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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 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

On the spectral stability of time integration algorithms for a class of constrained dynamics problems

Incomplete field formulations have recently been the subject of intense research because of their potential in coupled analysis of independently modeled substructures, adaptive refinement, domain decomposition, and parallel processing. This paper discusses the design and analysis of time-integration algorithms for these formulations and emphasizes the treatment of their inter-subdomain constraint equations. These constraints are shown to introduce a destabilizing effect in the dynamic system that can be analyzed by investigating the behavior of the time-integration algorithm at infinite and zero frequencies. Three different approaches for constructing penalty-free unconditionally stable second-order accurate solution procedures for this class of hybrid formulations are presented, discussed and illustrated with numerical examples. The theoretical results presented in this paper also apply to a large family of nonlinear multibody dynamics formulations. Some of the algorithms outlined herein are important alternatives to the popular technique consisting of transforming differential/algebraic equations into ordinary differential equations via the introduction of a stabilization term that depends on arbitrary constants and that influences the computed so1ution.

Farhat, Charbel↗
NASA NTRS2002

Higher Order Time Integration Schemes for the Unsteady Navier-Stokes Equations on Unstructured Meshes

The rapid increase in available computational power over the last decade has enabled higher resolution flow simulations and more widespread use of unstructured grid methods for complex geometries. While much of this effort has been focused on steady-state calculations in the aerodynamics community, the need to accurately predict off-design conditions, which may involve substantial amounts of flow separation, points to the need to efficiently simulate unsteady flow fields. Accurate unsteady flow simulations can easily require several orders of magnitude more computational effort than a corresponding steady-state simulation. For this reason, techniques for improving the efficiency of unsteady flow simulations are required in order to make such calculations feasible in the foreseeable future. The purpose of this work is to investigate possible reductions in computer time due to the choice of an efficient time-integration scheme from a series of schemes differing in the order of time-accuracy, and by the use of more efficient techniques to solve the nonlinear equations which arise while using implicit time-integration schemes. This investigation is carried out in the context of a two-dimensional unstructured mesh laminar Navier-Stokes solver.

Jothiprasad, Giridhar↗
NASA NTRS2003

Effect of Variations in IRU Integration Time Interval On Accuracy of Aqua Attitude Estimation

During Aqua launch support, attitude analysts noticed several anomalies in Onboard Computer (OBC) rates and in rates computed by the ground Attitude Determination System (ADS). These included: 1) periodic jumps in the OBC pitch rate every 2 minutes; 2) spikes in ADS pitch rate every 4 minutes; 3) close agreement between pitch rates computed by ADS and those derived from telemetered OBC quaternions (in contrast to the step-wise pattern observed for telemetered OBC rates); 4) spikes of +/- 10 milliseconds in telemetered IRU integration time every 4 minutes (despite the fact that telemetered time tags of any two sequential IRU measurements were always 1 second apart from each other). An analysis presented in the paper explains this anomalous behavior by a small average offset of about 0.5 +/- 0.05 microsec in the time interval between two sequential accumulated angle measurements. It is shown that errors in the estimated pitch angle due to neglecting the aforementioned variations in the integration time interval by the OBC is within +/- 2 arcseconds. Ground attitude solutions are found to be accurate enough to see the effect of the variations on the accuracy of the estimated pitch angle.

Natanson, G. A.↗
NASA NTRS1982

Mixed time integration methods for transient thermal analysis of structures, appendix 5

Mixed time integration methods for transient thermal analysis of structures are studied. An efficient solution procedure for predicting the thermal behavior of aerospace vehicle structures was developed. A 2D finite element computer program incorporating these methodologies is being implemented. The performance of these mixed time finite element algorithms can then be evaluated employing the proposed example problem.

