Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “time integrator”

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 253 records · Page 14
All sourcesNASA NTRSDOE OSTI
NASA NTRS2017

Autonomous Acquisition of Science Quality Spectra from Unmanned Aerial Systems

This is a presentation on a technique for using Unmanned Aerial Systems with intelligent sensing to create science quality data. In this particular case, the team used two spectrometers with high spectral resolution and developed a technique to have the spectrometers self calibrate so that it is possible to take the measurements within the allocated 10 minute flight times. Because there is both upwelling and downwelling foreoptics on each of the two spectrometers, it becomes slow to set the calibration up for all four possibilities which relates to the integration time and then take the measurements. If light conditions change too rapidly then the measurements won't be scaled so that the spectra max is at least 85% of the instrument max but not saturated. This process was more difficult then it appeared due to the complexity of determining the integration time before light conditions changed and before the battery runs our of charge to fly the Unmanned Aerial System. This presentation goes over the results for the first few flight days and the planned future flight experiments.

Mandl, Daniel↗
DOE OSTI2021

Implicit-Explicit Multirate Infinitesimal GARK Methods

This work focuses on the development of a new class of high-order accurate methods for multirate time integration of systems of ordinary differential equations. Unlike other recent work in this area, the proposed methods support mixed implicit-explicit (IMEX) treatment of the slow time scale. In addition to allowing this slow time scale flexibility, the proposed methods utilize a so-called infinitesimal formulation for the fast time scale through definition of a sequence of modified “fast" initial-value problems that may be solved using any viable algorithm. We name the proposed class as implicit-explicit multirate infinitesimal generalized-structure additive Runge--Kutta (IMEX-MRI-GARK) methods. In addition to defining these methods, we prove that they may be viewed as specific instances of GARK methods and derive a set of order conditions on the IMEX-MRI-GARK coefficients to guarantee both third and fourth order accuracy for the overall multirate method. Additionally, we provide three specific IMEX-MRI-GARK methods, two of order three and one of order four. We conclude with numerical simulations on two multirate test problems, demonstrating the methods' predicted convergence rates and comparing their efficiency against both legacy IMEX multirate schemes and recent third and fourth order implicit MRI-GARK methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Fast Solution of Fully Implicit Runge--Kutta and Discontinuous Galerkin in Time for Numerical PDEs, Part I: the Linear Setting

Fully implicit Runge--Kutta (IRK) methods have many desirable properties as time integration schemes in terms of accuracy and stability, but high-order IRK methods are not commonly used in practice with numerical PDEs due to the difficulty of solving the stage equations. This paper introduces a theoretical and algorithmic preconditioning framework for solving the systems of equations that arise from IRK methods applied to linear numerical PDEs (without algebraic constraints). Additionally, this framework also naturally applies to discontinuous Galerkin discretizations in time. Under quite general assumptions on the spatial discretization that yield stable time integration, the preconditioned operator is proven to have condition number bounded by a small, order-one constant, independent of the spatial mesh and time-step size, and with only weak dependence on number of stages/polynomial order; for example, the preconditioned operator for 10th-order Gauss IRK has condition number less than two, independent of the spatial discretization and time step. The new method can be used with arbitrary existing preconditioners for backward Euler-type time-stepping schemes and is amenable to the use of three-term recursion Krylov methods when the underlying spatial discretization is symmetric. The new method is demonstrated to be effective on various high-order finite-difference and finite element discretizations of linear parabolic and hyperbolic problems, demonstrating fast, scalable solution of up to 10th-order accuracy. The new method consistently outperforms existing block preconditioning approaches, and in several cases, the new method can achieve 4th-order accuracy using Gauss integration with roughly half the number of preconditioner applications and wallclock time as required using standard diagonally IRK methods.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2019

Average Path Profile of Atmospheric Temperature and Humidity Structure Parameters from a Microwave Profiling Radiometer

