states into equilibrium by explicitly including the level-broadening of the retarded and advanced Green's functions. Here, we present equilibrium and nonequilibrium calculations of tr-ARPES spectrum from our model and discuss the signatures of different types of superconducting dynamics.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Marginal unbiased score expansion and application to CMB lensing

Here, we present the marginal unbiased score expansion (MUSE) method, an algorithm for generic high-dimensional hierarchical Bayesian inference. MUSE performs approximate marginalization over arbitrary non-Gaussian latent parameter spaces, yielding Gaussianized asymptotically unbiased and near-optimal constraints on global parameters of interest. It is computationally much cheaper than exact alternatives like Hamiltonian Monte Carlo (HMC), excelling on funnel problems which challenge HMC, and does not require any problem-specific user supervision like other approximate methods such as variational inference or many simulation-based inference methods. MUSE makes possible the first joint Bayesian estimation of the delensed Cosmic Microwave Background (CMB) power spectrum and gravitational lensing potential power spectrum, demonstrated here on a simulated data set as large as the upcoming South Pole Telescope 3G 1500 deg 2 survey, corresponding to a latent dimensionality of ~6 million and of order 100 global bandpower parameters. On a subset of the problem where an exact but more expensive HMC solution is feasible, we verify that MUSE yields nearly optimal results. We also demonstrate that existing spectrum-based forecasting tools which ignore pixel-masking underestimate predicted error bars by only ~10%. This method is a promising path forward for fast lensing and delensing analyses which will be necessary for future CMB experiments such as SPT-3G, Simons Observatory, or CMB-S4, and can complement or supersede existing HMC approaches. The success of MUSE on this challenging problem strengthens its case as a generic procedure for a broad class of high-dimensional inference problems.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRSDate not supplied

Sonic Boom Propagation Model Based on a Single-Ray Jacobian

A sonic boom is a nonlinear event whose propagation can be modeled involving two stages. The first stage consists of ray path calculations using linear approximations, while the second stage deals with a nonlinear transport of the acoustic energy along these paths. This presentation discusses a second-order finite difference numerical approach used to predict the ray paths in range-dependent atmospheres and compares it to existing finite difference schemes. The approach is validated using exact solutions obtained for stratified atmospheres. In the second stage, the geometrical spreading effect needed in determining sonic boom waveforms from a Burgers' equation is obtained using a method that only needs a single ray rather than four rays required by most existing sonic boom propagation codes. The single-ray method calculates the Jacobian, associated with the coordinate transformation from a suitable ray coordinate system to the Cartesian coordinate system, directly from the ray tracing equations. While the four-ray method approximates the geometrical spreading using a finite difference scheme involving the four rays, the single-ray method does not rely on this approximation and instead depends purely on the acoustical kinematic properties of the atmosphere. Comparisons of results using these two methods are discussed.

sonic boom↗
NASA NTRS2021

Thermal Inspection of a Composite Fuselage Section Using theMethod of Proper Generalized Decomposition

Proper Generalized Decomposition (PGD) is a reduced order modeling technique for the simulation of physical systems whose governing equations depend on boundary conditions, initial conditions, material properties, and geometric parameters. It uses separated representations of system covariates combined with an iterative approximation method known as successive enrichment in order to compute an accurate parameter-dependent approximation to the full governing equations. PGD can also be used as an alternative to the Singular Value Decomposition (SVD) of a matrix and therefore as an alternative to PCA thermography. In this paper PGD was used to analyze data derived from the inspection of a composite fuselage forward section using flash thermography, and the results were compared against the standard PCA approach.

Nondestructive Evaluation↗
DOE OSTI2021

Late-time small body disruptions for planetary defense

Here, diverting hazardous small bodies on impact trajectories with the Earth can in some circumstances be impossible without risking disrupting them. Disruption is a much more difficult planetary defense scenario to assess, being linked both to the response of the body to shock loading and the much more complicated gravitational dynamics of the fragments in the solar system relative to pure deflection scenarios. In this work we present a new simulation suite built on N-body gravitational methods that solves fragment orbits in the full gravitational system without recourse to more approximate methods. We assess the accuracy of our simulations and the simplifying assumptions we adopt to make the system tractable, and then discuss in more detail several specific, plausible planetary defense scenarios based on real close encounters. We find that disruption can be a very effective planetary defense strategy even for very late (sub-year) interventions, and should be considered an effective backup strategy should preferred methods, which require long warning times, fail.

42 ENGINEERING↗
DOE OSTI2015

Ion energy-angle distribution functions at the plasma-material interface in oblique magnetic fields

The ion energy-angle distribution (IEAD) at the wall of a magnetized plasma is of fundamental importance for the determination of the material processes occurring at the plasma-material interface, comprising secondary emissions and material sputtering. Here, we present a numerical characterization of the IEAD at the wall of a weakly collisional magnetized plasma with the magnetic field inclined at an arbitrary angle with respect to the wall. The analysis has been done using two different techniques: (1) a fluid-Monte Carlo method, and (2) particle-in-cell simulations, the former offering a fast but approximate method for the determination of the IEADs, the latter giving a computationally intensive but self-consistent treatment of the plasma behavior from the quasi-neutral region to the material boundary. The two models predict similar IEADs, whose similarities and differences are discussed. Data are presented for magnetic fields inclined at angles from normal to grazing incidence (0°–85°). We show the scaling factors of the average and peak ion energy and trends of the pitch angle at the wall as a function of the magnetic angle, for use in the correlation of fluid plasma models to material models.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1974

A recurrence matrix method for the analysis of longitudinal and torsional vibrations in non-uniform multibranch beams with variable boundary conditions

An approximate method for calculating the longitudinal and torsional natural frequencies and associated modal data of a beamlike, variable cross section multibranch structure is presented. The procedure described is the numerical integration of the first order differential equations that characterize the beam element in longitudinal motion and that satisfy the appropriate boundary conditions.

