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At least 991 records · Page 55
All sourcesNASA NTRSDOE OSTI
NASA NTRS1991

Numerical models of giant planet formation with rotation

A 1D quasi-spherical approximation is presently used under the assumption of hydrostatic equilibrium to model giant-planet formation processes that encompass the accretion and transport of angular momentum for both radiative and convective zones. These calculations have been conducted up to masses comparable to those of Saturn. Angular momentum transport is strong, leading to strong concentration of angular momentum in the outer convective zones which develop envelope masses greater than 30 earth masses. When the models are allowed to contract near the calculation's end, the ratio of centrifugal force to gravity at the outer radius rises sufficiently to validate the quasi-spherical approximation.

Korycansky, D. G.↗
NASA NTRS1978

The accuracy of the narrow seal approximation in analyzing radial face seals

The accuracy of the narrow seal approximation which enables closed form analytical solutions for radial face seals is examined in this paper. Both hydrostatic and hydrodynamic effects in a flat, misaligned seal are considered. Analytical results obtained from a simplified Reynolds equation, based on the neglect of circumferential pressure gradient and seal curvature, are compared with accurate results from numerical solution of the complete Reynolds equation. The agreement between the approximate and accurate solutions is quite reasonable over a wide range of a seal's inner-to-outer radius ratio. For radius ratios greater than 0.8, the accuracy of the narrow seal approximation is better than 1 percent over most of the range of angular misalignment.

Etsion, I.↗
NASA NTRS1994

Large Eddy simulation of turbulence: A subgrid scale model including shear, vorticity, rotation, and buoyancy

The Reynolds numbers that characterize geophysical and astrophysical turbulence (Re approximately equals 10(exp 8) for the planetary boundary layer and Re approximately equals 10(exp 14) for the Sun's interior) are too large to allow a direct numerical simulation (DNS) of the fundamental Navier-Stokes and temperature equations. In fact, the spatial number of grid points N approximately Re(exp 9/4) exceeds the computational capability of today's supercomputers. Alternative treatments are the ensemble-time average approach, and/or the volume average approach. Since the first method (Reynolds stress approach) is largely analytical, the resulting turbulence equations entail manageable computational requirements and can thus be linked to a stellar evolutionary code or, in the geophysical case, to general circulation models. In the volume average approach, one carries out a large eddy simulation (LES) which resolves numerically the largest scales, while the unresolved scales must be treated theoretically with a subgrid scale model (SGS). Contrary to the ensemble average approach, the LES+SGS approach has considerable computational requirements. Even if this prevents (for the time being) a LES+SGS model to be linked to stellar or geophysical codes, it is still of the greatest relevance as an 'experimental tool' to be used, inter alia, to improve the parameterizations needed in the ensemble average approach. Such a methodology has been successfully adopted in studies of the convective planetary boundary layer. Experienc e with the LES+SGS approach from different fields has shown that its reliability depends on the healthiness of the SGS model for numerical stability as well as for physical completeness. At present, the most widely used SGS model, the Smagorinsky model, accounts for the effect of the shear induced by the large resolved scales on the unresolved scales but does not account for the effects of buoyancy, anisotropy, rotation, and stable stratification. The latter phenomenon, which affects both geophysical and astrophysical turbulence (e.g., oceanic structure and convective overshooting in stars), has been singularly difficult to account for in turbulence modeling. For example, the widely used model of Deardorff has not been confirmed by recent LES results. As of today, there is no SGS model capable of incorporating buoyancy, rotation, shear, anistropy, and stable stratification (gravity waves). In this paper, we construct such a model which we call CM (complete model). We also present a hierarchy of simpler algebraic models (called AM) of varying complexity. Finally, we present a set of models which are simplified even further (called SM), the simplest of which is the Smagorinsky-Lilly model. The incorporation of these models into the presently available LES codes should begin with the SM, to be followed by the AM and finally by the CM.

Canuto, V. M.↗
DOE OSTI2020

Anharmonic phonon dispersion in polyethylene

The second-order Green's function method for anharmonic crystals has been applied to an infinite, periodic chain of polyethylene taking into account up to quartic force constants. The frequency-independent approximation to the Dyson self-energy gives rise to numerous divergent resonances, which are fortuitous. Instead, solving the Dyson equation self-consistently with a frequency-dependent self-energy resists divergences from resonances or zero-frequency acoustic vibrations. Here, the calculated anharmonic phonon dispersion, which nonetheless displays many true resonances, and anharmonic phonon density of states furnish hitherto unknown details that explain smaller features of observed vibrational spectra.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1976

Higher-order numerical solutions using cubic splines

A cubic spline collocation procedure was developed for the numerical solution of partial differential equations. This spline procedure is reformulated so that the accuracy of the second-derivative approximation is improved and parallels that previously obtained for lower derivative terms. The final result is a numerical procedure having overall third-order accuracy of a nonuniform mesh. Solutions using both spline procedures, as well as three-point finite difference methods, are presented for several model problems.

