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At least 469 records · Page 26

All sources NASA NTRS DOE OSTI

DOE OSTI2018

Analysis of fractional-order models for hepatitis B

This paper presents two models for hepatitis B, both given by fractional differential equations. The first model is formulated without parameters that indicate drug therapy, while the second one considers the drug therapy. The basic reproduction number and the stability analysis are considered for both models. Moreover, some numerical simulations by nonstandard finite difference schemes are presented. The numerical results show that the solutions converges to an equilibrium point as predicted in the stability analysis.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2009

Super-convergence of Discontinuous Galerkin Method Applied to the Navier-Stokes Equations

The practical benefits of the hyper-accuracy properties of the discontinuous Galerkin method are examined. In particular, we demonstrate that some flow attributes exhibit super-convergence even in the absence of any post-processing technique. Theoretical analysis suggest that flow features that are dominated by global propagation speeds and decay or growth rates should be super-convergent. Several discrete forms of the discontinuous Galerkin method are applied to the simulation of unsteady viscous flow over a two-dimensional cylinder. Convergence of the period of the naturally occurring oscillation is examined and shown to converge at 2p+1, where p is the polynomial degree of the discontinuous Galerkin basis. Comparisons are made between the different discretizations and with theoretical analysis.

Atkins, Harold L.↗

DOE OSTI2021

The Mechanism of Increasing Summer Water Vapor Over the Tibetan Plateau

Rapid warming over the Tibetan Plateau (TP) has been associated with a wetting trend in atmospheric water vapor content, which is critical for recharging the Asian water tower. However, the mechanism associated with the wetting phenomenon remains unclear. Long-term changes in moisture balance and precipitation recycling processes are investigated using the ERA5 reanalysis from 1979 to 2019. The wetting trend over TP is mainly due to the summer water vapor trend with signi?cantly increases over the western TP. Based on the moisture balance analysis, it is found that precipitation, evaporation, and the convergence of moisture are all increasing over the western TP but decreasing over the eastern TP. Based on the dynamical precipitation recycling model, the results suggest that both internal and external cycles contributes to the wetting over TP, with 63.87% and 36.13% contributions respectively. Further analysis found that the atmospheric heating source is also increasing over the western TP, which could shift the moisture transportation from east to west at the southern boundary of TP. The increasing moisture convergence could enhance precipitation, and the enhanced latent heating in the mid-atmosphere can further induced moisture convergence, which forms a positive feedback. However, an opposite situation occurred over the eastern TP. The internal and external cycle of the recycling process can stimulate (suppress) each other through precipitation over the western (eastern) TP. This mechanism linked the changes in the precipitation recycling and atmospheric circulation, and induced the wetting trend over TP in summer.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS2009

Multiscale Failure Analysis of Laminated Composite Panels Subjected to Blast Loading Using FEAMAC/Explicit

This preliminary report demonstrates the capabilities of the recently developed software implementation that links the Generalized Method of Cells to explicit finite element analysis by extending a previous development which tied the generalized method of cells to implicit finite elements. The multiscale framework, which uses explicit finite elements at the global-scale and the generalized method of cells at the microscale is detailed. This implementation is suitable for both dynamic mechanics problems and static problems exhibiting drastic and sudden changes in material properties, which often encounter convergence issues with commercial implicit solvers. Progressive failure analysis of stiffened and un-stiffened fiber-reinforced laminates subjected to normal blast pressure loads was performed and is used to demonstrate the capabilities of this framework. The focus of this report is to document the development of the software implementation; thus, no comparison between the results of the models and experimental data is drawn. However, the validity of the results are assessed qualitatively through the observation of failure paths, stress contours, and the distribution of system energies.