Liu, W. K.↗
DOE OSTI2020

An energy-conserving and asymptotic-preserving charged-particle orbit implicit time integrator for arbitrary electromagnetic fields

Here we present a new implicit asymptotic preserving time integration scheme for charged-particle orbit computation in arbitrary electromagnetic fields. The scheme is built on the Crank-Nicolson integrator and continues to recover full-orbit motion in the small time-step limit, but also recovers all the first-order guiding center drifts as well as the correct gyroradius when stepping over the gyration time-scale. In contrast to previous efforts in this direction, the new scheme also features exact energy conservation. In the derivation of the scheme, we find that a new numerical time-scale is introduced. This scale is analyzed and the resulting restrictions on time-step are derived. Based on this analysis, we develop an adaptive time-stepping strategy the respects these constraints while stepping over the gyration scale when physically justified. It is shown through numerical tests on single-particle motion that the scheme's energy conservation property results in tremendous improvements in accuracy, and that the scheme is able to transition smoothly between magnetized and unmagnetized regimes as a result of the adaptive time-stepping.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS2012

Neutrino Analysis of the September 2010 Crab Nebula Flare and Time-Integrated Constraints on Neutrino Emission from the Crab Using IceCube

We present the results for a search of high-energy muon neutrinos with the IceCube detector in coincidence with the Crab nebula flare reported on September 2010 by various experiments. Due to the unusual flaring state of the otherwise steady source we performed a prompt analysis of the 79-string configuration data to search for neutrinos that might be emitted along with the observed gamma-rays. We performed two different and complementary data selections of neutrino events in the time window of 10 days around the flare. One event selection is optimized for discovery of E(sub v)(sup -2) neutrino spectrum typical of 1st order Fermi acceleration. A similar event selection has also been applied to the 40-string data to derive the time-integrated limits to the neutrino emission from the Crab [35]. The other event selection was optimized for discovery of neutrino spectra with softer spectral index and TeV energy cut-offs as observed for various galactic sources in gamma-rays. The 90% CL best upper limits on the Crab flux during the 10 day flare are 4.73 x 10(exp -11) per square centimeter per second TeV(sup -1) for an E(sub v)(sup -2) neutrino spectrum and 2.50 x 10(exp -10) per square centimeter per second TeV(sup -1) for a softer neutrino spectra of E(sub v)(sup -2.7), as indicated by Fermi measurements during the flare. IceCube has also set a time-integrated limit on the neutrino emission of the Crab using 375.5 days of livetime of the 40-string configuration data. This limit is compared to existing models of neutrino production from the Crab and its impact on astrophysical parameters is discussed. The most optimistic predictions of some models are already rejected by the IceCube neutrino telescope with more than 90% CL.

Abbasi, R.↗
NASA NTRS2012

Neutrino Analysis of the September 2010 Crab Nebula Flare and Time-integrated Constraints on Neutrino Emission From the Crab Using IceCube

We present the results for a search of high-energy muon neutrinos with the IceCube detector in coincidence with the Crab nebula flare reported on September 2010 by various experiments. Due to the unusual flaring state of the otherwise steady source we performed a prompt analysis of the 79-string configuration data to search for neutrinos that might be emitted along with the observed gamma-rays. We performed two different and complementary data selections of neutrino events in the time window of 10 days around the flare. One event selection is optimized for discovery of E(sub nu)(sup -2) neutrino spectrum typical of 1st order Fermi acceleration. A similar event selection has also been applied to the 40-string data to derive the time-integrated limits to the neutrino emission from the Crab [35]. The other event selection was optimized for discovery of neutrino spectra with softer spectral index and TeV energy cut-offs as observed for various galactic sources in gamma-rays. The 90% CL best upper limits on the Crab flux during the 10 day flare are 4.73 x 10(exp -11) per square centimeter per second TeV (sup -1) for an E(sub nu) (sup -2) neutrino spectrum and 2.50 x 10(exp -10) per square centimeter per second TeV(sup -1) for a softer neutrino spectra of E(sub nu)(sup -2.7), as indicated by Fermi measurements during the flare. IceCube has also set a time-integrated limit on the neutrino emission of the Crab using 375.5 days of livetime of the 40-string configuration data. This limit is compared to existing models of neutrino production from the Crab and its impact on astrophysical parameters is discussed. The most optimistic predictions of some models are already rejected by the IceCube neutrino telescope with more than 90% CL.

