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At least 1,135 records · Page 63
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

The neutron number probability distribution in coupled lumped assemblies

Here, the validity of the gamma distribution in describing the neutron number probability distribution function for both isolated and coupled multiplying assemblies when constrained to reproduce the true mean and variance is investigated in lumped geometry by numerical comparison with kinetic Monte Carlo simulations. The mean and variance are obtained from numerical solution of moment equations constructed from the relevant forward Master equation with assembly coupling coefficients obtained from a view factor method. Numerical results for a two-group, two coupled assemblies model, with static and dynamic reactivity insertion, show that except for subcritical assemblies, the gamma distribution well-approximates the number distribution. Differences in the fast and thermal neutron population shapes are explained in terms of effective source strengths due to downscatter and coupling.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2018

Computing resonant modes of accelerator cavities by solving nonlinear eigenvalue problems via rational approximation

Here, we present an efficient and reliable algorithm for solving a class of nonlinear eigenvalue problems arising from the modeling of particle accelerator cavities. The eigenvalue nonlinearity in these problems results from the use of waveguides to couple external power sources or to allow certain excited electromagnetic modes to exit the cavity. We use a rational approximation to reduce the nonlinear eigenvalue problem first to a rational eigenvalue problem. We then apply a special linearization procedure to turn the rational eigenvalue problem into a larger linear eigenvalue problem with the same eigenvalues, which can be solved by existing iterative methods. By using a compact scheme to represent both the linearized operator and the eigenvectors to be computed, we obtain a numerical method that only involves solving linear systems of equations of the same dimension as the original nonlinear eigenvalue problem. We refer to this method as a compact rational Krylov (CORK) method. We implemented the CORK method in the Omega3P module of the Advanced Computational Electromagnetic 3D Parallel (ACE3P) simulation suite and validated it by comparing the computed cavity resonant frequencies and damping Q factors of a small model problem to those obtained from a fitting procedure that uses frequency responses computed by another ACE3P module called S3P. We also used the CORK method to compute trapped modes damped in an ideal eight 9-cell SRF cavity cryomodule. This was the first time it was possible to compute these modes directly. The damping Q factors of the computed modes match well with those measured in experiments and the difference in resonant frequencies is within the range introduced by cavity imperfection. Therefore, the CORK method is an extremely valuable tool for computational cavity design.

43 PARTICLE ACCELERATORS↗
DOE OSTI2022

Phase retrieval and reconstruction of coherent synthesis by genetic algorithm

Abstract In the context of diffractive optics, phase retrieval is a heavily investigated process of recreating an entire complex electric field from partial amplitude-only information through iterative algorithms. However, existing methods can fall into local minima during reconstructions or struggle to recover unusual and novel electric field distributions. We present a numerical method based on a global-optimization genetic algorithm that reconstructs non-trivial electric field distributions from single diffracted intensity distributions. Diffraction and propagation of the optical fields over arbitrary distances is modeled through implementation of the angular spectrum technique. Additionally, a coherently-locked laser array system is used as an experimental case-study demonstrating 0.09 π phase reconstruction accuracy of initial laser parameters from single intensity images.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2013

Efficient and robust gradient enhanced Kriging emulators.

%E2%80%9CNaive%E2%80%9D or straight-forward Kriging implementations can often perform poorly in practice. The relevant features of the robustly accurate and efficient Kriging and Gradient Enhanced Kriging (GEK) implementations in the DAKOTA software package are detailed herein. The principal contribution is a novel, effective, and efficient approach to handle ill-conditioning of GEK's %E2%80%9Ccorrelation%E2%80%9D matrix, RN%CC%83, based on a pivoted Cholesky factorization of Kriging's (not GEK's) correlation matrix, R, which is a small sub-matrix within GEK's RN%CC%83 matrix. The approach discards sample points/equations that contribute the least %E2%80%9Cnew%E2%80%9D information to RN%CC%83. Since these points contain the least new information, they are the ones which when discarded are both the easiest to predict and provide maximum improvement of RN%CC%83's conditioning. Prior to this work, handling ill-conditioned correlation matrices was a major, perhaps the principal, unsolved challenge necessary for robust and efficient GEK emulators. Numerical results demonstrate that GEK predictions can be significantly more accurate when GEK is allowed to discard points by the presented method. Numerical results also indicate that GEK can be used to break the curse of dimensionality by exploiting inexpensive derivatives (such as those provided by automatic differentiation or adjoint techniques), smoothness in the response being modeled, and adaptive sampling. Development of a suitable adaptive sampling algorithm was beyond the scope of this work; instead adaptive sampling was approximated by omitting the cost of samples discarded by the presented pivoted Cholesky approach.

