Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Convergence analysis”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 577 records · Page 32
All sourcesNASA NTRSDOE OSTI
NASA NTRSDate not supplied

Investigation of the Potential for Lidar & Polarimeter Combined Aerosol Retrievals Using Various Instrument Combinations

As a scientific community, we are motivated to achieve better observational capabilities for aerosols, to reduce uncertainties about aerosol’s role in climate. Encouraged by the National Academies Decadal Survey, many are looking to the synergy of lidar and polarimeter as a means of achieving improved measurements. Polarimetric observations of total-column radiances have excellent sensitivity to aerosol size distribution and absorption properties. Active lidar measurements have fewer wavelengths and view angles and therefore more limited sensitivity to aerosol microphysical properties such as complex refractive index. Yet the advantage of vertically resolved profiles is game-changing, especially given that models contain significant uncertainty about the vertical distribution of aerosol and that polarimeter and other passive retrievals must make assumptions about vertical distribution which can impact performance. To optimize the synergy, a joint polarimeter + lidar mission requires a joint retrieval. However, the exact instruments that will be launched on a future satellite are unknown, and the capabilities of polarimeters and lidars cover a large range. In this study, we perform information content analysis for a range of nominal instrument combinations. The methodology is ideal for assessing the impact of measurements and a priori information (assumptions and constraints) with respect to the desired retrieval products, and for comparing measurement systems. It has advantages that make it useful in advance of or in parallel with retrieval development, such as producing quantitatively useful comparisons even for retrieval scenarios that are significantly underdetermined and therefore impossible to retrieve without significant assumptions, and it is not impacted by retrieval-specific sources of error such as incomplete or incorrect convergence which can complicate the interpretation of a retrieval performance analysis. Here, we will derive the expected uncertainty in retrieved aerosol concentration, effective radius, fine mode fraction and single scattering albedo, for a combination of a polarimeter with various grades of lidar, from an elastic backscatter lidar, similar to the pathfinder CALIOP on the CALIPSO satellite, to a multi-wavelength high spectral resolution lidar.

Sharon P Burton↗
NASA NTRS1996

Pattern Search Algorithms for Bound Constrained Minimization

We present a convergence theory for pattern search methods for solving bound constrained nonlinear programs. The analysis relies on the abstract structure of pattern search methods and an understanding of how the pattern interacts with the bound constraints. This analysis makes it possible to develop pattern search methods for bound constrained problems while only slightly restricting the flexibility present in pattern search methods for unconstrained problems. We prove global convergence despite the fact that pattern search methods do not have explicit information concerning the gradient and its projection onto the feasible region and consequently are unable to enforce explicitly a notion of sufficient feasible decrease.

Lewis, Robert Michael↗
DOE OSTI2018

On semi-convergence and inexact iteration of the GSS iteration method for nonsymmetric singular saddle point problems

In this paper, the generalized shift-splitting (GSS) iteration method is used to solve nonsymmetric singular saddle point systems with the positive real (1, 1)-block sub-matrix. By a careful analysis of the spectral properties of the corresponding iteration matrix, we investigate the semi-convergence property of the GSS iteration method, give the sharper bounds of the eigenvalues for the GSS iteration method and propose the inexact GSS iteration method, also. Numerical experiments are given to show the correctness of the theoretical analysis and the feasibility of the GSS preconditioner with appropriate parameters.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2006

Gas Seal Pad With Herringbone-Grooved Rotor-Stiffness and Load Capacity

The principle of herringbone-grooved journal bearings has been applied to the case of a seal disc running under a finger seal pad. The inward pumping action of herringbone grooves on the disc generates load capacity and stiffness to maintain a fluid film and prevent contact of the pad and disc. This mechanism does not depend on a converging film under the pad, such as analyzed in previous works. Analysis shows that significant stiffness and load capacity can be supplied by herringbone grooves. In order for the grooves to be effective, the seal pressure drop must be taken outside of the grooved portion of the rotor, but this may be acceptable in order to gain freedom from maintaining a precise film convergence.

Flemming, David P.↗
DOE OSTI2011

A posteriori error analysis for a cut cell finite volume method

We study the solution of a diffusive process in a domain where the diffusion coefficient changes discontinuously across a curved interface. We consider discretizations that use regularly-shaped meshes, so that the interface “cuts” through the cells (elements or volumes) without respecting the regular geometry of the mesh. Consequently, the discontinuity in the diffusion coefficients has a strong impact on the accuracy and convergence of the numerical method. This motivates the derivation of computational error estimates that yield accurate estimates for specified quantities of interest. For this purpose, we adapt the well-known adjoint based a posteriori error analysis technique used for finite element methods. In order to employ this method, we describe a systematic approach to discretizing a cut-cell problem that handles complex geometry in the interface in a natural fashion yet reduces to the well-known Ghost Fluid Method in simple cases. We test the accuracy of the estimates in a series of examples.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1991

Analysis of a swirl stabilized arcjet thruster

Viscous swirling flow through transonic converging-diverging nozzles (with and without centerbodies) is examined numerically. An implicit technique is used to solve the axisymmetric Thin Layer Naiver-Stokes equations. The effect of swirl and viscosity on low Reynolds number flows is shown by examining integral parameters and flowfield details.