Stamatikos, M.↗
NASA NTRS1990

Radar and satellite area-time-integral techniques for estimating convective precipitation

The application of the area-time-integral (ATI) method (Doneaud et al, 1984) to radar and satellite measurements is reviewed. Results are presented from the calculation of ATI values from radar observations based on low-elevation-angle and low-altitude CAPPI data. Also, results from a satellite ATI calculation using IR images from a GEO platform are given. The results suggest that the radar and satellite applications produce good consistency.

Smith, Paul L.↗
DOE OSTI2025

Advancing simulations of coupled electron and phonon nonequilibrium dynamics using adaptive and multirate time integration

Electronic structure calculations in the time domain provide a deeper understanding of nonequilibrium dynamics in materials. The real-time Boltzmann equation (rt-BTE), used in conjunction with accurate interactions computed from first principles, has enabled reliable predictions of coupled electron and lattice dynamics. However, the timescales and system sizes accessible with this approach are still limited, with two main challenges being the different timescales of electron and phonon interactions and the cost of computing collision integrals. As a result, only a few examples of these calculations exist, mainly for two-dimensional (2D) materials. Here we leverage adaptive and multirate time integration methods to achieve a major step forward in solving the coupled rt-BTEs for electrons and phonons. Relative to conventional (non-adaptive) time-stepping, our approach achieves a 10x speedup for a target accuracy, or greater accuracy by 3–6 orders of magnitude for the same computational cost, enabling efficient calculations in both 2D and bulk materials. This efficiency is showcased by computing the coupled electron and lattice dynamics in graphene up to ~100 ps, as well as modeling ultrafast lattice dynamics and thermal diffuse scattering maps in bulk materials (silicon and gallium arsenide). In addition to improved efficiency, our adaptive method can resolve the characteristic rates of different physical processes, thus naturally bridging different timescales. This enables simulations of longer timescales and provides a framework for modeling multiscale dynamics of coupled degrees of freedom in matter. Our work opens new opportunities for quantitative studies of nonequilibrium physics in materials, including driven lattice dynamics with phonons coupled to electrons, spin, and other degrees of freedom.

Yao, Jia [California Institute of Technology (CalT↗
DOE OSTI2025

Moment-based adaptive time integration for thermal radiation transport

Here, in this paper we develop a framework for moment-based adaptive time integration of deterministic multifrequency thermal radiation transpot (TRT). We generalize our recent semi-implicit-explicit (IMEX) integration framework for gray TRT to multifrequency TRT, and also introduce a semi-implicit variation that facilitates higher-order integration of TRT, where each stage is implicit in all components except opacities. To appeal to the broad literature on adaptivity with Runge–Kutta methods, we derive new embedded methods for four asymptotic preserving IMEX Runge–Kutta schemes we have found to be robust in our previous work on TRT and radiation hydrodynamics. We then use a moment-based high-order-low-order representation of the transport equations. Due to the high dimensionality, memory is always a concern in simulating TRT. We form error estimates and adaptivity in time purely based on temperature and radiation energy, for a trivial overhead in computational cost and memory usage compared with the base second order integrators. We then test the adaptivity in time on the tophat and Larsen problem, demonstrating the ability of the adaptive algorithm to naturally vary the timestep across 4–5 orders of magnitude, ranging from the dynamical timescales of the streaming regime to the thick diffusion limit.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2001