Dalbey, Keith R.↗
NASA NTRS1974

Periodic solutions in a class of nonlinear dual-mass systems

A class of nonlinear spring-mass systems with two degrees of freedom is studied. A numerical method is developed for determining the periodic solutions in such systems. The method grows out of a recent paper of Yen (1974a) in which properties of such periodic solutions have been investigated theoretically. Numerical results, obtained for some example systems involving linear, cubic and quintic spring forces, support the findings of Yen and reveal further details of the properties of such periodic solutions.

Yen, D. H. Y.↗
NASA NTRS1988

On a modified streamline curvature method for the Euler equations

A modification of the streamline curvature method leads to a quasilinear second-order partial differential equation for the streamline coordinate function. The existence of a stream function is not required. The method is applied to subsonic and supersonic nozzle flow, and to axially symmetric flow with swirl. For many situations, the associated numerical method is both fast and accurate.

Cordova, Jeffrey Q.↗
NASA NTRS1988

Transient natural convection heat and mass transfer in crystal growth

A numerical analysis of transient combined heat and mass transfer across a rectangular cavity is performed by a numerical method based on the SIMPLE algorithm. The physical parameters are selected to represent a range of possible crystal growth in solutions. Numerical results are compared with available experimental data to confirm the accuracy of the results. Good qualitative agreements are obtained for the average mass transfer rate across the cavity. Also, qualitative agreements are observed for the global development of thermal and solute fields. It is found that the thermal and solute fields become highly oscillatory when the thermal and solute Grashof numbers are large. Oscillations are probably caused by a number of different instability mechanisms. By reducing the gravity some of these instabilities were made to disappear at the lower Grashof numbers. Transient temperature and solute distribution near the crystal growing surface are highly non-uniform at the higher Grashof numbers. These non-uniformities are less severe in the reduced gravity environments but still exist. The effects of convection on the rate of average mass transfer are more than one order of magnitude higher than those of conduction in the range of Grashof numbers studied. Dependency of mass transfer rate on the Grashof number indicates that the convection effects many not be negligible even in the microgravity environments for the range of parameters investigated.

Han, Samuel S.↗
NASA NTRS1992

The present state and future directions of PDF methods

The objectives of the workshop are presented in viewgraph format, as is this entire article. The objectives are to discuss the present status and the future direction of various levels of engineering turbulence modeling related to Computational Fluid Dynamics (CFD) computations for propulsion; to assure that combustion is an essential part of propulsion; and to discuss Probability Density Function (PDF) methods for turbulent combustion. Essential to the integration of turbulent combustion models is the development of turbulent model, chemical kinetics, and numerical method. Some turbulent combustion models typically used in industry are the k-epsilon turbulent model, the equilibrium/mixing limited combustion, and the finite volume codes.

Pope, S. B.↗
NASA NTRS1992

Multiblock grid generation for jet engine configurations

The goal was to create methods for generating grids with minimal human intervention that are applicable to a wide range of problems and compatible with existing numerical methods and with existing and proposed computers. The following topics that are related to multiblock grid generation are briefly covered in viewgraph form: finding a domain decomposition, dimensioning grids, grid smoothing, manipulating grids and decompositions, and some specializations for jet engine configurations.