Keith, Theo G., Jr.↗
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.↗
NASA NTRS2001

Wind-Stress Simulations and Equatorial Dynamics in an AGCM: Basic Results from a 1979-1999 Forced SST Experiment - Part 1

This is the first of a two part study examining the connection of the equatorial momentum budget in an AGCM (Atmospheric General Circulation Model), with simulated equatorial surface wind stresses over the Pacific. The AGCM used in this study forms part of a newly developed coupled forecasting system used at NASA's Seasonal- to-Interannual Prediction Project. Here we describe the model and present results from a 20-year (1979-1999) AMIP-type experiment forced with observed SSTs (Sea Surface Temperatures). Model results are compared them with available observational data sets. The climatological pattern of extra-tropical planetary waves as well as their ENSO-related variability is found to agree quite well with re-analysis estimates. The model's surface wind stress is examined in detail, and reveals a reasonable overall simulation of seasonal interannual variability, as well as seasonal mean distributions. However, an excessive annual oscillation in wind stress over the equatorial central Pacific is found. We examine the model's divergent circulation over the tropical Pacific and compare it with estimates based on re-analysis data. These comparisons are generally good, but reveal excessive upper-level convergence in the central Pacific. In Part II of this study a direct examination of individual terms in the AGCM's momentum budget is presented. We relate the results of this analysis to the model's simulation of surface wind stress.

Bacmeister, Julio T.↗
DOE OSTI2018

The Berry–Esseen Bound for General Markov Chains

A rate of convergence in the CLT is studied for recurrent Markov chains. The Berry–Esseen type bound is obtained with explicit dependence on parameters of the chain. The method of the proof is purely analytical. It is based on the complex analysis of generating functions.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2016

The Influence of Volcanic Eruptions on the Climate of Tropical South America During the Last Millennium in an Isotope-Enabled General Circulation Model

Currently, little is known on how volcanic eruptions impact large-scale climate phenomena such as South American paleo-intertropical Convergence Zone (ITCZ) position and summer monsoon behavior. In this paper, an analysis of observations and model simulations is employed to assess the influence of large volcanic eruptions on the climate of tropical South America. This problem is first considered for historically recent volcanic episodes for which more observations are available but where fewer events exist and the confounding effects of El Niño-Southern Oscillation (ENSO) lead to inconclusive interpretation of the impact of volcanic eruptions at the continental scale. Therefore, we also examine a greater number of reconstructed volcanic events for the period 850 CE to present that are incorporated into the NASA GISS ModelE2-R simulation of the last millennium. An advantage of this model is its ability to explicitly track water isotopologues throughout the hydrologic cycle and simulating the isotopic imprint following a large eruption. This effectively removes a degree of uncertainty associated with error-prone conversion of isotopic signals into climate variables, and allows for a direct comparison between GISS simulations and paleoclimate proxy records. Our analysis reveals that both precipitation and oxygen isotope variability respond with a distinct seasonal and spatial structure across tropical South America following an eruption. During austral winter, the heavy oxygen isotope in precipitation is enriched, likely due to reduced moisture convergence in the ITCZ domain and reduced rainfall over northern South America. During austral summer, however, more negative values of the precipitation isotopic composition are simulated over Amazonia, despite reductions in rainfall, suggesting that the isotopic response is not a simple function of the "amount effect". During the South American monsoon season, the amplitude of the temperature response to volcanic forcing is larger than the rather weak and spatially less coherent precipitation signal, complicating the isotopic response to changes in the hydrologic cycle.

