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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 829 records · Page 46
All sourcesNASA NTRSDOE OSTI
DOE OSTI2014

Communication: On the consistency of approximate quantum dynamics simulation methods for vibrational spectra in the condensed phase

Including quantum mechanical effects on the dynamics of nuclei in the condensed phase is challenging, because the complexity of exact methods grows exponentially with the number of quantum degrees of freedom. Efforts to circumvent these limitations can be traced down to two approaches: methods that treat a small subset of the degrees of freedom with rigorous quantum mechanics, considering the rest of the system as a static or classical environment, and methods that treat the whole system quantum mechanically, but using approximate dynamics. Here, we perform a systematic comparison between these two philosophies for the description of quantum effects in vibrational spectroscopy, taking the Embedded Local Monomer model and a mixed quantum-classical model as representatives of the first family of methods, and centroid molecular dynamics and thermostatted ring polymer molecular dynamics as examples of the latter. We use as benchmarks D{sub 2}O doped with HOD and pure H{sub 2}O at three distinct thermodynamic state points (ice Ih at 150 K, and the liquid at 300 K and 600 K), modeled with the simple q-TIP4P/F potential energy and dipole moment surfaces. With few exceptions the different techniques yield IR absorption frequencies that are consistent with one another within a few tens of cm{sup −1}. Comparison with classical molecular dynamics demonstrates the importance of nuclear quantum effects up to the highest temperature, and a detailed discussion of the discrepancies between the various methods let us draw some (circumstantial) conclusions about the impact of the very different approximations that underlie them. Such cross validation between radically different approaches could indicate a way forward to further improve the state of the art in simulations of condensed-phase quantum dynamics.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Verification and validation of the open-source plasma fluid code: Zapdos

Zapdos is an open-source finite element plasma fluid solver based on the MOOSE multiphysics framework. This paper outlines Zapdos verification, benchmarking, and validation efforts for 1D and 2D RF capacitively coupled plasma discharge models for mid-range pressures (0.1 - 1 Torr). The verification process involved using the method of manufactured solutions to assess Zapdos spatial and temporal error convergence. L2 errors ranged from 10 -2 to 10 -4 , while the convergence’s slope were in agreement with the predicted slopes for the tested variable and time integration orders. The benchmarking process involved comparisons to previously results from the validated finite element code, LSODI. These works included 1D and 2D simulations for a range of plasma parameters (densities, temperatures, voltage, etc.). For the 1D cases, Zapdos and LSODI results were in very good agreement. In the 2D cases, variable behaviors matched, with slight discrepancies in peak values. The validation process involved comparisons to experimental works including electron density measurements by microwave interferometry and metastable density measurements by planar laser-induced fluorescence imaging. Results shown reasonable agreement at higher pressure, with results starting to diverge at low pressures. Furthermore, probable causes for this diverges are the limitation of the fluid assumption for plasmas at low pressure, or the need for more robust boundary conditions. Overall, Zapdos shown reasonable results for the verification, benchmarking, and validation efforts, and Zapdos can be downloaded at https://github.com/shannon-lab/zapdos.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Physically interpretable approximations of many-body spectral functions

The rational function approximation provides a natural and interpretable representation of response functions such as the many-body spectral functions. We apply the vector fitting (VFIT) algorithm to fit a variety of spectral functions calculated from the Holstein model of electron-phonon interactions. We show that the resulting rational functions are highly efficient in their fitting of sharp features in the spectral functions, and could provide a means to infer physically relevant information from a spectral data set. The position of the peaks in the approximated spectral function are determined by the location of poles in the complex plane. Additionally, we developed a variant of VFIT that incorporates regularization to improve the quality of fits. With this procedure, we demonstrate it is possible to achieve accurate spectral function fits that vary smoothly as a function of physical conditions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1979

Perturbation solutions of combustion instability problems

A method involving approximate modal analysis using the Galerkin method followed by an approximate solution of the resulting modal-amplitude equations by the two-variable perturbation method (method of multiple scales) is applied to two problems of pressure-sensitive nonlinear combustion instability in liquid-fuel rocket motors. One problem exhibits self-coupled instability while the other exhibits mode-coupled instability. In both cases it is possible to carry out the entire linear stability analysis and significant portions of the nonlinear stability analysis in closed form. In the problem of self-coupled instability the nonlinear stability boundary and approximate forms of the limit-cycle amplitudes and growth and decay rates are determined in closed form while the exact limit-cycle amplitudes and growth and decay rates are found numerically. In the problem of mode-coupled instability the limit-cycle amplitudes are found in closed form while the growth and decay rates are found numerically. The behavior of the solutions found by the perturbation method are in agreement with solutions obtained using complex numerical methods.

