Search NASA⌕ Search

SEARCH · Search NASA

Results for “numerical error”

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 235 records · Page 13
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Emergence of Microphysical Bulk Viscosity in Binary Neutron Star Postmerger Dynamics

Abstract In nuclear matter in isolated neutron stars, the flavor content (e.g., proton fraction) is subject to weak interactions, establishing flavor ( β -)equilibrium. However, there can be deviations from this equilibrium during the merger of two neutron stars. We study the resulting out-of-equilibrium dynamics during the collision by incorporating direct and modified Urca processes (in the neutrino-transparent regime) into general-relativistic hydrodynamics simulations with a simplified neutrino transport scheme. We demonstrate how weak-interaction-driven bulk viscosity in postmerger simulations can emerge and assess the bulk viscous dynamics of the resulting flow. We further place limits on the impact of the postmerger gravitational-wave strain. Our results show that weak-interaction-driven bulk viscosity can potentially lead to a phase shift of the postmerger gravitational-wave spectrum, although the effect is currently on the same level as the numerical errors of our simulation.

Astronomy & Astrophysics↗
DOE OSTI2016

Large Eddy Simulation of Autoignition Transients in a Model Diesel Injector Configuration

Developing an improved understanding of transient mixing and combustion processes inherent in diesel injection is an important element in the design of advanced engines. This paper provides a detailed analysis of these processes using an idealized benchmark configuration designed to facilitate precise comparisons between different models and numerical methods. The computational domain is similar to the Engine Combustion Network (www.sandia.gov/ECN) Spray-A injector with n-dodecane as the fuel. Quantified idealizations are made in the treatment of boundary conditions to eliminate ambiguities and unknowns associated with the actual injector(s) used in the experiment. These ambiguities hinder comparisons aimed at understanding the accuracy of different models and the coupled effects of potential numerical errors. Prior to understanding the impact of injector imperfections on their performance, it is first necessary to understand how models perform in a well-controlled environment with well-defined boundary conditions. Here, we focus on the latter while accurately matching the operating conditions used in the experiments. Relevant high-pressure phenomena are treated with real-fluid thermodynamics and transport for multicomponent mixtures. A highly resolved calculation is performed to study both scalar-mixing and initiation of combustion. Results are assembled into a database that can facilitate one-to-one comparisons between codes. The combined set of results is analyzed to provide physical insights related to localized broadband transient mixing and combustion processes that are typically not available from experiments.

Hakim, Layal↗
NASA NTRS1973

Potentialities of lunar laser ranging for measuring tectonic motions.

The lunar laser-ranging system at McDonald Observatory, Texas, is currently attaining accuracies of plus or minus 15 cm, and plus or minus 3 cm appears feasible. Numerical error analyses containing 97 parameters (35 of them for error sources) indicate that the plus or minus 3 cm system would measure station motions to plus or minus 1 cm/year accuracy within a year for east-west motions and within about 3 years for north-south. Furthermore, the correlations of station motions with other parameters are low, so that it is unlikely that the estimate is too optimistic because of modeling inadequacies of the error analysis.

Kaula, W. M.↗
NASA NTRS1973

Notions of analytic vs numerical stability as applied to the numerical calculation of orbits

This paper deals with the implications of 'stability' as applied to the numerical calculation of orbits. The study was motivated by the recent appearance of several proposed transformations of the classical Newtonian equations of motion which 'analytically stabilize' Cowell's method. This report analyzes the basic properties of such stabilizing transformations and shows the removal of the period as a parameter is the key to these transformations and, that although such transformations do not yield global numerical error bounds, the error propagation properties are more favorable - linear vs quadratic growth.

Velez, C. E.↗
NASA NTRS1979

Generation of linear dynamic models from a digital nonlinear simulation

The results and methodology used to derive linear models from a nonlinear simulation are presented. It is shown that averaged positive and negative perturbations in the state variables can reduce numerical errors in finite difference, partial derivative approximations and, in the control inputs, can better approximate the system response in both directions about the operating point. Both explicit and implicit formulations are addressed. Linear models are derived for the F 100 engine, and comparisons of transients are made with the nonlinear simulation. The problem of startup transients in the nonlinear simulation in making these comparisons is addressed. Also, reduction of the linear models is investigated using the modal and normal techniques. Reduced-order models of the F 100 are derived and compared with the full-state models.

Daniele, C. J.↗
NASA NTRS1981

Nonlinear magnetohydrodynamic stability

The computer code developed by Bauer et al. (1978) for the study of the magnetohydrodynamic equilibrium and stability of a plasma in toroidal geometry is extended so that the growth rates of instabilities may be estimated more accurately. The original code, which is based on the variational principle of ideal magnetohydrodynamics, is upgraded by the introduction of a nonlinear formula for the growth rate of an unstable mode which acts as a quantitative measure of instability that is important in estimating numerical errors. The revised code has been applied to the determination of the nonlinear saturation, ballooning modes and beta limits for tokamaks, stellarators and torsatrons.