Time Integration Schemes for the Unsteady Navier-stokes Equations

The efficiency and accuracy of several time integration schemes are investigated for the unsteady Navier-Stokes equations. This study focuses on the efficiency of higher-order Runge-Kutta schemes in comparison with the popular Backward Differencing Formulations. For this comparison an unsteady two-dimensional laminar flow problem is chosen, i.e., flow around a circular cylinder at Re = 1200. It is concluded that for realistic error tolerances (smaller than 10(exp -1)) fourth-and fifth-order Runge-Kutta schemes are the most efficient. For reasons of robustness and computer storage, the fourth-order Runge-Kutta method is recommended. The efficiency of the fourth-order Runge-Kutta scheme exceeds that of second-order Backward Difference Formula by a factor of 2.5 at engineering error tolerance levels (10(exp -1) to 10(exp -2)). Efficiency gains are more dramatic at smaller tolerances.

Bijl, Hester↗
NASA NTRS1990

Estimation of convective rain volumes utilizing the are-time-integral technique

Interest in the possibility of developing useful estimates of convective rainfall with Area-Time Integral (ATI) methods is increasing. The basis of the ATI technique is the observed strong correlation between rainfall volumes and ATI values. This means that rainfall can be estimated by just determining the ATI values, if previous knowledge of the relationship to rain volume is available to calibrate the technique. Examples are provided of the application of the ATI approach to gage, radar, and satellite measurements. For radar data, the degree of transferability in time and among geographical areas is examined. Recent results on transferability of the satellite ATI calculations are presented.

Johnson, L. Ronald↗
DOE OSTI2021

Flow-driven spectral chaos (FSC) method for long-time integration of second-order stochastic dynamical systems

For decades, uncertainty quantification techniques based on the spectral approach have been demonstrated to be computationally more efficient than the Monte Carlo method for a wide variety of problems, particularly when the dimensionality of the probability space is relatively low. The time-dependent generalized polynomial chaos (TD-gPC) is one such technique that uses an evolving orthogonal basis to better represent the stochastic part of the solution space in time. Here in this paper, we present a new numerical method that uses the concept of enriched stochastic flow maps to track the evolution of the stochastic part of the solution space in time. The computational cost of this proposed flow-driven stochastic chaos (FSC) method is an order of magnitude lower than TD-gPC for comparable solution accuracy. This gain in computational cost is realized because, unlike most existing methods, the number of basis vectors required to track the stochastic part of the solution space does not depend upon the dimensionality of the probability space. Four representative numerical examples are presented to demonstrate the performance of the FSC method for long-time integration of second-order stochastic dynamical systems in the context of stochastic dynamics of structures.

FSC↗
DOE OSTI2017

Acceleration of diffusive molecular dynamics simulations through mean field approximation and subcycling time integration

Highlights: • Two numerical methods are presented to accelerate DMD simulations. • The methods greatly reduce the computation time without much loss of accuracy. • The accelerated DMD model is capable of simulating long-term mass transport at atomistic length scales. • Demonstrated for the propagation of an atomically sharp phase boundary over 30 seconds. - Abstract: Diffusive Molecular Dynamics (DMD) is a class of recently developed computational models for the simulation of long-term diffusive mass transport at atomistic length scales. Compared to previous atomistic models, e.g., transition state theory based accelerated molecular dynamics, DMD allows the use of larger time-step sizes, but has a higher computational complexity at each time-step due to the need to solve a nonlinear optimization problem at every time-step. This paper presents two numerical methods to accelerate DMD based simulations. First, we show that when a many-body potential function, e.g., embedded atom method (EAM), is employed, the cost of DMD is dominated by the computation of the mean of the potential function and its derivatives, which are high-dimensional random variables. To reduce the cost, we explore both first- and second-order mean field approximations. Specifically, we show that the first-order approximation, which uses a point estimate to calculate the mean, can reduce the cost by two to three orders of magnitude, but may introduce relatively large error in the solution. We show that adding an approximate second-order correction term can significantly reduce the error without much increase in computational cost. Second, we show that DMD can be significantly accelerated through subcycling time integration, as the cost of integrating the empirical diffusion equation is much lower than that of the optimization solver. To assess the DMD model and the numerical approximation methods, we present two groups of numerical experiments that simulate the diffusion of hydrogen in palladium nanoparticles. In particular, we show that the computational framework is capable of capturing the propagation of an atomically sharp phase boundary over a time window of more than 30 seconds. The effects of the proposed numerical methods on solution accuracy and computation time are also assessed quantitatively.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Measurement of the time-integrated 𝐶⁢𝑃 asymmetry in 𝐷 0 → 𝜋 0 ⁢𝜋 0 decays at Belle II

