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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Variational Monte Carlo calculations of n + H 3 scattering

A paramount goal in nuclear physics is to unify ab initio treatments of bound and unbound states. The position-space quantum Monte Carlo (QMC) methods have a long history of successful bound-state calculations in light systems but have seen minimal implementation in unbound systems. Here, we introduce a numerical method to improve the efficiency and accuracy of unbound-state calculations in QMC. As an initial application, we compute scattering observables for the smallest system available to probe three-body forces, the neutron-triton system, using variational Monte Carlo (VMC) wave functions. The method involves inferring long-range amplitudes in the wave function from integrals over the short-range region where all the particles interact. This approach using integral relations is well established in the literature; here, we develop it for the QMC framework. We validate our approach with a consistency check between short-range spectroscopic overlap functions computed from direct evaluation and from the integral relations; scattering amplitudes are long-range asymptotics of those overlaps. Comparison against published benchmark calculations using the same potential demonstrates that when applied to the current VMC wave functions, the integral method produces more accurate scattering observables than direct evaluation from the same variational wave function. However, it still differs noticeably from the exact results. Using additional interactions, we then present phase shifts and mixing parameters for the n + 3 H system. In particular, we present one of the first applications of the Norfolk family of local coordinate-space chiral potentials in unbound systems of A > 2. The Norfolk results accurately describe s-wave scattering but predict p-wave cross sections too large. Compared with previous QMC scattering calculations, the integral method avoids difficulties associated with the precise computation of energy differences and with convergence outside the interaction region, which is particularly severe in the variational calculation. Application of the integral method here paves the way for its use in Green's function Monte Carlo (GFMC) calculations. In GFMC, the wave functions are more accurate, but the high-precision convergence of their tails is slow, and there are additional difficulties in reading out amplitudes. Here, the integral methods will address both of those remaining problems.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2016

MPACT Performance Improvements in VERA-CS

The report summarizes the initial profile of MPACT representative of the version that was distributed with VERA 3.4. It then describes several activities recently performed to increase the overall performance of the code. For the various improvements described in this report, several have been well known to the development team and reactor physics methods community for some time; while others proved novel in their combination of other existing ideas. Still, other improvements were the result of unanticipated breakthroughs in numerical methods research. These performance improvement activities focused on the following components of MPACT. Method of Characteristics Transport Kernel Iterative Methods for Coarse Mesh Finite Difference Linear System Macroscopic Cross Section and Effective Fission Spectrum Calculation Resonance self-shielding (Subgroup) calculation A summary of the overall improvement from this work as tested on a few representative problems is provided in the table below. The incremental improvements for various changes are shown in the figure below.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2013

The ICON-1.2 Hydrostatic Atmospheric Dynamical Core on Triangular Grids - Part 1: Formulation and Performance of the Baseline Version

A hydrostatic atmospheric dynamical core is developed for the purpose of global climate modelling. The model applies a finite difference method to discretize the primitive equations on spherical icosahedral grids, using C-type staggering with triangles as control volume for mass. This paper documents the numerical method employed in the baseline version of this model, discusses its properties, and presents results from idealized test cases. The evaluation shows that the new dynamical core is able to correctly represent the evolution of baroclinic eddies in the atmosphere and their role in meridional heat and momentum transport. The simulations compare well with the reference solutions, and converge as the horizontal resolution increases. First results from two aqua planet experiments are also presented, in which the equatorial wave spectra derived from tropical precipitation agree well with those simulated by a spectral transform model. The new dynamical core thus provides a good basis for further model development. Certain aspects of the model formulation that need further investigation and improvement are also pointed out.

atmospheric↗
NASA NTRS1987

Response of joint dominated space structures

An approximate method is developed for estimating the transient response of nonlinear systems in terms of linearized modes of response. Its advantages are that it is computationally more efficient than the time integration method and that it is possible to view the design problem in the more traditional physical terms of modal response. The major drawback of the approximate method is loss of accuracy. It seems that both approximate methods and time integration have their roles in design. Approximate methods provide efficient tools for performing parametric studies and they supply physical insights into how to optimize system performance that are not easily inferred from strictly numerical methods. Time integration provides a method for assessing the accuracy of the approximate solution for key simulations and for fine tuning the final design. In the procedure presented the nonlinear system is approximated by an equivalent linear system in which the system parameters are constant over the range of transient response.