Pineda, Evan J.↗

NASA NTRS1999

Solving Upwind-Biased Discretizations: Defect-Correction Iterations

This paper considers defect-correction solvers for a second order upwind-biased discretization of the 2D convection equation. The following important features are reported: (1) The asymptotic convergence rate is about 0.5 per defect-correction iteration. (2) If the operators involved in defect-correction iterations have different approximation order, then the initial convergence rates may be very slow. The number of iterations required to get into the asymptotic convergence regime might grow on fine grids as a negative power of h. In the case of a second order target operator and a first order driver operator, this number of iterations is roughly proportional to h-1/3. (3) If both the operators have the second approximation order, the defect-correction solver demonstrates the asymptotic convergence rate after three iterations at most. The same three iterations are required to converge algebraic error below the truncation error level. A novel comprehensive half-space Fourier mode analysis (which, by the way, can take into account the influence of discretized outflow boundary conditions as well) for the defect-correction method is developed. This analysis explains many phenomena observed in solving non-elliptic equations and provides a close prediction of the actual solution behavior. It predicts the convergence rate for each iteration and the asymptotic convergence rate. As a result of this analysis, a new very efficient adaptive multigrid algorithm solving the discrete problem to within a given accuracy is proposed. Numerical simulations confirm the accuracy of the analysis and the efficiency of the proposed algorithm. The results of the numerical tests are reported.

Diskin, Boris↗

DOE OSTI2016

Toward Linear Stability Analysis of Upper Plenum Flows

Linear stability analysis is a tool used to help identify the sensitivity of a particular domain to perturbations and evaluate the system dynamics as a transition, if any, occurs. The development of a time invariant base flow for future use in a linear stability analysis is the focus of this investigation. A test case, with a Reynolds number of 100, was brought to a steady state using the spectral element code Nek5000 and the method of selective frequency damping. The convergence criteria for this method is the volume averaged value of the forcing function which, after approximately 80,000 time-steps, decreased to 3.6x10{sup -4}. Analysis shows that the case has yet to have reached the tolerance desired, 1x10{sup -6}. With the simulation in the process of converging a preliminary perturbation analysis was conducted. Due to the low Reynolds number of this case, 100, it was hypothesized that the flow would be linearly stable. This preliminary stability analysis only focused on the largest fundamental mode and the energy growth of that perturbation over time. Upon evaluation of the perturbation energy, which was shown to be monotonically decreasing in time, it was concluded that, despite not yet being converged, the system is in fact linearly stable. Future work includes evaluating the domain at higher Reynolds numbers, solving the eigenvalue problem created when the linearized Navier-Stokes are written in operator form and calculating the energy evolution of the optimal perturbation. (authors)

42 ENGINEERING↗

DOE OSTI2013

Generalized fictitious methods for fluid–structure interactions: Analysis and simulations

We present a new fictitious pressure method for fluid–structure interaction (FSI) problems in incompressible flow by generalizing the fictitious mass and damping methods we published previously in [1]. The fictitious pressure method involves modification of the fluid solver whereas the fictitious mass and damping methods modify the structure solver. We analyze all fictitious methods for simplified problems and obtain explicit expressions for the optimal reduction factor (convergence rate index) at the FSI interface [2]. This analysis also demonstrates an apparent similarity of fictitious methods to the FSI approach based on Robin boundary conditions, which have been found to be very effective in FSI problems. We implement all methods, including the semi-implicit Robin based coupling method, in the context of spectral element discretization, which is more sensitive to temporal instabilities than low-order methods. However, the methods we present here are simple and general, and hence applicable to FSI based on any other spatial discretization. In numerical tests, we verify the selection of optimal values for the fictitious parameters for simplified problems and for vortex-induced vibrations (VIV) even at zero mass ratio (“for-ever-resonance”). We also develop an empirical a posteriori analysis for complex geometries and apply it to 3D patient-specific flexible brain arteries with aneurysms for very large deformations. We demonstrate that the fictitious pressure method enhances stability and convergence, and is comparable or better in most cases to the Robin approach or the other fictitious methods.

