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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 1,027 records · Page 57
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Global error analysis of the Chebyshev rational approximation method

The Chebyshev rational approximation method (CRAM) has become a widely adopted method for solving nuclear depletion problems. Therefore, understanding CRAM’s accuracy is important for the safe operation of nuclear power plants. This article performs a global error analysis of CRAM and finds that, as the length of the time step approaches zero, the relative error measured between the exact and CRAM solutions at a fixed end time approaches one and infinity for even and odd orders, respectively; for intermediate time step sizes, a minimum in relative error is observed. Finally, we show that the reason for CRAM’s behavior is that the method is inconsistent. Two best practices for using CRAM, derived from these results, are: (1) use CRAM order 16 or higher, (2) if necessary, increase the CRAM order when multiphysics coupling requires smaller time steps.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1976

On the accuracy of the 'decoupled l-dominant' approximation for atom-molecule scattering

Cross sections for rotational excitation and spectral pressure broadening of HD, HCl, CO, and HCN due to collisions with low energy He atoms have been computed within the 'decoupled l-dominant' (DLD) approximation and are compared with accurate close coupling results and also with two similar approximations, the effective potential of Rabitz and the coupled states of McGuire and Kouri. DLD predictions of state-to-state cross sections are rather good, being only slightly less accurate than coupled states results. DLD is far superior to either the coupled states or effective potential methods for pressure broadening calculations, although it may not be uniformly of the quantitative accuracy desirable for obtaining intermolecular potentials from experimental data.

Green, S.↗
DOE OSTI2026

Enhancing photoionization rate calculations in low-temperature plasmas using spectral methods

Photoionization plays a central role in the development of streamer discharges and other non-equilibrium plasma phenomena. It creates seed electrons, which are essential for positive streamer propagation, allowing the ionization front to move forward. Because of this, accurate modeling of photoionization is very important for predicting streamer behavior and plasma evolution. The photoionization process in air (N 2 – O 2 mixture) is often described by the Zheleznyak model (1982). This model is usually solved through Helmholtz-type equations that approximate the Zheleznyak photoionization model (Zheleznyak et al. 1982) as Partial Differential Equations (PDEs). Conventional numerical methods, such as the Finite Difference Method (FDM) or Finite Volume Method (FVM), are widely used to solve these equations. Although they are prevalent, the computational cost of these methods due to their need for matrix operations and iterative solver is demanding. To address this challenge, this work develops a spectral solver based on the Fast Fourier Transform (FFT) combined with Discrete Cosine Transform (DCT) and Discrete Sine Transform (DST) to calculate the photoionization rate efficiently in an axisymmetric cylindrical domain. This method naturally satisfies the boundary conditions used in the model and converts the PDE into algebraic ones in spectral space. Thus, avoids the need for iterative matrix solvers. When compared with FDM results, it is demonstrated that the new solver not only maintains accuracy, but also reduces the computational cost, showing a performance increase of approximately 100 compared to FDM over a wide range of problem sizes. The method is parallelized using Message Passing Interface (MPI) and has been integrated into a fluid plasma model for streamer simulation. Here, this FFT-based approach provides a fast and reliable alternative for calculating photoionization in fluid models, helping large-scale plasma simulations run faster and efficiently, and allows higher-resolution simulation without extra computational cost.

Axisymmetric system↗
NASA NTRS1973

A computer program for calculating the perfect gas inviscid flow field about blunt axisymmetric bodies at an angle of attack of 0 deg

A method for the rapid calculation of the inviscid shock layer about blunt axisymmetric bodies at an angle of attack of 0 deg has been developed. The procedure is of an inverse nature, that is, a shock wave is assumed and calculations proceed along rays normal to the shock. The solution is iterated until the given body is computed. The flow field solution procedure is programed at the Langley Research Center for the Control Data 6600 computer. The geometries specified in the program are sphores, ellipsoids, paraboloids, and hyperboloids which may conical afterbodies. The normal momentum equation is replaced with an approximate algebraic expression. This simplification significantly reduces machine computation time. Comparisons of the present results with shock shapes and surface pressure distributions obtained by the more exact methods indicate that the program provides reasonably accurate results for smooth bodies in axisymmetric flow. However, further research is required to establish the proper approximate form of the normal momentum equation for the two-dimensional case.