Source record↗
NASA NTRS1987

Numerical simulations of unsteady airfoil-vortex interactions

Numerical methods based on the thin layer Navier-Stokes, Euler and transonic small disturbance equations, all three of which use the perturbation form of an implicit numerical algorithm, are used to formulate the unsteady interactions of a moving vortex with a stationary airfoil. Results are presented for both transonic and subsonic flows, as well as for weak and strong interactions. In general, the results exhibit an overwhelming influence of the vortex on the flow field around the airfoil, especially when the convecting vortex is within one chord of the airfoil. It is noted that even the ostensibly weak interactions produced vortex/shock-induced boundary layer separation.

Srinivasan, G. R.↗
NASA NTRS1990

Shape optimization for maximum stability and dynamic stiffness

Any optimization of structures for maximum stability or for maximum dynamic stiffness deals with an eigenvalue problem. The goal of this optimization is to raise the lowest eigenvalue (or eigenvalues) of the problem to its highest (optimal) level at a constant volume of the structure. Likely the lowest eigenvalue may be either inherently multi-modal or it can become multi-modal as a result of the optimization process. The multimodeness introduces some ambiguity to the eigenvalue problem and make the optimization difficult to handle. Thus far, only the simplest cases of multi-modal structures have been effectively optimized using rather elaborate analytical methods. Numerous publications report design of a minimum volume structure with different eigenvalues constraints, in which, however, the modality of the problem is assumed a priori. The method presented here utilizes a multi-modal optimality criteria and allows for inclusion of an arbitrary number of buckling or vibrations modes which might influence the optimization process. The real multi-modality of the problem, that is the number of modes participating in the final optimal design is determined iteratively. Because of a natural use of the FEM technique the method is easy to program and might be helpful in design of large flexible space structures.

Szyszkowski, W.↗
NASA NTRS1997

Multiresolution and Explicit Methods for Vector Field Analysis and Visualization

This is a request for a second renewal (3d year of funding) of a research project on the topic of multiresolution and explicit methods for vector field analysis and visualization. In this report, we describe the progress made on this research project during the second year and give a statement of the planned research for the third year. There are two aspects to this research project. The first is concerned with the development of techniques for computing tangent curves for use in visualizing flow fields. The second aspect of the research project is concerned with the development of multiresolution methods for curvilinear grids and their use as tools for visualization, analysis and archiving of flow data. We report on our work on the development of numerical methods for tangent curve computation first.

Nielson, Gregory M.↗
NASA NTRS2013

Why Is the Overheating Problem Difficult: the Role of Entropy

The development of computational fluid dynamics over the last few decades has yielded enormous successes and capabilities being routinely employed today; however there remain some open problems to be properly resolved-some are fundamental in nature and some resolvable by operational changes. These two categories are distinguished and broadly explored previously. One, that belongs to the former, is the so-called overheating problem, especially in rarefying flow. This problem up to date still dogs every method known to the author; a solution to it remains elusive. The study in this paper concludes that: (1) the entropy increase is quantitatively linked to the increase in the temperature increase, (2) it is argued that the overheating is inevitable in the current shock capturing or traditional finite difference framework, and (3) a simple hybrid method is proposed that removes the overheating problem in the rarefying problems, but also retains the property of accurate shock capturing. This remedy (enhancement of current numerical methods) can be included easily in the present Eulerian codes.