Rubin, S. G.↗
NASA NTRS1989

Some notes on shock resolving flux functions. Part 1: Stationary characteristics

Numerical flux functions for solving the Euler equations using exact and/or approximate solutions of the Riemann problem of gasdynamics are discussed. Under certain restrictive conditions, schemes using these flux functions produce systems of equations which can exhibit a single degree of freedom. In some instances, the solutions represented by this degree of freedom are unstable to perturbations. This local instability can seriously degrade the temporal convergence of numerical schemes. This point is demonstrated by numerical example.

Barth, Timothy J.↗
NASA NTRS1991

Numerical recovery of certain discontinuous electrical conductivities

The inverse problem of recovering an electrical conductivity of the form Gamma(x) = 1 + (k-1)(sub Chi(D)) (Chi(D) is the characteristic function of D) on a region omega is a subset of 2-dimensional Euclid space from boundary data is considered, where D is a subset of omega and k is some positive constant. A linearization of the forward problem is formed and used in a least squares output method for approximately solving the inverse problem. Convergence results are proved and some numerical results presented.

Bryan, Kurt↗
NASA NTRS1995

The effects of redshifts and focusing on the spectrum of an accretion disk in the galactic center black hole candidate Sagittarius A(sup *)

There are firm indications that Sgr A(sup *), a compact, nonthermal radio source at the Galactic center, may be powered by the dissipation of gravitational energy as gas trapped from an ambient wind descends down the potential well, first through a quasi-spherical inflow (extending out to approximately 3 x 10(exp 16) cm) and then through a small accretion disk at less than or approximately = 5-10 Schwarzschild radii. Earlier three-dimensional Bondi-Hoyle numerical simulations have indicated that fluctuations in the accreted specific angular momentum can lead to a variability in the disk flux on a timescale of years. With greatly improved flux measurements at K and H, and the hint of a approximately 10 minute modulation in the IR luminosity, it is crucial to model the disk emission much more precisely than has been attempted thus far. In this Letter we take into account the effects of Doppler and gravitational redshifts, the light-travel time factor, and the light bending near the black hole to determine the measurable spectrum of Sgr A(sup *) in the increasingly important 10(exp 13) Hz less than or approximately = v less than or approximately = 10(exp 16) Hz frequency range. We find that the relativistic disk spectrum is much softer than its Newtonian counterpart, with a predicted UV flux roughly an order of magnitude smaller than had previously been anticipated. In addition, we find that when the physical conditions in the disk are taken to be consistent with the properties of the quasi-spherical infall (specifically, in terms of the accretion rate and disk size), only a slowly spinning or Schwarzschild black hole appears to fit the observations. Our calculations also reveal that the disk flux is much more weakly dependent on the observer's inclination angle than had been suspected on the basis of earlier Newtonian estimates.

Hollywood, J. M.↗
NASA NTRS1994

Multi-dimensional combustor flowfield analyses in gas-gas rocket engine

The objectives of the present research are to improve design capabilities for low thrust rocket engines through understanding of the detailed mixing and combustions processes. Of particular interest is a small gaseous hydrogen-oxygen thruster which is considered as a coordinated part of an on-going experimental program at NASA LeRC. Detailed computational modeling requires the application of the full three-dimensional Navier Stokes equations, coupled with species diffusion equations. The numerical procedure is performed on both time-marching and time-accurate algorithms and using an LU approximate factorization in time, flux split upwinding differencing in space. The emphasis in this paper is focused on using numerical analysis to understand detailed combustor flowfields, including the shear layer dynamics created between fuel film cooling and the core gas in the vicinity on the nearby combustor wall; the integrity and effectiveness of the coolant film; three-dimensional fuel jets injection/mixing/combustion characteristics; and their impacts on global engine performance.

Tsuei, Hsin-Hua↗
NASA NTRS1974

On the passage of radiation through inhomogeneous, moving media. XI - Nonlinear effects on ray paths in the geometrical optics approximation

Study illustrating how the presence of a high-intensity pulse of radiation can distort its own passage through a plane differentially shearing medium. It is demonstrated that the distortion is a sensitive function of the precise, and detailed, variation of the medium's refractive index by considering a couple of simple examples which are worked out numerically. In view of the high-intensity pulses observed from pulsars (approximately 10 to the 30th ergs per pulse), it is believed that the present calculations are of more than academic interest in helping unravel the fundamental properties of pulse production in, and propagating through, differentially sheared media - such as pulsars' magnetospheres within the so-called speed-of-light circle.