Zoby, E. V.↗
DOE OSTI2022

Fermi–Löwdin orbital self-interaction correction of adsorption energies on transition metal ions

Density functional theory (DFT)-based descriptions of the adsorption of small molecules on transition metal ions are prone to self-interaction errors. Here, we show that such errors lead to a large over-estimation of adsorption energies of small molecules on Cu + , Zn + , Zn 2+ , and Mn + in local spin density approximation (LSDA) and Perdew, Burke, Ernzerhof (PBE) generalized gradient approximation calculations compared to reference values computed using the coupled-cluster with single, doubles, and perturbative triple excitations method. These errors are significantly reduced by removing self-interaction using the Perdew–Zunger self-interaction correction (PZ-SIC) in the Fermi–Löwdin Orbital (FLO) SIC framework. In the case of FLO-PBE, typical errors are reduced to less than 0.1 eV. Furthermore, analysis of the results using DFT energies evaluated on self-interaction-corrected densities [DFT(@FLO)] indicates that the density-driven contributions to the FLO-DFT adsorption energy corrections are roughly the same size in DFT = LSDA and PBE, but the total corrections due to removing self-interaction are larger in LSDA.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Fast explicit solutions for neutrino-electron scattering: Explicit asymptotic methods

Here, we present results of explicit asymptotic approximations applied to neutrino-electron scattering in a representative model of neutrino population evolution under conditions characteristic of core-collapse supernova explosions or binary neutron star mergers. It is shown that this approach provides stable solutions of these stiff systems of equations, with accuracy and time stepping comparable to that for standard implicit treatments such as backward Euler, fixed point iteration, and Anderson-accelerated fixed point iteration. Because each time step can be computed more rapidly with the explicit asymptotic approximation than with implicit methods, this suggests that algebraically stabilized explicit integration methods could be used to compute neutrino evolution coupled to hydrodynamics more efficiently in stellar explosions and mergers than the methods currently in use.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1980

Laser-heated thruster

The development of computer codes for the thrust chamber of a rocket of which the propellant gas is heated by a CW laser beam was investigated. The following results are presented: (1) simplified models of laser heated thrusters for approximate parametric studies and performance mapping; (3) computer programs for thrust chamber design; and (3) shock tube experiment to measure absorption coefficients. Two thrust chamber design programs are outlined: (1) for seeded hydrogen, with both low temperature and high temperature seeds, which absorbs the laser radiation continuously, starting at the inlet gas temperature; and (2) for hydrogen seeded with cesium, in which a laser supported combustion wave stands near the gas inlet, and heats the gas up to a temperature at which the gas can absorb the laser energy.

Kemp, N. H.↗
NASA NTRS1983

A grid-embedding transonic flow analysis computer program for wing/nacelle configurations

An efficient grid-interfacing zonal algorithm was developed for computing the three-dimensional transonic flow field about wing/nacelle configurations. the algorithm uses the full-potential formulation and the AF2 approximate factorization scheme. The flow field solution is computed using a component-adaptive grid approach in which separate grids are employed for the individual components in the multi-component configuration, where each component grid is optimized for a particular geometry such as the wing or nacelle. The wing and nacelle component grids are allowed to overlap, and flow field information is transmitted from one grid to another through the overlap region using trivariate interpolation. This report represents a discussion of the computational methods used to generate both the wing and nacelle component grids, the technique used to interface the component grids, and the method used to obtain the inviscid flow solution. Computed results and correlations with experiment are presented. also presented are discussions on the organization of the wing grid generation (GRGEN3) and nacelle grid generation (NGRIDA) computer programs, the grid interface (LK) computer program, and the wing/nacelle flow solution (TWN) computer program. Descriptions of the respective subroutines, definitions of the required input parameters, a discussion on interpretation of the output, and the sample cases illustrating application of the analysis are provided for each of the four computer programs.