Liou, Meng-Sing↗
NASA NTRS2017

Improving Estimation of Ground Casualty Risk From Reentering Space Objects

A recent improvement to the long-term estimation of ground casualties from reentering space debris is the further refinement and update to the human population distribution. Previous human population distributions were based on global totals with simple scaling factors for future years, or a coarse grid of population counts in a subset of the world's countries, each cell having its own projected growth rate. The newest population model includes a 5-fold refinement in both latitude and longitude resolution. All areas along a single latitude are combined to form a global population distribution as a function of latitude, creating a more accurate population estimation based on non-uniform growth at the country and area levels. Previous risk probability calculations used simplifying assumptions that did not account for the ellipsoidal nature of the Earth. The new method uses first, a simple analytical method to estimate the amount of time spent above each latitude band for a debris object with a given orbit inclination and second, a more complex numerical method that incorporates the effects of a non-spherical Earth. These new results are compared with the prior models to assess the magnitude of the effects on reentry casualty risk.

Ostrom, Chris L.↗
NASA NTRS2017

Improving Estimation of Ground Casualty Risk from Reentering Space Objects

A recent improvement to the long-term estimation of ground casualties from reentering space debris is the further refinement and update to the human population distribution. Previous human population distributions were based on global totals with simple scaling factors for future years, or a coarse grid of population counts in a subset of the world's countries, each cell having its own projected growth rate. The newest population model includes a 5-fold refinement in both latitude and longitude resolution. All areas along a single latitude are combined to form a global population distribution as a function of latitude, creating a more accurate population estimation based on non-uniform growth at the country and area levels. Previous risk probability calculations used simplifying assumptions that did not account for the ellipsoidal nature of the earth. The new method uses first, a simple analytical method to estimate the amount of time spent above each latitude band for a debris object with a given orbit inclination, and second, a more complex numerical method that incorporates the effects of a non-spherical Earth. These new results are compared with the prior models to assess the magnitude of the effects on reentry casualty risk.

Ostrom, C.↗
DOE OSTI2017

Application of State Quantization-Based Methods in HEP Particle Transport Simulation

Simulation of particle-matter interactions in complex geometries is one of the main tasks in high energy physics (HEP) research. An essential aspect of it is an accurate and efficient particle transportation in a non-uniform magnetic field, which includes the handling of volume crossings within a predefined 3D geometry. Quantized State Systems (QSS) is a family of numerical methods that provides attractive features for particle transportation processes, such as dense output (sequences of polynomial segments changing only according to accuracy-driven discrete events) and lightweight detection and handling of volume crossings (based on simple root-finding of polynomial functions). In this work we present a proof-of-concept performance comparison between a QSS-based standalone numerical solver and an application based on the Geant4 simulation toolkit, with its default Runge-Kutta based adaptive step method. In a case study with a charged particle circulating in a vacuum (with interactions with matter turned off), in a uniform magnetic field, and crossing up to 200 volume boundaries twice per turn, simulation results showed speedups of up to 6 times in favor of QSS while it being 10 times slower in the case with zero volume boundaries.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2015

Multiresolution quantum chemistry in multiwavelet bases: excited states from time-dependent Hartree–Fock and density functional theory via linear response

Using the fully numerical method for time-dependent Hartree–Fock and density functional theory (TD-HF/DFT) with the Tamm–Dancoff (TD) approximation we use a multiresolution analysis (MRA) approach to present our findings. From a reformulation with effective use of the density matrix operator, we obtain a general form of the HF/DFT linear response equation in the first quantization formalism. It can be readily rewritten as an integral equation with the bound-state Helmholtz (BSH) kernel for the Green's function. The MRA implementation of the resultant equation permits excited state calculations without virtual orbitals. Moreover, the integral equation is efficiently and adaptively solved using a numerical multiresolution solver with multiwavelet bases. Our implementation of the TD-HF/DFT methods is applied for calculating the excitation energies of H 2 , Be, N 2 , H 2 O, and C 2 H 4 molecules. The numerical errors of the calculated excitation energies converge in proportion to the residuals of the equation in the molecular orbitals and response functions. The energies of the excited states at a variety of length scales ranging from short-range valence excitations to long-range Rydberg-type ones are consistently accurate. It is shown that the multiresolution calculations yield the correct exponential asymptotic tails for the response functions, whereas those computed with Gaussian basis functions are too diffuse or decay too rapidly. Finally, we introduce a simple asymptotic correction to the local spin-density approximation (LSDA) so that in the TDDFT calculations, the excited states are correctly bound.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1989