Computer Science↗

DOE OSTI2016

Apparent Monte Carlo Source Convergence Problem with BWR Fuel Depleted with Partial Control Blade Insertion

Oak Ridge National Laboratory (ORNL) and the US Nuclear Regulatory Commission (NRC) have initiated a multiyear project to investigate application of burnup credit (BUC) to boiling-water reactor (BWR) fuel in storage and transportation casks and spent fuel pools (SFPs). Ideally, a single combination of all operating parameters including moderator density and axial burnup profiles, control blade exposure, and others can be identified to allow a simple, bounding approach to BWR BUC. One aspect of this investigation involves examining the effect of control blade insertion during operation on discharged assembly reactivity. In the course of these calculations, an apparent source convergence problem was discovered for fuel that has experienced partial blade insertion for the entire lifetime of the assembly. The source convergence problem appears not to impact k{sub eff}, but it manifests in predictions of the axial fission density profile. This phenomenon is of interest in identifying areas of concern with BWR BUC since it has not been studied as thoroughly as BUC for pressurized-water (PWR) reactor fuel. There may also be interest in this configuration for further study of a realistic source Monte Carlo convergence problem as opposed to some earlier manufactured source convergence problems through careful selection of initial conditions. This summary presents the depletion conditions used to generate the problem, a description of the models, a background based on well-behaved calculations, the identification of the problem, and attempts made to resolve the problem. Only a brief description of the depletion conditions and models is possible within the limited scope of this summary. Finally, conclusions are presented. This summary identifies a source convergence problem in the process of investigating BUC for BWR spent fuel. The depletion scenario which created the depleted fuel and burnable absorber compositions included a control blade inserted in the bottom 14 nodes throughout the entire depletion. This insertion is slightly over half the length of the assembly, and it appears to create two regions of nearly equal reactivity. As expected, one region is near the top of the assembly, and the other region is near the middle of the assembly. This node includes significant {sup 239}Pu generation as a result of rodded operation, but it is also the top node of the full lattice zone. While the calculated k{sub eff} values appear to be statistically equivalent, the axial neutron production profile varies significantly among independent simulations of the same model. A range of standard approaches has been used to attempt to resolve the source convergence problem and determine the true axial neutron production profile. This profile is of interest in cask criticality safety analysis because it influences the interaction among assemblies loaded in the cask. The forthcoming SCALE 6.2 release will include source convergence testing based on Shannon entropy, which may assist in identifying these types of problems in the future. It should be noted that this source convergence problem results from the depletion conditions and the final distribution of fissile and absorber material within the discharged fuel assembly. The results, while entirely generated within the SCALE code system, are representative of any Monte Carlo program attempting to calculate k{sub eff} for such a system. The most important conclusion of this work is that the BUC criticality safety community must be aware of the potential for this type of source convergence problem. Analysts must approach such partially rodded scenarios with caution and critically examine the results. Fortunately, it is extremely unlikely that BWR assemblies would experience the bladed operation necessary to create this particular source convergence problem. These results may also have some bearing on the analysis of PWR BUC for new plant designs such as AP1000 that incorporate significant rodded operations. In a broader context, the source convergence problem identified here could have been magnified if it had occurred in a Monte Carlo depletion simulation. It may be possible to identify this type of problem in a depletion calculation by comparing the apparently converged fluxes between steps to ensure that no oscillations or other serious shifts are occurring. The depletion calculations performed in this work were performed with a two-dimensional deterministic code and are therefore not subject to this problem. These results may also raise questions about the validity of 2D depletion models with extruded geometry in the 3D k{sub eff} calculation. (authors)

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2015

PHOTOSPHERIC FLOW FIELD RELATED TO THE EVOLUTION OF THE SUN'S POLAR MAGNETIC PATCHES OBSERVED BY HINODE SOLAR OPTICAL TELESCOPE