The values of the key atmospheric turbulence parameters (structure constants) for temperature and water vapor, that is, C(exp 2)(sub T), and C(exp 2)(sub Q), are highly dependent upon the vertical height within the atmosphere thus making it necessary to specify profiles of these values along the atmospheric propagation path. The remote sensing method suggested and described in this work makes use of a rapidly integrating microwave profiling radiometer to capture profiles of temperature and humidity through the atmosphere. The integration times of currently available profiling radiometers are such that they are approaching the temporal intervals over which one can possibly make meaningful assessments of these key atmospheric parameters. These integration times, coupled with the boundary effects of the Earth’s surface are, however, unconventional for turbulence characterization; the classical Kolmogorov turbulence theory and related 2/3 law for structure functions prevalent in the inertial subrange are no longer appropriate. An alternative to this classical approach is derived from first principles to account for the nuances of turbulent mechanics met with using radiometer sensing, that is, the large-scale turbulence driven by the various possible boundary conditions within the buoyancy subrange. Analytical expressions connecting the measured structure functions to the corresponding structure parameters are obtained. The theory is then applied to an experimental scenario involving radiometric profile measurements of temperature and shows very good results.

Manning, Robert M.↗
NASA NTRS1987

Imaginary time path integral Monte Carlo route to rate coefficients for nonadiabatic barrier crossing

Nonadiabatic transitions are central to many areas of chemical and condensed matter physics, ranging from biological electron transfer to the optical properties of one-dimensional conductors. Here, a path integral Monte Carlo method is used to simulate such transitions, based on the observation that nonadiabatic rate coefficients are often dominated by saddle point trajectories that correspond to an imaginary time. Simple analytic theories can be used to continue these imaginary time correlation functions to determine rate coefficients. The advantages and drawbacks of this approach are discussed.

Wolynes, Peter G.↗
NASA NTRS2013

Visible Contrast Energy Metrics for Detection and Discrimination

Contrast energy was proposed by Watson, Robson, & Barlow as a useful metric for representing luminance contrast target stimuli because it represents the detectability of the stimulus in photon noise for an ideal observer. Like the eye, the ear is a complex transducer system, but relatively simple sound level meters are used to characterize sounds. These meters provide a range of frequency sensitivity functions and integration times depending on the intended use. We propose here the use of a range of contrast energy measures with different spatial frequency contrast sensitivity weightings, eccentricity sensitivity weightings, and temporal integration times. When detection threshold are plotting using such measures, the results show what the eye sees best when these variables are taken into account in a standard way. The suggested weighting functions revise the Standard Spatial Observer for luminance contrast detection and extend it into the near periphery. Under the assumption that the detection is limited only by internal noise, discrimination performance can be predicted by metrics based on the visible energy of the difference images

Ahumada, Albert↗
NASA NTRS1988

Nd isotopes and crustal growth rate

Sm/Nd isotopic constraints on crustal growth is discussed. In order to constrain Sm/Nd fractionation between continental crust and depleted mantle, an extensive data base of isotopic measurements (assumed to be adequately representative of continental crust) was compiled. The results imply that the evolution of depleted mantles was roughly linear, with no major discontinuities over the course of geologic time. This is different from other determinations of depleting mantle evolution, which show nonlinear behavior. The Sm/Nd evolution lines for continental crust and depleted mantle intersect between 3.8 to 4.0 Ga, which may indicate that the onset of continental growth was later than 4.5 Ga. A mathematical model is described, the results of which imply that time integrated crustal additions from the mantle are about 1.8 to 2.5 cu km/a, whereas crustal subtractions by sediment recycling are about 0.6 to 1.5 cu km/a. This results in a net time integrated crustal growth rate of about 1 cu km/a, which is similar to present day rates determined, for example, by Reymer and Schubert.

Albarede, F.↗
NASA NTRS1992

Unfulfilled needs in IR astronomy focal-plane readout electronics

The NOAO's 8-m IR optimized telescope for Mauna Kea and NASA's SIRTF show that from 1 to 200 microns there are a number of unfulfilled needs in readout electronics. These include: extremely low readnoise, less than 10 electrons, stable operation at temperatures as low as 2 K, high well capacity, greater than 1 e 7 electrons, and integration times from 30 msec to over 100 sec. Sensors for adaptive optics systems are required with readnoise less than 10 electrons and response times of 30 msec. They should be highly efficient from 1 to 2.5 microns, but may have small formats. Ground-based imagers at these wavelengths need comparable readnoise but longer integration times, and the largest possible formats are essential. To achieve these goals improved cryogenic MOSFETS are essential and complete cryogenic CMOS circuits are highly desirable. Experimental cryoptimized MFETS promise to exceed the above noise requirements at 77 K and approach the needs at 2 K.