Projection methods for the numerical solution of Markov chain models

Projection methods for computing stationary probability distributions for Markov chain models are presented. A general projection method is a method which seeks an approximation from a subspace of small dimension to the original problem. Thus, the original matrix problem of size N is approximated by one of dimension m, typically much smaller than N. A particularly successful class of methods based on this principle is that of Krylov subspace methods which utilize subspaces of the form span(v,av,...,A(exp m-1)v). These methods are effective in solving linear systems and eigenvalue problems (Lanczos, Arnoldi,...) as well as nonlinear equations. They can be combined with more traditional iterative methods such as successive overrelaxation, symmetric successive overrelaxation, or with incomplete factorization methods to enhance convergence.

Saad, Youcef↗
DOE OSTI2023

Results of the Micromorphic Upscaling Workflow for the PSAAP III Year 3 Report

Predicting the mechanical response and failure of heterogeneous materials has proven difficult. Multiscale numerical methods based in higher order continuum theories attempt to bridge the gap between microscale and macroscale structural behavior. Micromorphic continuum theories have shown promise. The Tardigrade software package is an implementation of Eringen’s micromorphic continuum theory with capabilities to support multiscale material modeling workflows. These include homogenization through the Micromorphic Filter, calibration of micromorphic material models, and macroscale simulation in Tardigrade-MOOSE. This work discusses micromorphic upscaling efforts of the University of Colorado Boulder PSAAP III multidisciplinary simulation center (MSC). Verification studies are presented that compare the accuracy of the upscaling workflow with analytical solutions for a trivial stress state and homogeneous material using direct numerical simulations (DNS) conducted in the Ratel finite element method (FEM) and GEOS material point method (MPM) codes. These verification studies consider upscaling using the Micromorphic Filter for a “single filter domain”. Finally, DNS of a heterogeneous composite material is upscaled using a “multiple filter domain” method.

36 MATERIALS SCIENCE↗
DOE OSTI2022

First principles thermal transport modeling in GaN and related materials

Gallium nitride is a wide bandgap material utilized in a variety of technologies, including high-power electronics and light-emitting diodes, partly due to its favorable thermal properties. This chapter describes modern first-principles-based modeling of phonons and lattice thermal conductivity (k) of GaN, III-nitrides and related materials. In particular, we describe the theoretical underpinnings of calculating phonon dispersions, intrinsic phonon interactions, and other lattice dynamical properties from quantum perturbation theory and density functional theory (DFT) methods. Description of how these methods are then coupled with the Peierls-Boltzmann transport (PBT) equation to determine phonon distributions and lifetimes relevant for thermal transport is given. These theoretical and numerical methods have demonstrated quantitative accuracy and predictive power for calculating pristine k and defect-limited k from first principles for a variety of materials. We present a review of the literature utilizing DFT-PBT methods to understand novel k behaviors in III-nitrides and related materials.

Lindsay, Lucas↗
DOE OSTI2019

Development of an Ultra-Low Head Siphon Hydro Turbine Using Computational Fluid Dynamics

Structural simplification and efficient hydraulic performance are key to effectively utilizing ultra-low head water power resources and reducing hydroelectric unit costs. In this study, a computational fluid dynamics (CFD) method was used to predict hydraulic performance of an axial turbine at the Gaoliangjian power station. CFD results agreed well with field test data. Using the same numerical method, a new siphon turbine was then designed based on the original distributor and turbine runner equipment. This study investigated the effect of different siphon outlet passage geometry parameters, runner blade shapes, and distributors on the hydraulic performance of the siphon turbine. The maximum hydraulic efficiency increased to 87.9% under a head of 2.87 m. Finally, the hydraulic performance of the turbine was compared for four different distributor designs after adding an intake sump at the turbine entrance. The bell-shaped distributor with four guide vanes resulted in the highest power output at the lowest head. Therefore, the siphon turbine is a good option for energy conversion in ultra-low water head settings.