Lee, M. A.↗
NASA NTRS1981

Rapid inversion of limb radiance data using an emissivity growth approximation

The time-consuming nature of limb relaxation-type inversion algorithms is due primarily to the numerous integrations over an absorption band to obtain forward radiance values with which to compare measured values. A new method has been devised for the quick and accurate (0.5% error) calculation of single gas broadband (approximately 100 per cm) limb radiance. The method uses a precalculated data base consisting of homogeneous path emissivity vs mass path data for a wide range of temperature and pressure. A 50-km altitude range, 1-km resolution, constituent inversion employing this method requires under 1 sec of computational time when run on modern computer hardware. The method does not rely upon a priori statistical knowledge.

Gordley, L. L.↗
DOE OSTI2022

Learning stochastic dynamics with statistics-informed neural network

We introduce a machine-learning framework named statistics-informed neural network (SINN) for learning stochastic dynamics from data. This new architecture was theoretically inspired by a universal approximation theorem for stochastic systems, which we introduce in this paper, and the projection-operator formalism for stochastic modeling. Here, we devise mechanisms for training the neural network model to reproduce the correct statistical behavior of a target stochastic process. Numerical simulation results demonstrate that a well-trained SINN can reliably approximate both Markovian and non-Markovian stochastic dynamics. We demonstrate the applicability of SINN to coarse-graining problems and the modeling of transition dynamics. Furthermore, we show that the obtained reduced-order model can be trained on temporally coarse-grained data and hence is well suited for rare-event simulations.

97 MATHEMATICS AND COMPUTING↗
NASA NTRSDate not supplied

Comparison of Multivariate Time Series Prediction Techniques for Emulating Noah-LSM Soil Moisture Outputs

Land surface models are crucial tools for many earth science applications including numerical weather prediction, water resource and crop monitoring, and climatological analysis. Given a set of atmospheric forcings, seasonal data, and static parameters, models like Noah-LSM solve for land surface quantities including skin temperature, sensible heat flux, and soil moisture. While these calculations are theoretically robust, they are often computationally expensive. Since artificial neural networks (ANNs) are universal function approximators, they can learn to emulate the output of a deterministic numerical model given a time series of input forcings, with the learned ANN having substantially shorter execution time. The ANN could efficiently parameterize other models, generate ensembles, and provide first-guess inputs for retrievals. As such, with the goal of developing a model that efficiently mimics the output of Noah-LSM given NLDAS2 forcings on a region covering much of the central US, we examine and compare several neural network architectures for the multi-horizon multivariate time series forecasting problem. Recent literature includes a diverse set of approaches including autoregressive architectures like LSTM and GRU, parametric and non-parametric statistical predictors (ForecastNet and MQRNN), self-attention (LSTM-attention-LSTM), and temporal convovlution (DeepTCN). We implement several of these models for the Noah-LSM prediction task, highlighting the features and challenges for each and providing practical insight on the training process.

Mitchell Dodson↗
NASA NTRS1989

Chebyshev Polynomials Are Not Always Optimal

The authors are concerned with the problem of finding among all polynomials of degree at most n and normalized to be 1 at c the one with minimal uniform norm on Epsilon. Here, Epsilon is a given ellipse with both foci on the real axis and c is a given real point not contained in Epsilon. Problems of this type arise in certain iterative matrix computations, and, in this context, it is generally believed and widely referenced that suitably normalized Chebyshev polynomials are optimal for such constrained approximation problems. In this note, the authors show that this is not true in general. Moreover, the authors derive sufficient conditions which guarantee that Chebyshev polynomials are optimal. Also, some numerical examples are presented.

CHEBYSHEV APPROXIMATION↗
DOE OSTI2021

Implementation of Monte Carlo Transport in the General Relativistic SpEC Code

Neutrino transport and neutrino-matter interactions are known to play an important role in the evolution of neutron star mergers and of their post-merger remnants. Neutrinos cool remnants, drive post-merger winds, and deposit energy in the low-density polar regions where relativistic jets may eventually form. Neutrinos also modify the composition of the ejected material, impacting the outcome of nucleosynthesis in merger outflows and the properties of the optical/infrared transients that they power (kilonovae). So far, merger simulations have largely relied on approximate treatments of the neutrinos (leakage, moments) that simplify the equations of radiation transport in a way that makes simulations more affordable but also introduces unquantifiable errors in the results. To improve on these methods, we recently published a first simulation of neutron star mergers using a low-cost Monte Carlo algorithm for neutrino radiation transport. Our transport code limits costs in optically thick regions by placing a hard ceiling on the value of the absorption opacity of the fluid, yet all approximations made within the code are designed to vanish in the limit of infinite numerical resolution. We provide here an in-depth description of this algorithm, of its implementation in the SpEC merger code, and of the expected impact of our approximations in optically thick regions. We argue that the last is a subdominant source of error at the accuracy reached by current simulations and for the interactions currently included in our code. We also provide tests of the most important features of this code.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1989

Ancient lakes on Mars?