Googerdy, A.↗
DOE OSTI2021

An adaptive Hessian approximated stochastic gradient MCMC method

Bayesian approaches have been successfully integrated into training deep neural networks. One popular family is stochastic gradient Markov chain Monte Carlo methods (SG-MCMC), which have gained increasing interest due to their ability to handle large datasets and the potential to avoid overfitting. Although standard SG-MCMC methods have shown great performance in a variety of problems, they may be inefficient when the random variables in the target posterior densities have scale differences or are highly correlated. Here, we present an adaptive Hessian approximated stochastic gradient MCMC method to incorporate local geometric information while sampling from the posterior. The idea is to apply stochastic approximation (SA) to sequentially update a preconditioning matrix at each iteration. The preconditioner possesses second-order information and can guide the random walk of a sampler efficiently. Instead of computing and saving the full Hessian of the log posterior, we use limited memory of the samples and their stochastic gradients to approximate the inverse Hessian-vector multiplication in the updating formula. Moreover, by smoothly optimizing the preconditioning matrix via SA, our proposed algorithm can asymptotically converge to the target distribution with a controllable bias under mild conditions. To reduce the training and testing computational burden, we adopt a magnitude-based weight pruning method to enforce the sparsity of the network. Our method is user-friendly and demonstrates better learning results compared to standard SG-MCMC updating rules. The approximation of inverse Hessian alleviates storage and computational complexities for large dimensional models. Numerical experiments are performed on several problems, including sampling from 2D correlated distribution, synthetic regression problems, and learning the numerical solutions of heterogeneous elliptic PDE. The numerical results demonstrate great improvement in both the convergence rate and accuracy.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1986

Comparative accuracy of selected multiple scattering approximations

Doubling method computational results which have yielded plane albedo, total transmission and fractional absorption for plane-parallel atmospheres composed of cloud droplets are presently compared with data obtained with selected radiative transfer approximations. The relative and absolute accuracies of asymptotic theory for thick layers and delta-Eddington, Meador-Weaver (1980) and Coakley-Chylek (1975) approximations are compared as a function of optical thickness, solar zenith angle, and single scattering albedo. The delta-Eddington approximation is the most accurate for conservative scattering when the solar zenith angle is small, while Meador-Weaver is the most accurate for nonconservative scattering.

King, M. D.↗
NASA NTRS1989

Methods for local gravity field approximation

The most widely known modern method for estimating gravity field values from observed data is least-squares collocation. Its advantages are that it can make estimates at arbitrary locations based on irregularly spaced observations, and that it makes use of statistical information about errors in the input data while providing corresponding information about the quality of the output estimates. Disadvantages of collocation include the necessity of inverting square matrices of dimension equal to the number of data values and the need to assume covariance models for the gravity field and the data errors. Fourier methods are an important alternative to collocation; having the advantage of greater computational efficiency, but requiring data estimates to be on a regular grid and not using or providing statistical accuracy information. The GEOFAST algorithm is an implementation of collocation that achieves high computational efficiency by transforming the estimation equations into the frequency domain where an accurate approximation may be made to reduce the workload. The forward and inverse Fast Fourier Transforms (FFTs) are utilized. The accuracy and computational efficiency of the GEOFAST algorithm is demonstrated using two sets of synthetic gravity data: marine gravity for an ocean trench region including wavelengths longer than 200 km; and local land gravity containing wavelengths as short as 5 km. These results are discussed along with issues such as the advantages of first removing reference field models before carrying out the estimation algorithm.