Atta, E. H.↗
DOE OSTI2021

Incorporating Flexibility Effects into Metal–Organic Framework Adsorption Simulations Using Different Models

High-throughput calculations based on molecular simulations to predict the adsorption of molecules inside metal–organic frameworks (MOFs) have become a useful complement to experimental efforts to identify promising adsorbents for chemical separations and storage. For computational convenience, all existing efforts of this kind have relied on simulations in which the MOF is approximated as rigid. In this paper, we use extensive adsorption–relaxation simulations that fully include MOF flexibility effects to explore the validity of the rigid framework approximation. We also examine the accuracy of several approximate methods to incorporate framework flexibility that are more computationally efficient than adsorption–relaxation calculations. We first benchmark various models of MOF flexibility for four MOFs with well-established CO 2 experimental consensus isotherms. We then consider a range of adsorption properties, including Henry’s constants, nondilute loadings, and adsorption selectivity, for seven adsorbates in 15 MOFs randomly selected from the CoRE MOF database. Our results indicate that in many MOFs adsorption–relaxation simulations are necessary to make quantitative predictions of adsorption, particularly for adsorption at dilute concentrations, although more standard calculations based on rigid structures can provide useful information. Finally, we investigate whether a correlation exists between the elastic properties of empty MOFs and the importance of including framework flexibility in making accurate predictions of molecular adsorption. Our results did not identify a simple correlation of this type.

36 MATERIALS SCIENCE↗
NASA NTRS2012

Error Estimates of the Ares I Computed Turbulent Ascent Longitudinal Aerodynamic Analysis

Numerical predictions of the longitudinal aerodynamic characteristics for the Ares I class of vehicles, along with the associated error estimate derived from an iterative convergence grid refinement, are presented. Computational results are based on an unstructured grid, Reynolds-averaged Navier-Stokes analysis. The validity of the approach to compute the associated error estimates, derived from a base grid to an extrapolated infinite-size grid, was first demonstrated on a sub-scaled wind tunnel model at representative ascent flow conditions for which the experimental data existed. Such analysis at the transonic flow conditions revealed a maximum deviation of about 23% between the computed longitudinal aerodynamic coefficients with the base grid and the measured data across the entire roll angles. This maximum deviation from the wind tunnel data was associated with the computed normal force coefficient at the transonic flow condition and was reduced to approximately 16% based on the infinite-size grid. However, all the computed aerodynamic coefficients with the base grid at the supersonic flow conditions showed a maximum deviation of only about 8% with that level being improved to approximately 5% for the infinite-size grid. The results and the error estimates based on the established procedure are also presented for the flight flow conditions.

Abdol-Hamid, Khaled S.↗
DOE OSTI2022

GenMod: A generative modeling approach for spectral representation of PDEs with random inputs

Here, we propose a method for quantifying uncertainty in high-dimensional PDE systems with random parameters, where the number of solution evaluations is small. Parametric PDE solutions are often approximated using a spectral decomposition based on polynomial chaos expansions. For the class of systems we consider (i.e., high dimensional with limited solution evaluations) the coefficients are given by an underdetermined linear system in a regression formulation. This implies additional assumptions, such as sparsity of the coefficient vector, are needed to approximate the solution. Here, we present an approach where we assume the coefficients are close to the range of a generative model that maps from a low to a high dimensional space of coefficients. Our approach is inspired be recent work examining how generative models can be used for compressed sensing in systems with random Gaussian measurement matrices. Using results from PDE theory on coefficient decay rates, we construct an explicit generative model that predicts the polynomial chaos coefficient magnitudes. The algorithm we developed to find the coefficients, which we call GenMod, is composed of two main steps. First, we predict the coefficient signs using Orthogonal Matching Pursuit. Then, we assume the coefficients are within a sparse deviation from the range of a sign-adjusted generative model. This allows us to find the coefficients by solving a nonconvex optimization problem, over the input space of the generative model and the space of sparse vectors. We obtain theoretical recovery results for a Lipschitz continuous generative model and for a more specific generative model, based on coefficient decay rate bounds. We examine three high-dimensional problems and show that, for all three examples, the generative model approach outperforms sparsity promoting methods at small sample sizes.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1974