Bauer, F.↗
NASA NTRS1981

The planetary nebula NGC 6826

Monochromatic photographs have established the NGC 6826 nebula as the third member of a group of very rare triple-shell planetaries (Feibelman, 1971, 1974). Kaler (1974) also characterized NGC 6826 as a giant halo planetary. Numerous errors and confusing statements regarding its size, structure and stratification are discussed, and the correct dimensions of the nebula are reported: the inner ring is 12.7 arcsec x 8.7 arcsec (Feibelman, 1971); the outer ring is 27 arcsec x 24 arcsec according to Curtis (1918), 25.7 arcsec x 24.4 arcsec according to Feibelman (1971), and 36 arcsec x 36 arcsec according to Coleman et al. (1975). The halo measurements range in diameter from 110 arcsec (Duncan, 1937) to 130 arcsec (Kaler, 1974) to 142 arcsec (Millikan, 1974). Values for the distance of NGC 6826 range from 0.75-1.16 kpc (Cahn and Kaler, 1971) to 2.265 kpc (Cudworth, 1974).

Feibelman, W. A.↗
NASA NTRS1981

Mixed spectral/finite difference approximations for slightly viscous flows

A numerical scheme is presented, which employs a standard finite difference approximation for the viscous terms in high Reynolds number flows, and resorts to pseudo-spectral methods for the advection terms to greatly reduce the major source of numerical error without dramatically increasing computational cost. The spectral/finite difference (SFD) method evaluates the advection term and second-order differences to evaluate the diffusion term. The fully finite difference (FFD) method with second-order central differences on both terms is also used. The SFD method can handle strong shocks and can outperform the FFD method at moderate viscosity.

Zang, T. A.↗
NASA NTRS1983

Research on the control of large space structures

The research effort on the control of large space structures at the University of Houston has concentrated on the mathematical theory of finite-element models; identification of the mass, damping, and stiffness matrix; assignment of damping to structures; and decoupling of structure dynamics. The objective of the work has been and will continue to be the development of efficient numerical algorithms for analysis, control, and identification of large space structures. The major consideration in the development of the algorithms has been the large number of equations that must be handled by the algorithm as well as sensitivity of the algorithms to numerical errors.

Denman, E. D.↗
NASA NTRS1983

Analytical calculation of a single jet in cross-flow and comparison with experiment

A series of progressively finer grid systems to calculate the single jet in cross-flow experimentally measured were employed. The experimental measurements provide a collection of velocities, turbulence intensities, and jet concentration profiles with measurements of the inlet field. The use of a series of progressively finer grid systems allows a differentiation between numerical errors and the hydrodynamic modeling assumptions embodied in the 3D combustor code.

Claus, R. W.↗
NASA NTRS1983

An improved lambda-scheme for one-dimensional flows

A code for the calculation of one-dimensional flows is presented, which combines a simple and efficient version of the lambda-scheme with tracking of discontinuities. The latter is needed to identify points where minor departures from the basic integration scheme are applied to prevent infiltration of numerical errors. Such a tracking is obtained via a systematic application of Boolean algebra. It is, therefore, very efficient. Fifteen examples are presented and discussed in detail. The results are exceptionally good. All discontinuites are captured within one mesh interval.

Moretti, G.↗
NASA NTRS1982

Modelling of TGS growth in space

Attention is called to the necessity of programming the temperature downward in order to maintain a constant growth rate in the absence of convection. Trial and error numerical computations are performed to find the first approximation for the required isothermal dissolution period, linear ramp, and polynomial temperature variation period. The linear ramp rate is limited by the specified maximum temperature gradient. The isothermal dissolution turns out to be unnecessary. The linear ramp must be stopped before the polynomial period is begun in order to avoid overshooting the specified maximum growth rate. After a few hours, the temperature profile approaches steady-state behavior.

Liu, L. C.↗
NASA NTRS1983

Application of identification techniques to remote manipulator system flight data

This paper addresses the application of identification techniques to flight data from the Space Shuttle Remote Manipulator System (RMS). A description of the remote manipulator, including structural and control system characteristics, sensors, and actuators is given. A brief overview of system identification procedures is presented, and the practical aspects of implementing system identification algorithms are discussed. In particular, the problems posed by desampling rate, numerical error, and system nonlinearities are considered. Simulation predictions of damping, frequency, and system order are compared with values identified from flight data to support an evaluation of RMS structural and control system models. Finally, conclusions are drawn regarding the application of identification techniques to flight data obtained from a flexible space structure.