Sailor, R. V.↗
DOE OSTI2017

Approximate tensor-product preconditioners for very high order discontinuous Galerkin methods

In this study, we develop a new tensor-product based preconditioner for discontinuous Galerkin methods with polynomial degrees higher than those typically employed. This preconditioner uses an automatic, purely algebraic method to approximate the exact block Jacobi preconditioner by Kronecker products of several small, one-dimensional matrices. Traditional matrix-based preconditioners require O ( p 2d ) storage and O ( p 3d ) computational work, where p is the degree of basis polynomials used, and d is the spatial dimension. Our SVD-based tensor-product preconditioner requires O ( p d+1 ) storage, O ( p d+1 ) work in two spatial dimensions, and O ( p d+2 ) work in three spatial dimensions. Combined with a matrix-free Newton–Krylov solver, these preconditioners allow for the solution of DG systems in linear time in p per degree of freedom in 2D, and reduce the computational complexity from O ( p 9 ) to O ( p 5 ) in 3D. Numerical results are shown in 2D and 3D for the advection, Euler, and Navier–Stokes equations, using polynomials of degree up to p = 30. For many test cases, the preconditioner results in similar iteration counts when compared with the exact block Jacobi preconditioner, and performance is significantly improved for high polynomial degrees p .

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Randomized methods to characterize large-scale vortical flow networks

We demonstrate the effective use of randomized methods for linear algebra to perform network-based analysis of complex vortical flows. Network theoretic approaches can reveal the connectivity structures among a set of vortical elements and analyze their collective dynamics. These approaches have recently been generalized to analyze high-dimensional turbulent flows, for which network computations can become prohibitively expensive. In this work, we propose efficient methods to approximate network quantities, such as the leading eigendecomposition of the adjacency matrix, using randomized methods. Specifically, we use the Nyström method to approximate the leading eigenvalues and eigenvectors, achieving significant computational savings and reduced memory requirements. The effectiveness of the proposed technique is demonstrated on two high-dimensional flow fields: two-dimensional flow past an airfoil and two-dimensional turbulence. We find that quasi-uniform column sampling outperforms uniform column sampling, while both feature the same computational complexity.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Parallel domain decomposition method for finite element approximation of 3D steady state non‐Newtonian fluids

Summary We introduce a stabilized finite element method for the 3D non‐Newtonian Navier–Stokes equations and a parallel domain decomposition method for solving the sparse system of nonlinear equations arising from the discretization. Non‐Newtonian flow problems are, generally speaking, more challenging than Newtonian flows because the nonlinearities are not only in the convection term but also in the viscosity term, which depends on the shear rate. Many good iterative methods and preconditioning techniques that work well for the Newtonian flows do not work well for the non‐Newtonian flows. We employ a Galerkin/least squares finite element method, with stabilization parameters adjusted to count the non‐Newtonian effect, to discretize the equations, and the resulting highly nonlinear system of equations is solved by a Newton–Krylov–Schwarz algorithm. In this study, we apply the proposed method to some inelastic power‐law fluid flows through the eccentric annuli with inner cylinder rotation and investigate the robustness of the method with respect to some physical parameters, including the power‐law index and the Reynolds number ratios. We then report the superlinear speedup achieved by the domain decomposition algorithm on a computer with up to 512 processors. Copyright © 2015 John Wiley & Sons, Ltd.

Shiu, Wen‐Shin↗
DOE OSTI2016

Extended application of Kohn-Sham first-principles molecular dynamics method with plane wave approximation at high energy—From cold materials to hot dense plasmas

An extended first-principles molecular dynamics (FPMD) method based on Kohn-Sham scheme is proposed to elevate the temperature limit of the FPMD method in the calculation of dense plasmas. The extended method treats the wave functions of high energy electrons as plane waves analytically and thus expands the application of the FPMD method to the region of hot dense plasmas without suffering from the formidable computational costs. In addition, the extended method inherits the high accuracy of the Kohn-Sham scheme and keeps the information of electronic structures. This gives an edge to the extended method in the calculation of mixtures of plasmas composed of heterogeneous ions, high-Z dense plasmas, lowering of ionization potentials, X-ray absorption/emission spectra, and opacities, which are of particular interest to astrophysics, inertial confinement fusion engineering, and laboratory astrophysics.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2014

Hyperfine excitation of linear molecules by para- and ortho-H{sub 2}: Application to the HCl–H{sub 2} system