Low, Frank J.↗
NASA NTRS1996

Laser-Induced Incandescence: Detection Issues

Experimental LII (laser-induced incandescence) measurements were performed in a laminar gasjet flame to test the sensitivity of different LII signal collection strategies to particle size. To prevent introducing a particle size dependent bias in the LII signal, signal integration beginning with the excitation laser pulse is necessary . Signal integration times extending to 25 or 100 nsec after the laser pulse do not produce significant differences in radial profiles of the LII signal due to particle size effects with longer signal integration times revealing a decreased sensitivity to smaller primary particles. Long wavelength detection reduces the sensitivity of the LII signal to primary particle size. Excitation of LII using 1064 nm light is recommended to avoid creating photochemical interferences thus allowing LII signal collection to occur during the excitation pulse without spectral interferences.

VanderWal, Randall L.↗
DOE OSTI2024

DG-IMEX method for a two-moment model for radiation transport in the $\mathscr{O}$($v$/$c$) limit

Here, we consider neutral particle systems described by moments of a phase-space density and propose a realizability-preserving numerical method to evolve a spectral two-moment model for particles interacting with a background fluid moving with nonrelativistic velocities. The system of nonlinear moment equations, with special relativistic corrections to $\mathscr{O}$($v$/$c$), expresses a balance between phase-space advection and collisions and includes velocity-dependent terms that account for spatial advection, Doppler shift, and angular aberration. The model is conservative for the correct $\mathscr{O}$($v$/$c$) Eulerian-frame number density and is consistent, to $\mathscr{O}$($v$/$c$), with Eulerian-frame energy and momentum conservation. This model is closely related to the one promoted by Lowrie et al. and similar to models currently used to study transport phenomena in large-scale simulations of astrophysical environments. The proposed numerical method is designed to preserve moment realizability, which guarantees that the moments correspond to a nonnegative phase-space density. The realizability-preserving scheme consists of the following key components: (i) a strong stability-preserving implicit-explicit (IMEX) time-integration method; (ii) a discontinuous Galerkin (DG) phase-space discretization with carefully constructed numerical uxes; (iii) a realizability-preserving implicit collision update; and(iv) a realizability-enforcing limiter. In time integration, nonlinearity of the moment model necessitates solution of nonlinear equations, which we formulate as fixed-point problems and solve with tailored iterative solvers that preserve moment realizability with guaranteed global convergence. We also analyze the simultaneous Eulerian-frame number and energy conservation properties of the semi-discrete DG scheme and propose a "spectral redistribution" scheme that promotes Eulerian-frame energy conservation. Through numerical experiments, we demonstrate the accuracy and robustness of this DG-IMEX method and investigate its Eulerian-frame energy conservation properties.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1972

Gravimetric geodesy and sea surface topography studies by means of satellite-to-satellite tracking and satellite altimetry

A satellite-to-satellite tracking experiment is planned between ATS-F and GEOS-C with a range accuracy of 2-meters and a range rate accuracy of 0.035 centimeters per second for a 10-second integration time. This experiment is planned for 1974. It is anticipated that it will improve the spatial resolution of the satellite geoid by half an order of magnitude to about 6 degrees. Longer integration times should also permit a modest increase in the acceleration resolution. Satellite altimeter data will also be obtained by means of GEOS-C. An overall accuracy of 5-meters in altitude is the goal. The altimeter, per se, is expected to have an instrumental precision of about 2 meters, and an additional capability to observe with a precision of about 0.2 meters for limited periods.