Davis, R. B.↗
NASA NTRS1979

Comparison of three-dimensional panel methods with strip boundary-layer simulations to experiment

Several three dimensional surface panel methods coupled on a streamwise strip basis to two dimensional boundary layer methods were compared to experimental data. Several different boundary layer simulations were investigated. Comparable boundary layer effects which converge to the expected two dimensional result wind increasing aspect ratio were indicated by either a transpiration or camber line displacement simulation. The method was applied to several varied configurations. The lift predictions agreed well with an approximate method based on correcting the inviscid lift using the two dimensional section viscous characteristics. The wing pressures and the effect of the boundary layer on the wing pressures were predicted accurately.

Kjelgaard, S. O.↗
NASA NTRS1981

Helicopter rotor loads using a matched asymptotic expansion technique

The theoretical basis and computational feasibility of the Van Holten method, and its performance and range of validity by comparison with experiment and other approximate methods was examined. It is found that within the restrictions of incompressible, potential flow and the assumption of small disturbances, the method does lead to a valid description of the flow. However, the method begins to break down under conditions favoring nonlinear effects such as wake distortion and blade/rotor interaction.

Pierce, G. A.↗
NASA NTRS1993

Nongray gas analyses for reflecting walls utilizing a flux technique

A flux formulation for a planar slab of molecular gas radiation bounded by diffuse reflecting walls is developed. While this formulation is limited to the planar geometry, it is useful for studying approximations necessary in modeling nongray radiative heat transfer. The governing equations are derived by considering the history of multiple reflections between the walls. Accurate solutions are obtained by explicitly accounting for a finite number of reflections and approximating the spectral effects of the remaining reflections. Four approximate methods are presented and compared using a single absorption band of H2O. All four methods reduce to an identical zeroth-order formulation, which accounts for all reflections approximately but does handle nonreflected radiation correctly. A single absorption band of CO2 is also considered using the best-behaved approximation for higher orders. A zeroth-order formulation is sufficient to predict the radiative transfer accurately for many cases considered. For highly reflecting walls, higher order solutions are necessary for better accuracy. Including all the important bands of H2O, the radiative source distributions are also obtained for two different temperature and concentration profiles.

Menart, J. A.↗
DOE OSTI2016

Application of Variance Reduction Techniques in RMC Burnup and Thermal-Hydraulic Coupled Calculation

In reactor analog simulation, the Monte Carlo method has relatively high fidelity since it can reduce calculation errors resulting from using approximation methods by describing complex geometry and neutron energy spectra. The Monte Carlo method is, in essence, a stochastic simulation of the neutron transport process, and statistical uncertainty of all the computed results must be provided. In large-scale reactor computation, this method can accurately estimate integral quantities such as the effective multiplication factor (K{sub eff}), and it can limit the uncertainty within an acceptable range via reasonably selecting simulation particles. Nevertheless, it faces great challenges in estimating local quantities like neutron flux and fission power, with uncertainty of estimators beyond acceptance. To decrease the uncertainty of local quantities by increasing simulation particles may cost much time and reduce efficiency. The main reasons are as follows. Firstly, the scale of reactors is so large that common pressurized water reactors have tens of thousands of lattice cells; secondly, uneven distribution of neutron flux and fission power causes uneven distribution of uncertainty. Smith K. puts forward the 95/95 principle to estimate whether uncertainty calculated with Monte Carlo Code satisfies the requirement. According to the principle, with a confidence level of 95%, statistical errors of power density in more than 95% of the regions should be less than 1%. To meet the requirement of the principle, the uniform fission site (UFS) method is raised currently. UFS aims at redistributing fission sources to uniformize the fission source sampling, which can make statistical variance distribution more uniform. This method, which is easy to use, will not obviously increase computation time. Many studies show that UFS has a good variance reduction effect in Monte Carlo criticality calculation, but less attention is paid to its performance in burnup calculation and thermal-hydraulic coupled calculation. Uncertainty arising from the Monte Carlo method has a large impact on burnup calculation and thermal-hydraulic coupled calculation. Variance propagates between burnup steps and between iterative steps of coupled calculation, which causes asymmetry of results of the physical symmetrical regions and instability of coupled iterative convergence errors. To further verify the effect of UFS, this study uses it in the RMC (the Reactor Monte Carlo code) burnup calculation module and the neutronics/thermohydraulics coupled calculation module, and conducts two-dimensional pressurized water reactor burnup calculation and BEAVRS benchmark thermalhydraulic coupled calculation. In this way, it verifies the improvement effect of UFS on variance propagation. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