Evaluation of atomic constants for optical radiation, volume 1

Atomic constants for optical radiation are discussed which include transition probabilities, line strengths, and oscillator strengths for both dipole and quadrupole transitions, as well as the associated matrix elements needed for line broadening calculations. Atomic constants were computed for a wide selection of elements and lines. An existing computer program was used, with modifications to include, in an approximate manner, the effect of equivalent electrons, and to enable reordering and restructuring of the output for publication. This program is suitable for fast, low cost computation of the optical constants, using the Coulomb approximation formalism for LS coupling.

Kylstra, C. D.↗
DOE OSTI2021

Data-Driven Learning for the Mori--Zwanzig Formalism: A Generalization of the Koopman Learning Framework

A theoretical framework which unifies the conventional Mori--Zwanzig formalism and the approximate Koopman learning of deterministic dynamical systems from noiseless observation is presented. In this framework, the Mori--Zwanzig formalism, developed in statistical mechanics to tackle the hard problem of construction of reduced-order dynamics for high-dimensional dynamical systems, can be considered as a natural generalization of the Koopman description of the dynamical system. We next show that, similar to the approximate Koopman learning methods, data-driven methods can be developed for the Mori--Zwanzig formalism with Mori's linear projection operator. We have developed two algorithms to extract the key operators, the Markov and the memory kernel, using time series of a reduced set of observables in a dynamical system. We have adopted the Lorenz `96 system as a test problem and solved for the above operators. These operators exhibit complex behaviors, which are unlikely to be captured by traditional modeling approaches in Mori--Zwanzig analysis. The nontrivial generalized fluctuation-dissipation relationship, which relates the memory kernel with the two-time correlation statistics of the orthogonal dynamics, was numerically verified as a validation of the solved operators. Here we present numerical evidence that the generalized Langevin equation, a key construct in the Mori--Zwanzig formalism, is more advantageous in predicting the evolution of the reduced set of observables than the conventional approximate Koopman operators.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1997

Validation of an Accurate Three-Dimensional Helical Slow-Wave Circuit Model

The helical slow-wave circuit embodies a helical coil of rectangular tape supported in a metal barrel by dielectric support rods. Although the helix slow-wave circuit remains the mainstay of the traveling-wave tube (TWT) industry because of its exceptionally wide bandwidth, a full helical circuit, without significant dimensional approximations, has not been successfully modeled until now. Numerous attempts have been made to analyze the helical slow-wave circuit so that the performance could be accurately predicted without actually building it, but because of its complex geometry, many geometrical approximations became necessary rendering the previous models inaccurate. In the course of this research it has been demonstrated that using the simulation code, MAFIA, the helical structure can be modeled with actual tape width and thickness, dielectric support rod geometry and materials. To demonstrate the accuracy of the MAFIA model, the cold-test parameters including dispersion, on-axis interaction impedance and attenuation have been calculated for several helical TWT slow-wave circuits with a variety of support rod geometries including rectangular and T-shaped rods, as well as various support rod materials including isotropic, anisotropic and partially metal coated dielectrics. Compared with experimentally measured results, the agreement is excellent. With the accuracy of the MAFIA helical model validated, the code was used to investigate several conventional geometric approximations in an attempt to obtain the most computationally efficient model. Several simplifications were made to a standard model including replacing the helical tape with filaments, and replacing rectangular support rods with shapes conforming to the cylindrical coordinate system with effective permittivity. The approximate models are compared with the standard model in terms of cold-test characteristics and computational time. The model was also used to determine the sensitivity of various circuit parameters including typical manufacturing dimensional tolerances and support rod permittivity. By varying the circuit parameters of an accurate model using MAFIA, these sensitivities can be computed for manufacturing concerns, and design optimization previous to fabrication, thus eliminating the need for costly experimental iterations. Several variations were made to a standard helical circuit using MAFIA to investigate the effect that variations on helical tape and support rod width, metallized loading height and support rod permittivity, have on TWT cold-test characteristics.