Colose, Christopher M.↗
NASA NTRS2016

Supplement of: The Influence of Volcanic Eruptions on the Climate of Tropical South America During the Last Millennium in an Isotope-Enabled General Circulation Model

Currently, little is known on how volcanic eruptions impact large-scale climate phenomena such as South American paleo-intertropical Convergence Zone (ITCZ) position and summer monsoon behavior. In this paper, an analysis of observations and model simulations is employed to assess the influence of large volcanic eruptions on the climate of tropical South America. This problem is first considered for historically recent volcanic episodes for which more observations are available but where fewer events exist and the confounding effects of El NioSouthern Oscillation (ENSO) lead to inconclusive interpretation of the impact of volcanic eruptions at the continental scale. Therefore, we also examine a greater number of reconstructed volcanic events for the period 850CE to present that are incorporated into the NASA GISS ModelE2-R simulation of the last millennium.An advantage of this model is its ability to explicitly track water isotopologues throughout the hydrologic cycle and simulating the isotopic imprint following a large eruption. This effectively removes a degree of uncertainty associated with error-prone conversion of isotopic signals into climate variables, and allows for a direct comparison between GISS simulations and paleoclimate proxy records.Our analysis reveals that both precipitation and oxygen isotope variability respond with a distinct seasonal and spatial structure across tropical South America following an eruption. During austral winter, the heavy oxygen isotope in precipitation is enriched, likely due to reduced moisture convergence in the ITCZ domain and reduced rainfall over northern South America. During austral summer, however, more negative values of the precipitation isotopic composition are simulated over Amazonia, despite reductions in rainfall, suggesting that the isotopic response is not a simple function of the amount effect. During the South American monsoon season, the amplitude of the temperature response to volcanic forcing is larger than the rather weak and spatially less coherent precipitation signal, complicating the isotopic response to changes in the hydrologic cycle.

Colose, Christopher↗
DOE OSTI2024

Deep Learning and Likelihood Approaches for Viral Phylogeography Converge on the Same Answers Whether the Inference Model Is Right or Wrong

Abstract Analysis of phylogenetic trees has become an essential tool in epidemiology. Likelihood-based methods fit models to phylogenies to draw inferences about the phylodynamics and history of viral transmission. However, these methods are often computationally expensive, which limits the complexity and realism of phylodynamic models and makes them ill-suited for informing policy decisions in real-time during rapidly developing outbreaks. Likelihood-free methods using deep learning are pushing the boundaries of inference beyond these constraints. In this paper, we extend, compare, and contrast a recently developed deep learning method for likelihood-free inference from trees. We trained multiple deep neural networks using phylogenies from simulated outbreaks that spread among 5 locations and found they achieve close to the same levels of accuracy as Bayesian inference under the true simulation model. We compared robustness to model misspecification of a trained neural network to that of a Bayesian method. We found that both models had comparable performance, converging on similar biases. We also implemented a method of uncertainty quantification called conformalized quantile regression that we demonstrate has similar patterns of sensitivity to model misspecification as Bayesian highest posterior density (HPD) and greatly overlap with HPDs, but have lower precision (more conservative). Finally, we trained and tested a neural network against phylogeographic data from a recent study of the SARS-Cov-2 pandemic in Europe and obtained similar estimates of region-specific epidemiological parameters and the location of the common ancestor in Europe. Along with being as accurate and robust as likelihood-based methods, our trained neural networks are on average over 3 orders of magnitude faster after training. Our results support the notion that neural networks can be trained with simulated data to accurately mimic the good and bad statistical properties of the likelihood functions of generative phylogenetic models.

Evolutionary Biology↗
NASA NTRS1990

Free wake analysis of hover performance using a new influence coefficient method

A new approach to the prediction of helicopter rotor performance using a free wake analysis was developed. This new method uses a relaxation process that does not suffer from the convergence problems associated with previous time marching simulations. This wake relaxation procedure was coupled to a vortex-lattice, lifting surface loads analysis to produce a novel, self contained performance prediction code: EHPIC (Evaluation of Helicopter Performance using Influence Coefficients). The major technical features of the EHPIC code are described and a substantial amount of background information on the capabilities and proper operation of the code is supplied. Sample problems were undertaken to demonstrate the robustness and flexibility of the basic approach. Also, a performance correlation study was carried out to establish the breadth of applicability of the code, with very favorable results.

Quackenbush, Todd R.↗
DOE OSTI2014

High-fidelity numerical solution of the time-dependent Dirac equation

A stable high-order accurate finite difference method for the time-dependent Dirac equation is derived. Grid-convergence studies in 1-D and 3-D corroborate the analysis. The method is applied to time-resolved quantum tunneling where a comparison with the solution to the time-dependent Schrödinger equation in 1-D illustrates the differences between the two equations. In contrast to the conventional tunneling probability decay predicted by the Schrödinger equation, the Dirac equation exhibits Klein tunneling. Solving the time-dependent Dirac equation with a step potential in 3-D reveals that particle spin affects the tunneling process. The observed spin-dependent reflection allows for a new type of spin-selective measurements.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2012