We investigated the role of photospheric plasma motions in the formation and evolution of polar magnetic patches using time-sequence observations with high spatial resolution. The observations were obtained with the spectropolarimeter on board the Hinode satellite. From the statistical analysis using 75 magnetic patches, we found that they are surrounded by strong converging, supergranulation associated flows during their apparent lifetime and that the converging flow around the patch boundary is better observed in the Doppler velocity profile in the deeper photosphere. Based on our analysis, we suggest that the like-polarity magnetic fragments in the polar region are advected and clustered by photospheric converging flows, thereby resulting in the formation of polar magnetic patches. Our observations show that, in addition to direct cancellation, magnetic patches decay by fragmentation followed by unipolar disappearance or unipolar disappearance without fragmentation. It is possible that the magnetic patches of existing polarity fragment or diffuse away into smaller elements and eventually cancel out with opposite polarity fragments that reach the polar region around the solar cycle maximum. This could be one of the possible mechanisms by which the existing polarity decays during the reversal of the polar magnetic field.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1992

Asymptotic modal analysis of a rectangular acoustic cavity excited by wall vibration

Asymptotic modal analysis, a method that has recently been developed for structural dynamical systems, has been applied to a rectangular acoustic cavity. The cavity had a flexible vibrating portion on one wall, and the other five walls were rigid. Banded white noise was transmitted through the flexible portion (plate) only. Both the location along the wall and the size of the plate were varied. The mean square pressure levels of the cavity interior were computed as a ratio of the result obtained from classical modal analysis to that obtained from asymptotic modal analysis for the various plate configurations. In general, this ratio converged to 1.0 as the number of responding modes increased. Intensification effects were found due to both the excitation location and the response location. The asymptotic modal analysis method was both efficient and accurate in solving the given problem. The method has advantages over the traditional methods that are used for solving dynamics problems with a large number of responding modes.

Peretti, Linda F.↗

DOE OSTI2012

Summary of Fast Pyrolysis and Upgrading GHG Analyses

The Energy Independence and Security Act (EISA) of 2007 established new renewable fuel categories and eligibility requirements (EPA 2010). A significant aspect of the National Renewable Fuel Standard 2 (RFS2) program is the requirement that the life cycle greenhouse gas (GHG) emissions of a qualifying renewable fuel be less than the life cycle GHG emissions of the 2005 baseline average gasoline or diesel fuel that it replaces. Four levels of reduction are required for the four renewable fuel standards. Table 1 lists these life cycle performance improvement thresholds. Table 1. Life Cycle GHG Thresholds Specified in EISA Fuel Type Percent Reduction from 2005 Baseline Renewable fuel 20% Advanced biofuel 50% Biomass-based diesel 50% Cellulosic biofuel 60% Notably, there is a specialized subset of advanced biofuels that are the cellulosic biofuels. The cellulosic biofuels are incentivized by the Cellulosic Biofuel Producer Tax Credit (26 USC 40) to stimulate market adoption of these fuels. EISA defines a cellulosic biofuel as follows (42 USC 7545(o)(1)(E)): The term “cellulosic biofuel” means renewable fuel derived from any cellulose, hemicellulose, or lignin that is derived from renewable biomass and that has lifecycle greenhouse gas emissions, as determined by the Administrator, that are at least 60 percent less than the baseline lifecycle greenhouse gas emissions. As indicated, the Environmental Protection Agency (EPA) has sole responsibility for conducting the life cycle analysis (LCA) and making the final determination of whether a given fuel qualifies under these biofuel definitions. However, there appears to be a need within the LCA community to discuss and eventually reach consensus on discerning a 50–59 % GHG reduction from a ≥ 60% GHG reduction for policy, market, and technology development. The level of specificity and agreement will require additional development of capabilities and time for the sustainability and analysis community, as illustrated by the rich dialogue and convergence around the energy content and GHG reduction of cellulosic ethanol (an example of these discussions can be found in Wang 2011). GHG analyses of fast pyrolysis technology routes are being developed and will require significant work to reach the levels of development and maturity of cellulosic ethanol models. This summary provides some of the first fast pyrolysis analyses and clarifies some of the reasons for differing results in an effort to begin the convergence on assumptions, discussion of quality of models, and harmonization.