Shepard, G. D.↗
NASA NTRS1984

Airfoil computation at high angles of attack, inviscid and viscous phenomena

An implicit central difference code is used to calculate two dimensional inviscid and thin-layer Navier-Stokes solutions for flow about an NACA0012 airfoil at high angles of attack. Among the issues addressed are whether separation can occur in an inviscid calculation and what the causes would be of such separation. Examples are shown of inviscid shocked flow with and without separation and shock-free flow with separation. An Euler solution with self-induced oscillation and separation driven by a strong shock is contrasted with a shock-free solution whose separation is caused by numerical error. Computed solutions to the Euler equations are compared to those of the potential equations. Comparisons are also made between experimental data from wind tunnel tests and viscous calculations at similar conditions.

Barton, J. T.↗
NASA NTRS1985

Recovering pointwise values of discontinuous data within spectral accuracy

The pointwise values of a function, f(x), can be accurately recovered either from its spectral or pseudospectral approximations, so that the accuracy solely depends on the local smoothness of f in the neighborhood of the point x. Most notably, given the equidistant function grid values, its intermediate point values are recovered within spectral accuracy, despite the possible presence of discontinuities scattered in the domain. (Recall that the usual spectral convergence rate decelerates otherwise to first order, throughout). To this end, a highly oscillatory smoothing kernel is employed in contrast to the more standard positive unit-mass mollifiers. In particular, post-processing of a stable Fourier method applied to hyperbolic equations with discontinuous data, recovers the exact solution modulo a spectrally small error. Numerical examples are presented.

Gottlieb, D.↗
NASA NTRS1986

Computation of leading-edge vortex flows

The simulation of the leading edge vortex flow about a series of conical delta wings through solution of the Navier-Stokes and Euler equations is studied. The occurrence, the validity, and the usefulness of separated flow solutions to the Euler equations of particular interest. Central and upwind difference solutions to the governing equations are compared for a series of cross sectional shapes, including both rounded and sharp tip geometries. For the rounded leading edge and the flight condition considered, viscous solutions obtained with either central or upwind difference methods predict the classic structure of vortical flow over a highly swept delta wing. Predicted features include the primary vortex due to leading edge separation and the secondary vortex due to crossflow separation. Central difference solutions to the Euler equations show a marked sensitivity to grid refinement. On a coarse grid, the flow separates due to numerical error and a primary vortex which resembles that of the viscous solution is predicted. In contrast, the upwind difference solutions to the Euler equations predict attached flow even for first-order solutions on coarse grids. On a sufficiently fine grid, both methods agree closely and correctly predict a shock-curvature-induced inviscid separation near the leeward plane of symmetry. Upwind difference solutions to the Navier-Stokes and Euler equations are presented for two sharp leading edge geometries. The viscous solutions are quite similar to the rounded leading edge results with vortices of similar shape and size. The upwind Euler solutions predict attached flow with no separation for both geometries. However, with sufficient grid refinement near the tip or through the use of more accurate spatial differencing, leading edge separation results. Once the leading edge separation is established, the upwind solution agrees with recently published central difference solutions to the Euler equations.

Newsome, R. W.↗
NASA NTRS1986

A numerical model of acoustic choking. II - Shocked solutions

The one dimensional equations of gas dynamics are used to model subsonic acoustic choking. This model can accommodate non-linear distortion of waves and the eventual formation of shock waves. Several finite differencing schemes are adapted to obtain solutions. The results obtained with the various schemes are compared with the asymptotic results available. The results suggest that no one finite differencing scheme gives solutions significantly better than the others and that most of the difference solutions are close to the asymptotic results. If the acoustic shock wave is sufficiently strong it almost annihilates the acoustic wave; in this situation numerical errors may dominate the results. Such solutions involve very large acoustic attenuations.

Walkington, N. J.↗
NASA NTRS1985

Recovering pointwise values of discontinuous data within spectral accuracy

The pointwise values of a function, f(x), can be accurately recovered either from its spectral or pseudospectral approximations, so that the accuracy solely depends on the local smoothness of f in the neighborhood of the point x. Most notably, given the equidistant function grid values, its intermediate point values are recovered within spectral accuracy, despite the possible presence of discontinuities scattered in the domain. (Recall that the usual spectral convergence rate decelerates otherwise to first order, throughout). To this end, a highly oscillatory smoothing kernel is employed in contrast to the more standard positive unit-mass mollifiers. In particular, post-processing of a stable Fourier method applied to hyperbolic equations with discontinuous data, recovers the exact solution modulo a spectrally small error. Numerical examples are presented.

Gottlieb, D.↗