Zhou, Daqing↗
NASA NTRS2011

Tests of the Grobner Basis Solution for Lightning Ground Flash Fraction Retrieval

Satellite lightning imagers such as the NASA Tropical Rainfall Measuring Mission Lightning Imaging Sensor (TRMM/LIS) and the future GOES-R Geostationary Lightning Mapper (GLM) are designed to detect total lightning (ground flashes + cloud flashes). However, there is a desire to discriminate ground flashes from cloud flashes from the vantage point of space since this would enhance the overall information content of the satellite lightning data and likely improve its operational and scientific applications (e.g., in severe weather warning, lightning nitrogen oxides studies, and global electric circuit analyses). A Bayesian inversion method was previously introduced for retrieving the fraction of ground flashes in a set of flashes observed from a satellite lightning imager. The method employed a constrained mixed exponential distribution model to describe the lightning optical measurements. To obtain the optimum model parameters (one of which is the ground flash fraction), a scalar function was minimized by a numerical method. In order to improve this optimization, a Grobner basis solution was introduced to obtain analytic representations of the model parameters that serve as a refined initialization scheme to the numerical optimization. In this study, we test the efficacy of the Grobner basis initialization using actual lightning imager measurements and ground flash truth derived from the national lightning network.

Koshak, William↗
DOE OSTI2017

An Investigation into Solution Verification for CFD-DEM

This report presents the study of the convergence behavior of the computational fluid dynamicsdiscrete element method (CFD-DEM) method, specifically National Energy Technology Laboratory’s (NETL) open source MFiX code (MFiX-DEM) with a diffusion based particle-tocontinuum filtering scheme. In particular, this study focused on determining if the numerical method had a solution in the high-resolution limit where the grid size is smaller than the particle size. To address this uncertainty, fixed particle beds of two primary configurations were studied: i) fictitious beds where the particles are seeded with a random particle generator, and ii) instantaneous snapshots from a transient simulation of an experimentally relevant problem. Both problems considered a uniform inlet boundary and a pressure outflow. The CFD grid was refined from a few particle diameters down to 1/6 th of a particle diameter. The pressure drop between two vertical elevations, averaged across the bed cross-section was considered as the system response quantity of interest. A least-squares regression method was used to extrapolate the grid-dependent results to an approximate “grid-free” solution in the limit of infinite resolution. The results show that the diffusion based scheme does yield a converging solution. However, the convergence is more complicated than encountered in simpler, single-phase flow problems showing strong oscillations and, at times, oscillations superimposed on top of globally non-monotonic behavior. The challenging convergence behavior highlights the importance of using at least four grid resolutions in solution verification problems so that (over-determined) regression-based extrapolation methods may be applied to approximate the grid-free solution. The grid-free solution is very important in solution verification and VVUQ exercise in general as the difference between it and the reference solution largely determines the numerical uncertainty. By testing different randomized particle configurations of the same general problem (for the fictitious case) or different instances of freezing a transient simulation, the numerical uncertainties appeared to be on the same order of magnitude as ensemble or time averaging uncertainties. By testing different drag laws, almost all cases studied show that model form uncertainty in this one, very important closure relation was larger than the numerical uncertainty, at least with a reasonable CFD grid, roughly five particle diameters. In this study, the diffusion width (filtering length scale) was mostly set at a constant of six particle diameters. A few exploratory tests were performed to show that similar convergence behavior was observed for diffusion widths greater than approximately two particle diameters. However, this subject was not investigated in great detail because determining an appropriate filter size is really a validation question which must be determined by comparison to experimental or highly accurate numerical data. Future studies are being considered targeting solution verification of transient simulations as well as validation of the filter size with direct numerical simulation data.

97 MATHEMATICS AND COMPUTING↗