Biofuel↗

NASA NTRS2007

Nonlinear Structural Analysis Methodology and Dynamics Scaling of Inflatable Parabolic Reflector Antenna Concepts

Ultra-light weight and ultra-thin membrane inflatable antenna concepts are fast evolving to become the state-of-the-art antenna concepts for deep-space applications. NASA Langley Research Center has been involved in the structural dynamics research on antenna structures. One of the goals of the research is to develop structural analysis methodology for prediction of the static and dynamic response characteristics of the inflatable antenna concepts. This research is focused on the computational studies to use nonlinear large deformation finite element analysis to characterize the ultra-thin membrane responses of the antennas. Recently, structural analyses have been performed on a few parabolic reflector antennas of varying size and shape, which are referred in the paper as 0.3 meters subscale, 2 meters half-scale, and 4 meters full-scale antenna. The various aspects studied included nonlinear analysis methodology and solution techniques, ways to speed convergence in iterative methods, the sensitivities of responses with respect to structural loads, such as inflation pressure, gravity, and pretension loads in the ground and in-space conditions, and the ultra-thin membrane wrinkling characteristics. Several such intrinsic aspects studied have provided valuable insight into evaluation of structural characteristics of such antennas. While analyzing these structural characteristics, a quick study was also made to assess the applicability of dynamics scaling of the half-scale antenna. This paper presents the details of the nonlinear structural analysis results, and discusses the insight gained from the studies on the various intrinsic aspects of the analysis methodology. The predicted reflector surface characteristics of the three inflatable ultra-thin membrane parabolic reflector antenna concepts are presented as easily observable displacement fringe patterns with associated maximum values, and normal mode shapes and associated frequencies. Wrinkling patterns are presented to show how surface wrinkle progress with increasing tension loads. Antenna reflector surface accuracies were found to be very much dependent on the type and size of the antenna, the reflector surface curvature, reflector membrane supports in terms of spacing of catenaries, as well as the amount of applied load.

Sreekantamurthy, Tham↗

NASA NTRS2010

Methodology for the Assessment of 3D Conduction Effects in an Aerothermal Wind Tunnel Test

This slide presentation reviews a method for the assessment of three-dimensional conduction effects during test in a Aerothermal Wind Tunnel. The test objectives were to duplicate and extend tests that were performed during the 1960's on thermal conduction on proturberance on a flat plate. Slides review the 1D versus 3D conduction data reduction error, the analysis process, CFD-based analysis, loose coupling method that simulates a wind tunnel test run, verification of the CFD solution, Grid convergence, Mach number trend, size trends, and a Sumary of the CFD conduction analysis. Other slides show comparisons to pretest CFD at Mach 1.5 and 2.16 and the geometries of the models and grids.

Oliver, Anthony Brandon↗

DOE OSTI2020

Asynchronous Richardson iterations: theory and practice

We consider asynchronous versions of the first- and second-order Richardson methods for solving linear systems of equations. These methods depend on parameters whose values are chosen a priori. We explore the parameter values that can be proven to give convergence of the asynchronous methods. This is the first such analysis for asynchronous second-order methods. We find that for the first-order method, the optimal parameter value for the synchronous case also gives an asynchronously convergent method. For the second-order method, the parameter ranges for which we can prove asynchronous convergence do not contain the optimal parameter values for the synchronous iteration. In practice, however, the asynchronous second-order iterations may still converge using the optimal parameter values, or parameter values close to the optimal ones, despite this result. We explore this behavior with a multithreaded parallel implementation of the asynchronous methods.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