Kory, Carol L.↗
DOE OSTI2024

Static Subspace Approximation for Random Phase Approximation Correlation Energies: Implementation and Performance

Developing theoretical understanding of complex reactions and processes at interfaces requires using methods that go beyond semilocal density functional theory to accurately describe the interactions between solvent, reactants and substrates. Methods based on many-body perturbation theory, such as the random phase approximation (RPA), have previously been limited due to their computational complexity. However, this is now a surmountable barrier due to the advances in computational power available, in particular through modern GPU-based supercomputers. In this work, we describe the implementation of RPA calculations within BerkeleyGW and show its favorable computational performance on large complex systems relevant for catalysis and electrochemistry applications. Our implementation builds off of the static subspace approximation which, by employing a compressed representation of the frequency dependent polarizability, enables the evaluation of the RPA correlation energy with significant acceleration and systematically controllable accuracy. We find that the computational cost of calculating the RPA correlation energy scales only linearly with system size for systems containing up to 50 thousand bands, and is expected to scale quadratically thereafter. We also show excellent strong scaling results across several supercomputers, demonstrating the performance and portability of this implementation.

algorithmic development↗
DOE OSTI2022

A Fast Time-Stepping Strategy for Dynamical Systems Equipped with a Surrogate Model

Simulation of complex dynamical systems arising in many applications is computationally challenging due to their size and complexity. Model order reduction, machine learning, and other types of surrogate modeling techniques offer cheaper and simpler ways to describe the dynamics of these systems but are inexact and introduce additional approximation errors. In order to overcome the computational difficulties of the full complex models, on one hand, and the limitations of surrogate models, on the other, this work proposes a new accelerated time-stepping strategy that combines information from both. This approach is based on the multirate infinitesimal general-structure additive Runge--Kutta framework. The inexpensive surrogate model is integrated with a small time step to guide the solution trajectory, and the full model is treated with a large time step to occasionally correct for the surrogate model error and ensure convergence. Here, we provide a theoretical error analysis, and several numerical experiments, to show that this approach can be significantly more efficient than using only the full or only the surrogate model for the integration.

Surrogate models↗
DOE OSTI2025

Recent Developments in DFTB+, a Software Package for Efficient Atomistic Quantum Mechanical Simulations

DFTB+ is a flexible, open-source software package developed by its community, designed for fast and efficient atomistic quantum mechanical simulations. It employs various methods that approximate density functional theory (DFT), such as density functional-based tight binding (DFTB) and the extended tight binding (xTB) approach allowing simulations of large systems over extended time scales with reasonable accuracy, while being significantly faster than traditional ab initio methods. In recent years, several new extensions of the DFTB method have been developed and implemented in the DFTB+ program package in order to improve the accuracy and generality of the available simulation results. In this paper, we review those enhancements, show several use case examples and discuss the strengths and limitations of its features.

36 MATERIALS SCIENCE↗
NASA NTRS1984

Algebraic grid generation for wing-fuselage bodies

An algebraic procedure for the generation of boundary-fitted grids about wing-fuselage configurations is presented. A wing-fuselage configuration is specified by cross sections and mathematically represented by Coons' patches. A configuration is divided into sections so that several grid blocks that either adjoin each other or partially overlap each other can be generated, and each grid has six surfaces that map into a computational cube. Grids are first determined on the six boundary surfaces and then in the interior. Grid curves that are on the surface of the configuration are derived using plane-patch intersections, and single-valued functions relating approximate arc lengths along the curves to computational coordinates define the distribution of grid points. The two-boundary technique and transfinite interpolation are used to determine the boundary surface grids that are not on the configuration, and transfinite interpolation with linear blending functions is used to determine the interior grids.

Smith, R. E.↗