Stewart, Mark E. M.↗
DOE OSTI2017

A summary comparison of design evaluation techniques - 270

Many nuclear power plants in the United States have recently been granted a 20 year extension to their operation license and are considering modernization. The Idaho National Laboratory is committed to successful modernizations and has been identifying and developing candidate technologies for power plants using methods that match the requirements of an integrated system validation. To do so this paper discusses current and potential workload, situation awareness and other performance methods used in evaluating control room design against the criteria defined by the Nuclear Regulatory Commission. The analysis provided is narrowed to the scope of methods surrounding the Light Water Reactor Sustainability research at the Idaho National Laboratory and therefore evaluates only a handful of the numerous methods used in control room modernizing efforts. As such, it was determined the most popular methods for measuring situation awareness, workload, and performance are measurements that rarely measure their intended construct directly and must be inferred. Physiological measures of workload have matured and become more accessible, sensitive, unobtrusive, valid, and objective but are reliant on variable technology. Situation Awareness measures possess little construct validity but eye-tracking technology is a measure progressing in sensitivity, objectivity, and continues to improve in unobtrusiveness. All things considered, this paper has identified a significant need for a more extensive review of the various performance measures used in modernizing control rooms and integrated system validation. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2023

Code-verification techniques for the method-of-moments implementation of the magnetic-field integral equation

For computational physics simulations, code verification plays a major role in establishing the credibility of the results by assessing the correctness of the implementation of the underlying numerical methods. In computational electromagnetics, surface integral equations, such as the method-of-moments implementation of the magnetic-field integral equation, are frequently used to solve Maxwell's equations on the surfaces of electromagnetic scatterers. These electromagnetic surface integral equations yield many code-verification challenges due to the various sources of numerical error and their possible interactions. In this paper, we provide approaches to separately measure the numerical errors arising from these different error sources. We demonstrate the effectiveness of these approaches for cases with and without coding errors.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Gradient-based stochastic estimation of the density matrix

Fast estimation of the single-particle density matrix is key to many applications in quantum chemistry and condensed matter physics. The best numerical methods leverage the fact that the density matrix elements f(H) ij decay rapidly with distance rij between orbitals. This decay is usually exponential. However, for the special case of metals at zero temperature, algebraic decay of the density matrix appears and poses a significant numerical challenge. Here, we introduce a gradient-based probing method to estimate all local density matrix elements at a computational cost that scales linearly with system size. For zero-temperature metals, the stochastic error scales like S -(d+2)/2d , where d is the dimension and S is a prefactor to the computational cost. The convergence becomes exponential if the system is at finite temperature or is insulating.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Optimization-based, property-preserving finite element methods for scalar advection equations and their connection to Algebraic Flux Correction

In this paper, we continue our efforts to exploit optimization and control ideas as a common foundation for the development of property-preserving numerical methods. Here we focus on a class of scalar advection equations whose solutions have fixed mass in a given Eulerian region and constant bounds in any Lagrangian volume. Our approach separates discretization of the equations from the preservation of their solution properties by treating the latter as optimization constraints. This relieves the discretization process from having to comply with additional restrictions and makes stability and accuracy the sole considerations in its design. A property-preserving solution is then sought as a state that minimizes the distance to an optimally accurate but not property-preserving target solution computed by the scheme, subject to constraints enforcing discrete proxies of the desired properties. Furthermore, we consider two such formulations in which the optimization variables are given by the nodal solution values and suitably defined nodal fluxes, respectively. A key result of the paper reveals that a standard Algebraic Flux Correction (AFC) scheme is a modified version of the second formulation obtained by shrinking its feasible set to a hypercube. In conclusion, we present numerical studies illustrating the optimization-based formulations and comparing them with AFC

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

The Santa Barbara Binary-disk Code Comparison

We have performed numerical calculations of a binary interacting with a gas disk, using 11 different numerical methods and a standard binary-disk setup. The goal of this study is to determine whether all codes agree on a numerically converged solution and to determine the necessary resolution for convergence and the number of binary orbits that must be computed to reach an agreed-upon relaxed state of the binary-disk system. We find that all codes can agree on a converged solution (depending on the diagnostic being measured). The zone spacing required for most codes to reach a converged measurement of the torques applied to the binary by the disk is roughly 1% of the binary separation in the vicinity of the binary components. For our disk model to reach a relaxed state, codes must be run for at least 200 binary orbits, corresponding to about a viscous time for our parameters, 0.2(a 2 Ω B /v) is the kinematic viscosity. The largest discrepancies between codes resulted from the dimensionality of the setup (3D vs. 2D disks). We find good agreement in the total torque on the binary between codes, although the partition of this torque between the gravitational torque, orbital accretion torque, and spin accretion torque depends sensitively on the sink prescriptions employed. In agreement with previous studies, we find a modest difference in torques and accretion variability between 2D and 3D disk models. We find cavity precession rates to be appreciably faster in 3D than in 2D.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1981