Siry, J. W.↗
NASA NTRS1994

Differential absorption lidar measurements of atmospheric water vapor using a pseudonoise code modulated AlGaAs laser

Lidar measurements using pseudonoise code modulated AlGaAs lasers are reported. Horizontal path lidar measurements were made at night to terrestrial targets at ranges of 5 and 13 km with 35 mW of average power and integration times of one second. Cloud and aerosol lidar measurements were made to thin cirrus clouds at 13 km altitude with Rayleigh (molecular) backscatter evident up to 9 km. Average transmitter power was 35 mW and measurement integration time was 20 minutes. An AlGaAs laser was used to characterize spectral properties of water vapor absorption lines at 811.617, 816.024, and 815.769 nm in a multipass absorption cell using derivative spectroscopy techniques. Frequency locking of an AlGaAs laser to a water vapor absorption line was achieved with a laser center frequency stability measured to better than one-fifth of the water vapor Doppler linewidth over several minutes. Differential absorption lidar measurements of atmospheric water vapor were made in both integrated path and range-resolved modes using an externally modulated AlGaAs laser. Mean water vapor number density was estimated from both integrated path and range-resolved DIAL measurements and agreed with measured humidity values to within 6.5 percent and 20 percent, respectively. Error sources were identified and their effects on estimates of water vapor number density calculated.

Rall, Jonathan A. R.↗
NASA NTRS1993

ENO-Osher schemes for Euler equations

The combination of the Osher approximate Riemann solver for the Euler equations and various ENO schemes is discussed for one-dimensional flow. The three basic approaches, viz., the ENO scheme using primitive variable reconstruction, either with the Cauchy-Kowalewski procedure for time integration or the TVD Runge-Kutta scheme, and the flux-ENO method are tested on different shock tube cases. The ENO-Osher scheme using the Cauchy-Kowalewski procedure for time integration is found to be the most accurate and robust compared with the other methods and is also computationally efficient. The tests showed that the ENO schemes perform reasonably well, but have problems in cases where two discontinuites are close together. In that case there are not enough points in the smooth part of the flow to create a nonoscillatory interpolation.

Van Der Vegt, Jacobus J.↗
DOE OSTI2021

End-gas autoignition fraction and flame propagation rate in laser-ignited primary reference fuel mixtures at elevated temperature and pressure

Knock in spark-ignited (SI) engines is initiated by autoignition of the unburned gasses upstream of spark-ignited, propagating, turbulent premixed flames. Knock propensity of fuel/air mixtures is typically quantified using research octane number (RON), motor octane number (MON), or methane number (MN; for gaseous fuels), which are measured using single-cylinder, variable compression ratio engines. In this study, knock propensity of SI fuels was quantified via observations of end-gas autoignition (EGAI) in unburned gasses upstream of laser-ignited, premixed flames at elevated pressures and temperatures in a rapid compression machine. Stoichiometric primary reference fuel (PRF; n-heptane/isooctane) blends of varying reactivity (50 ≤ PRF ≤ 100) were ignited using an Nd:YAG laser over a range of temperatures and pressures, all in excess of 545 K and 16.1 bar. Laser ignition produced outwardly-propagating premixed flames. High-speed pressure measurements and schlieren images indicated the presence of EGAI. The fraction of the total heat release attributed to EGAI (i.e., EGAI fraction) varied with fuel reactivity (i.e., octane number) and the time-integrated temperature of the end-gas prior to ignition. Flame propagation rates, which were measured using schlieren images, were only weakly correlated with octane number but were affected by turbulence caused by variation in piston timing. Under conditions of low turbulence, measured flame propagation rates approached one-dimensional premixed laminar flame speed computations performed at the same conditions. Experiments were simulated with a three-dimensional CONVERGE™ model using reduced chemical kinetics (121 species, 538 reactions). The simulations accurately captured the measured flame propagation rates, as well as the variation in EGAI fraction with fuel reactivity and time-integrated end-gas temperature. The simulations also revealed low-temperature heat release as well as formaldehyde and hydrogen peroxide formation in the end-gas upstream of the propagating flame, which increased the temperature and degree of chain branching in the end-gas, ultimately leading to EGAI.