The valley systems in Mars' ancient cratered terrain provide strong evidence for a warmer and wetter climate very early in planetary history. The valley systems in some instances debouch into closed depressions that could have acted as local ponding basins for the flow. A survey of the Martian equatorial region shows that numerous local depressions at the confluence of valley systems exist. These depressions (approximately 100 km) typically are characterized by many valleys flowing into them and few or none flowing out. If ponding did take place, these basin would have contained lakes for some period during Mars' early warmer epoch. Although the collection basins are numerous, location of ones that have not suffered significant subsequent geologic modification is difficult. Some morphologic features suggest that volcanic lavas may have filled them subsequent to any early fluvial activity. Two detailed maps of valley systems and local ponding basins in USGC 1:2,000,000 subquadrangles were completed and a third is in progress. The completed regions are in Mare Tyrrhenum (MC-22 SW) and Margarifter Sinus (MC-19 SE), and the region in progress is in Iapygia (MC-21 NW). On the maps, the valley systems and interpreted margins of ponding basins are indicated. The depressions are of interest for two reasons. First, the depressions were surely the sites in which the materials eroded from the valleys were deposited. Such sediments could preserve important information about the physical conditions at the time of deposition. Second, the sediments could preserve evidence of water-atmosphere interactions during the early period of the Martian climate. Atmospheric carbon dioxide would dissolve in water, and solid carbonate minerals would tend to precipitate out to form carbonate sedimentary deposits. Formation of carbonates in this manner might account for some of the CO2 lost from the early more dense atmosphere.

Goldspiel, J. M.↗
NASA NTRS1999

Improving the Accuracy of Quadrature Method Solutions of Fredholm Integral Equations That Arise from Nonlinear Two-Point Boundary Value Problems

In this paper we are concerned with high-accuracy quadrature method solutions of nonlinear Fredholm integral equations of the form y(x) = r(x) + definite integral of g(x, t)F(t,y(t))dt with limits between 0 and 1,0 less than or equal to x les than or equal to 1, where the kernel function g(x,t) is continuous, but its partial derivatives have finite jump discontinuities across x = t. Such integral equations arise, e.g., when one applied Green's function techniques to nonlinear two-point boundary value problems of the form y "(x) =f(x,y(x)), 0 less than or equal to x less than or equal to 1, with y(0) = y(sub 0) and y(l) = y(sub l), or other linear boundary conditions. A quadrature method that is especially suitable and that has been employed for such equations is one based on the trepezoidal rule that has a low accuracy. By analyzing the corresponding Euler-Maclaurin expansion, we derive suitable correction terms that we add to the trapezoidal rule, thus obtaining new numerical quadrature formulas of arbitrarily high accuracy that we also use in defining quadrature methods for the integral equations above. We prove an existence and uniqueness theorem for the quadrature method solutions, and show that their accuracy is the same as that of the underlying quadrature formula. The solution of the nonlinear systems resulting from the quadrature methods is achieved through successive approximations whose convergence is also proved. The results are demonstrated with numerical examples.

Sidi, Avram↗
NASA NTRS1999

Improving the Accuracy of Quadrature Method Solutions of Fredholm Integral Equations that Arise from Nonlinear Two-Point Boundary Value Problems

In this paper we are concerned with high-accuracy quadrature method solutions of nonlinear Fredholm integral equations of the form y(x) = r(x) + integral(0 to 1) g(x,t) F(t, y(t)) dt, 0 less than or equal to x less than or equal to 1, where the kernel function g(x,t) is continuous, but its partial derivatives have finite jump discontinuities across x = t. Such integrals equations arise, e.g., when one applies Green's function techniques to nonlinear two-point boundary value problems of the form U''(x) = f(x,y(x)), 0 less than or equal to x less than or equal to 1, with y(0) = y(sub 0) and g(l) = y(sub 1), or other linear boundary conditions. A quadrature method that is especially suitable and that has been employed for such equations is one based on the trapezoidal rule that has a low accuracy. By analyzing the corresponding Euler-Maclaurin expansion, we derive suitable correction terms that we add to the trapezoidal thus obtaining new numerical quadrature formulas of arbitrarily high accuracy that we also use in defining quadrature methods for the integral equations above. We prove an existence and uniqueness theorem for the quadrature method solutions, and show that their accuracy is the same as that of the underlying quadrature formula. The solution of the nonlinear systems resulting from the quadrature methods is achieved through successive approximations whose convergence is also proved. The results are demonstrated with numerical examples.

Sidi, Avram↗