Pull-out fibers from composite materials at high rate of loading

Numerical and experimental results are presented on the pullout phenomenon in composite materials at a high rate of loading. The finite element method was used, taking into account the existence of a virtual shear deformation layer as the interface between fiber and matrix. Experimental results agree well with those obtained by the finite element method. Numerical results show that the interlaminar shear stress is time dependent, in addition, it is shown to depend on the applied load time history. Under step pulse loading, the interlaminar shear stress fluctuates, finally decaying to its value under static loading.

Amijima, S.↗
NASA NTRS1987

Stability of streamwise vortices

A brief overview of some theoretical and computational studies of the stability of streamwise vortices is given. The local induction model and classical hydrodynamic vortex stability theories are discussed in some detail. The importance of the three-dimensionality of the mean velocity profile to the results of stability calculations is discussed briefly. The mean velocity profile is provided by employing the similarity solution of Donaldson and Sullivan. The global method of Bridges and Morris was chosen for the spatial stability calculations for the nonlinear eigenvalue problem. In order to test the numerical method, a second order accurate central difference scheme was used to obtain the coefficient matrices. It was shown that a second order finite difference method lacks the required accuracy for global eigenvalue calculations. Finally the problem was formulated using spectral methods and a truncated Chebyshev series.

Khorrami, M. K.↗
NASA NTRS1994

Stability and error estimation for Component Adaptive Grid methods

Component adaptive grid (CAG) methods for solving hyperbolic partial differential equations (PDE's) are discussed in this paper. Applying recent stability results for a class of numerical methods on uniform grids. The convergence of these methods for linear problems on component adaptive grids is established here. Furthermore, the computational error can be estimated on CAG's using the stability results. Using these estimates, the error can be controlled on CAG's. Thus, the solution can be computed efficiently on CAG's within a given error tolerance. Computational results for time dependent linear problems in one and two space dimensions are presented.

Oliger, Joseph↗
NASA NTRS2007

New, Improved Bulk-microphysical Schemes for Studying Precipitation Processes in WRF: Comparisons with Other Schemes - Part 1

Advances in computing power allow atmospheric prediction models to be mn at progressively finer scales of resolution, using increasingly more sophisticated physical parameterizations and numerical methods. The representation of cloud microphysical processes is a key component of these models, over the past decade both research and operational numerical weather prediction models have started using more complex microphysical schemes that were originally developed for high-resolution cloud-resolving models (CRMs). A recent report to the United States Weather Research Program (USWRP) Science Steering Committee specifically calls for the replacement of implicit cumulus parameterization schemes with explicit bulk schemes in numerical weather prediction (NWP) as part of a community effort to improve quantitative precipitation forecasts (QPF). An improved Goddard bulk microphysical parameterization is implemented into a state-of the-art of next generation of Weather Research and Forecasting (WRF) model. High-resolution model simulations are conducted to examine the impact of microphysical schemes on two different weather events (a midlatitude linear convective system and an Atllan"ic hurricane). The results suggest that microphysics has a major impact on the organization and precipitation processes associated with a summer midlatitude convective line system. The 31CE scheme with a cloud ice-snow-hail configuration led to a better agreement with observation in terms of simulated narrow convective line and rainfall intensity. This is because the 3ICE-hail scheme includes dense ice precipitating (hail) particle with very fast fall speed (over 10 m/s). For an Atlantic hurricane case, varying the microphysical schemes had no significant impact on the track forecast but did affect the intensity (important for air-sea interaction)

Tao, W.-K.↗