42 ENGINEERING↗
DOE OSTI2024

On Properties of Adjoint Systems for Evolutionary PDEs

We investigate the geometric structure of adjoint systems associated with evolutionary partial differential equations at the fully continuous, semi-discrete, and fully discrete levels and the relations between these levels. We show that the adjoint system associated with an evolutionary partial differential equation has an infinite-dimensional Hamiltonian structure, which is useful for connecting the fully continuous, semi-discrete, and fully discrete levels. We subsequently address the question of discretize-then-optimize versus optimize-then-discrete for both semi-discretization and time integration, by characterizing the commutativity of discretize-then-optimize methods versus optimize-then-discretize methods uniquely in terms of an adjoint-variational quadratic conservation law. For Galerkin semi-discretizations and one-step time integration methods in particular, we explicitly construct these commuting methods by using structure-preserving discretization techniques.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Quantifying and attributing time step sensitivities in present-day climate simulations conducted with EAMv1

Abstract. This study assesses the relative importance of time integration error in present-day climate simulations conducted with the atmosphere component of the Energy Exascale Earth System Model version 1 (EAMv1) at 1∘ horizontal resolution. We show that a factor-of-6 reduction of time step size in all major parts of the model leads to significant changes in the long-term mean climate. Examples of changes in 10-year mean zonal averages include the following: up to 0.5 K of warming in the lower troposphere and cooling in the tropical and subtropical upper troposphere, 1 %–10 % decreases in relative humidity throughout the troposphere, and 10 %–20 % decreases in cloud fraction in the upper troposphere and decreases exceeding 20 % in the subtropical lower troposphere. In terms of the 10-year mean geographical distribution, systematic decreases of 20 %–50 % are seen in total cloud cover and cloud radiative effects in the subtropics. These changes imply that the reduction of temporal truncation errors leads to a notable although unsurprising degradation of agreement between the simulated and observed present-day climate; to regain optimal climate fidelity in the absence of those truncation errors, the model would require retuning. A coarse-grained attribution of the time step sensitivities is carried out by shortening time steps used in various components of EAM or by revising the numerical coupling between some processes. Our analysis leads to the finding that the marked decreases in the subtropical low-cloud fraction and total cloud radiative effect are caused not by the step size used for the collectively subcycled turbulence, shallow convection, and stratiform cloud macrophysics and microphysics parameterizations but rather by the step sizes used outside those subcycles. Further analysis suggests that the coupling frequency between the subcycles and the rest of EAM significantly affects the subtropical marine stratocumulus decks, while deep convection has significant impacts on trade cumulus. The step size of the cloud macrophysics and microphysics subcycle itself appears to have a primary impact on cloud fraction in the upper troposphere and also in the midlatitude near-surface layers. Impacts of step sizes used by the dynamical core and the radiation parameterization appear to be relatively small. These results provide useful clues for future studies aiming at understanding and addressing the root causes of sensitivities to time step sizes and process coupling frequencies in EAM. While this study focuses on EAMv1 and the conclusions are likely model-specific, the presented experimentation strategy has general value for weather and climate model development, as the methodology can help researchers identify and understand sources of time integration error in sophisticated multi-component models.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1977

A numerical scheme to solve unstable boundary value problems

The considered scheme makes it possible to determine an unstable steady state solution in cases in which, because of lack of symmetry, such a solution cannot be obtained analytically, and other time integration or relaxation schemes, because of instability, fail to converge. The iterative solution of a single complex equation is discussed and a nonlinear system of equations is considered. Described applications of the scheme are related to a steady state solution with shear instability, an unstable nonlinear Ekman boundary layer, and the steady state solution of a baroclinic atmosphere with asymmetric forcing. The scheme makes use of forward and backward time integrations of the original spatial differential operators and of an approximation of the adjoint operators. Only two computations of the time derivative per iteration are required.

Kalnay-Rivas, E.↗
DOE OSTI2023

ARKODE: A Flexible IVP Solver Infrastructure for One-step Methods

We describe the ARKODE library of one-step time integration methods for ordinary differential equation (ODE) initial-value problems (IVPs). In addition to providing standard explicit and diagonally implicit Runge–Kutta methods, ARKODE supports one-step methods designed to treat additive splittings of the IVP, including implicit-explicit (ImEx) additive Runge–Kutta methods and multirate infinitesimal (MRI) methods. We present the role of ARKODE within the SUNDIALS suite of time integration and nonlinear solver libraries, the core ARKODE infrastructure for utilities common to large classes of one-step methods, as well as its use of “time stepper” modules enabling easy incorporation of novel algorithms into the library. Numerical results show example problems of increasing complexity, highlighting the algorithmic flexibility afforded through this infrastructure, and include a larger multiphysics application leveraging multiple algorithmic features from ARKODE and SUNDIALS.

97 MATHEMATICS AND COMPUTING↗