The determination of hyperfine structure resolved excitation cross sections and rate coefficients due to H{sub 2} collisions is required to interpret astronomical spectra. In this paper, we present several theoretical approaches to compute these data. An almost exact recoupling approach and approximate sudden methods are presented. We apply these different approaches to the HCl–H{sub 2} collisional system in order to evaluate their respective accuracy. HCl–H{sub 2} hyperfine structure resolved cross sections and rate coefficients are then computed using recoupling and approximate sudden methods. As expected, the approximate sudden approaches are more accurate when the collision energy increases and the results suggest that these approaches work better for para-H{sub 2} than for ortho-H{sub 2} colliding partner. For the first time, we present HCl–H{sub 2} hyperfine structure resolved rate coefficients, computed here for temperatures ranging from 5 to 300 K. The usual Δj{sub 1} = ΔF{sub 1} propensity rules are observed for the hyperfine transitions. The new rate coefficients will significantly help the interpretation of interstellar HCl emission lines observed with current and future telescopes. We expect that these new data will allow a better determination of the HCl abundance in the interstellar medium, that is crucial to understand the interstellar chlorine chemistry.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Approximate DFT-based methods for generating diabatic states and calculating electronic couplings: models of two and more states

Four types of density functional theory (DFT)-based approaches are assessed in this work for the approximate construction of diabatic states and the evaluation of electronic couplings between these states. These approaches include the constrained DFT (CDFT) method, the constrained noninteracting electron (CNE) model to post-process Kohn–Sham operators, the approximate block-diagonalization (BD) of the Kohn–Sham operators, and the generalized Mulliken–Hush method. It is shown that the first three approaches provide a good description for long-distance intermolecular electron transfer (ET) reactions. On the other hand, inconsistent results were found when applying these approaches to intramolecular ET in strongly coupled, mixed-valence systems. Model analysis shows that this discrepancy is caused by the inappropriate use of the two-state model rather than the defects of the approaches themselves. The situation is much improved when more states are included in the model electronic Hamiltonian. The CNE and BD approaches can thus serve as efficient and robust alternatives for building ET models based on DFT calculations.

Yang, Chou-Hsun↗
DOE OSTI2022

Evaluating Grid Strength under Uncertain Renewable Generation

The increasing displacement of synchronous generators with renewable resources such as wind and solar via power electronic interfaces causes a reduction in short-circuit strength and weak grid issues. The variation and uncertainty of renewable energy increase challenges for identifying weak grid conditions. This paper proposes an efficient method to analyze the impact of uncertain renewable energy on grid strength. The proposed method uses the probabilistic collocation method (PCM) to approximate the results of grid strength assessment under uncertain renewable generation, in order to reduce computational burden without compromising result accuracy when compared with traditional Monte Carlo simulation (MCS). To improve the accuracy of the approximation results, the proposed method integrates the K-means clustering technique with PCM to select the approximation samples of input variables. The efficacy of the proposed method is demonstrated by comparison with MCS on the modified IEEE 9-bus system and modified IEEE 39-bus system with multiple renewable generators.

grid strength↗
NASA NTRS1988

Explicit and implicit solution of the Navier-Stokes equations on a massively parallel computer

The design, implementation, and performance of a two-dimensional time-accurate Navier-Stokes solver for the CM2 supercomputer are described. The program uses a single processor for each grid point. Two different time-stepping methods have so far been implemented: an explicit third-order Runge-Kutta method and an implicit approximation-factorization method. The CM2 results are checked against those of a mature well-vectorized Cray 2 program, both for correctness and performance. The code is found to be correct, and the performance in some cases is up to several times that of the Cray 2.

Levit, Creon↗
NASA NTRSDate not supplied

Intent Modeling and Intent Conflict Probability Calculation for Operations in Upper Class E Airspace

This work presents probabilistic intent models for two typical vehicles in ETM operational environment. Several methods, including analytical methods for approximated solutions and a numerical method for exact solution, are presented and applied to compute the intent conflict probability for ETM operations. A comparison of these methods will be conducted in the final paper. Furthermore, simulations will be performed to verify the probabilistic intent model and verify the results of intent conflict probability from different methods.

Operational intent↗