A priori error analysis of high-order LL* (FOSLL*) finite element methods

A number of non-standard finite element methods have been proposed in recent years, each of which derives from a specific class of PDE-constrained norm minimization problems. The most notable examples are LL* methods. In this work, we argue that all high-order methods in this class should be expected to deliver substandard uniform h-refinement convergence rates. In fact, one may not even see rates proportional to the polynomial order p > 1 when the exact solution is a constant function. Here, we show that the convergence rate is limited by the regularity of an extraneous Lagrange multiplier variable which naturally appears via a saddle-point analysis. In turn, limited convergence rates appear because the regularity of this Lagrange multiplier is determined, in part, by the geometry of the domain. Numerical experiments support our conclusions.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2016

Ames S-32 O-16 O-18 Line List for High-Resolution Experimental IR Analysis

By comparing to the most recent experimental data and spectra of the SO2 628 ν1/ν3 bands (see Ulenikov et al., JQSRT 168 (2016) 29-39), this study illustrates the reliability and accuracy of the Ames-296K SO2 line list, which is accurate enough to facilitate such high-resolution spectroscopic analysis. The SO2 628 IR line list is computed on a recently improved potential energy surface (PES) refinement, denoted Ames-Pre2, and the published purely ab initio CCSD(T)/aug-cc-pVQZ dipole moment surface. Progress has been made in both energy level convergence and rovibrational quantum number assignments agreeing with laboratory analysis models. The accuracy of the computed 628 energy levels and line list is similar to what has been achieved and reported for SO2 626 and 646, i.e. 0.01-0.03 cm(exp −1) for bands up to 5500 cm(exp −1). During the comparison, we found some discrepancies in addition to overall good agreements. The three-IR-list based feature-by-feature analysis in a 0.25 cm(exp −1) spectral window clearly demonstrates the power of the current Ames line lists with new assignments, correction of some errors, and intensity contributions from varied sources including other isotopologues. We are inclined to attribute part of detected discrepancies to an incomplete experimental analysis and missing intensity in the model. With complete line position, intensity, and rovibrational quantum numbers determined at 296 K, spectroscopic analysis is significantly facilitated especially for a spectral range exhibiting such an unusually high density of lines. The computed 628 rovibrational levels and line list are accurate enough to provide alternatives for the missing bands or suspicious assignments, as well as helpful to identify these isotopologues in various celestial environments. The next step will be to revisit the SO2 828 and 646 spectral analyses.

Sulfur dioxide↗

NASA NTRS1981

Recent developments in quasi-Newton methods for structural analysis and synthesis

Unlike the Newton-Raphson method, quasi-Newton methods by virture of the updates and step length control procedures are globally convergent and hence better suited for the solution of nonlinear problems of structural analysis and synthesis. Extension of quasi-Newton algorithms to large scale problems has led to the development of sparse update algorithms and to economical strategies for evaluating sparse Hessians. Ill-conditioning problems have led to the development of self-scaled variable metric and conjugate gradient algorithms, as well as the use of the singular perturbation theory. This paper emphasizes the effectiveness of such quasi-Newton algorithms for nonlinear structural analysis and synthesis.

Kamat, M. P.↗

DOE OSTI2019

Modeling the asynchronous Jacobi method without communication delays

Asynchronous iterative methods for solving linear systems are gaining renewed interest due to the high cost of synchronization points in massively parallel codes. Historically, theory on asynchronous iterative methods has focused on asymptotic behavior, while the transient behavior remains poorly understood. In this paper, we study a model of the asynchronous Jacobi method without communication delays, which we call simplified asynchronous Jacobi. Simplified asynchronous Jacobi can be used to model asynchronous Jacobi implemented in shared memory or distributed memory with fast communication networks. Our analysis uses the idea of a propagation matrix, which is similar in concept to an iteration matrix. We show that simplified asynchronous Jacobi can continue to reduce the residual when some processes are slower than other processes. We also show that simplified asynchronous Jacobi can converge when synchronous Jacobi does not. We verify our analysis of simplified asynchronous Jacobi using results from asynchronous Jacobi implemented in shared and distributed memory.

97 MATHEMATICS AND COMPUTING↗