We measure the time-integrated 𝐶⁢𝑃 asymmetry, 𝐴 𝐶⁢𝑃 , in 𝐷 0 → 𝜋 0 ⁢𝜋 0 decays reconstructed in 𝑒 + ⁢𝑒 − → $𝑐⁢\bar{𝑐}$ events collected by Belle II during 2019–2022. The data corresponds to an integrated luminosity of 428 fb −1 . The 𝐷 0 decays are required to originate from the flavor-conserving 𝐷 *+ → 𝐷 0 ⁢𝜋 + decay to determine the charm flavor at production time. Control samples of 𝐷 0 → 𝐾 − ⁢𝜋 + decays, with or without an associated pion from a 𝐷 *+ decay, are used to correct for detection asymmetries. The result, 𝐴 𝐶⁢𝑃 ⁡(𝐷 0 → 𝜋 0 ⁢𝜋 0 ) = (0.30 ± 0.72 ± 0.20)%, where the first uncertainty is statistical and the second systematic, is consistent with 𝐶⁢𝑃 symmetry.

CP violation↗
DOE OSTI2023

Additive Polynomial Time Integrators, Part I: Framework and Fully Implicit-Explicit Collocation Methods

In this paper we generalize the polynomial time integration framework to additively partitioned initial value problems. The framework we present is general and enables the construction of many new families of additive integrators with arbitrary order-of-accuracy and varying degree of implicitness. In this first work, we focus on a new class of implicit-explicit polynomial block methods that are based on fully implicit Runge–Kutta methods with Radau nodes and that possess high stage order. Here, we show that the new fully implicit-explicit (FIMEX) integrators have improved stability compared to existing IMEX Runge–Kutta methods, while also being more computationally efficient due to recent developments in preconditioning techniques for solving the associated systems of nonlinear equations. For PDEs on periodic domains where the implicit component is trivial to invert, we will show how parallelization of the right-hand side evaluations can be exploited to obtain significant speedup compared to existing serial IMEX Runge–Kutta methods. For parallel (in space) finite element discretizations, the new methods can achieve orders of magnitude better accuracy than existing IMEX Runge–Kutta methods and/or achieve a given accuracy several times times faster in terms of computational runtime.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Multiphysics Time-Integration for Turbulent Combustion at the Exascale

Turbulent reacting flow systems are often modeled with coupled time-dependent partial differential equations (PDEs). Solving such equations can easily tax the world's largest supercomputers. One pragmatic strategy for attacking such problems is to split the PDEs into components that can more easily be solved in isolation. This generic operator-splitting strategy leads to a set of ordinary differential equations (ODEs) that need to be solved as part of an "outer-loop" time-stepping approach. In many combustion applications, the ODEs to be solved can be very stiff, exhibiting timescales that span many orders of magnitude. The SUNDIALS library provides a plethora of robust time integration algorithms for solving these ODEs on exascale-capable computing hardware, yet for many complex applications (such multicomponent fuels or emissions predictions), the chemical models remain too complex to solve using reasonable resources. The Quasi-Steady State Approximation (QSSA) can be an effective tool for reducing the size and stiffness of the simulations. In this talk, I will discuss the use of the SUDIALS library of ODE solvers together with automatic code generation tools to solve complex turbulent reacting flow problems using QSSA models.

chemistry↗