Advanced Mesh-Enabled Monte Carlo Capability for Multi-Physics Reactor Analysis

This project will accumulate high-precision fluxes throughout reactor geometry on a non-orthogonal grid of cells to support multi-physics coupling, in order to more accurately calculate parameters such as reactivity coefficients and to generate multi-group cross sections. This work will be based upon recent developments to incorporate advanced geometry and mesh capability in a modular Monte Carlo toolkit with computational science technology that is in use in related reactor simulation software development. Coupling this capability with production-scale Monte Carlo radiation transport codes can provide advanced and extensible test-beds for these developments. Continuous energy Monte Carlo methods are generally considered to be the most accurate computational tool for simulating radiation transport in complex geometries, particularly neutron transport in reactors. Nevertheless, there are several limitations for their use in reactor analysis. Most significantly, there is a trade-off between the fidelity of results in phase space, statistical accuracy, and the amount of computer time required for simulation. Consequently, to achieve an acceptable level of statistical convergence in high-fidelity results required for modern coupled multi-physics analysis, the required computer time makes Monte Carlo methods prohibitive for design iterations and detailed whole-core analysis. More subtly, the statistical uncertainty is typically not uniform throughout the domain, and the simulation quality is limited by the regions with the largest statistical uncertainty. In addition, the formulation of neutron scattering laws in continuous energy Monte Carlo methods makes it difficult to calculate adjoint neutron fluxes required to properly determine important reactivity parameters. Finally, most Monte Carlo codes available for reactor analysis have relied on orthogonal hexahedral grids for tallies that do not conform to the geometric boundaries and are thus generally not well-suited to coupling with the unstructured meshes that are used in other physics simulations.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2023

Lack of robustness and accuracy of many numerical schemes for phase-field simulations

In this paper, we study the stability, accuracy and convergence behavior of various numerical schemes for phase-field modeling through a simple ODE model. Both theoretical analysis and numerical experiments are carried out on this ODE model to demonstrate the limitation of most numerical schemes that have been used in practice. One main conclusion is that the first-order fully implicit scheme is the only robust algorithm for phase-field simulations while all other schemes (that have been analyzed) may have convergence issue if the time step size is not exceedingly small. More specifically, by rigorous analysis in most cases, we have the following conclusions: (i) The first-order fully implicit scheme converges to the correct steady state solution for all time step sizes. In the case of multiple solutions, one of the solution branches always converges to the correct steady state solution. (ii) The first-order convex splitting scheme, which is equivalent to the first-order fully implicit scheme with a different time scaling, always converges to the correct steady state solution but may seriously lack numerical accuracy for transient solutions. (iii) For the second-order fully implicit and convex splitting schemes, for any time step size $δt > 0$, there exists an initial condition $u_0$ , with $|u_0| > 1$, such that the numerical solution converges to the wrong steady state solution. (iv) For $|u_0|$ ≤ 1, all second-order schemes studied in this paper converge to the correct steady state solution although severe numerical oscillations occur for most of them if the time step size is not sufficiently small. (v) An unconditionally energy-stable scheme (such as the modified Crank–Nicolson scheme) is not necessarily better than a conditionally energy-stable scheme (such as the Crank–Nicolson scheme). Finally, most, if not all, of the above conclusions are expected to be true for more general Allen–Cahn and other phase-field models.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1988

Modal cost analysis for simple continua

The most popular finite element codes are based upon appealing theories of convergence of modal frequencies. For example, the popularity of cubic elements for beam-like structures is due to the rapid convergence of modal frequencies and stiffness properties. However, for those problems in which the primary consideration is the accuracy of response of the structure at specified locations, it is more important to obtain accuracy in the modal costs than in the modal frequencies. The modal cost represents the contribution of a mode in the norm of the response vector. This paper provides a complete modal cost analysis for simple continua such as beam-like structures. Upper bounds are developed for mode truncation errors in the model reduction process and modal cost analysis dictates which modes to retain in order to reduce the model for control design purposes.

Hu, A.↗
DOE OSTI2015

Conformational sampling enhancement of replica exchange molecular dynamics simulations using swarm particle intelligence

In this paper, we present a new method based on swarm particle social intelligence for use in replica exchange molecular dynamics simulations. In this method, the replicas (representing the different system configurations) are allowed communicating with each other through the individual and social knowledge, in additional to considering them as a collection of real particles interacting through the Newtonian forces. The new method is based on the modification of the equations of motion in such way that the replicas are driven towards the global energy minimum. The method was tested for the Lennard-Jones clusters of N = 4, 5, and 6 atoms. Our results showed that the new method is more efficient than the conventional replica exchange method under the same practical conditions. In particular, the new method performed better on optimizing the distribution of the replicas among the thermostats with time and, in addition, ergodic convergence is observed to be faster. We also introduce a weighted histogram analysis method allowing analyzing the data from simulations by combining data from all of the replicas and rigorously removing the inserted bias.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