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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

A comparison of locally adaptive multigrid methods: LDC, FAC and FIC

This study is devoted to a comparative analysis of three 'Adaptive ZOOM' (ZOom Overlapping Multi-level) methods based on similar concepts of hierarchical multigrid local refinement: LDC (Local Defect Correction), FAC (Fast Adaptive Composite), and FIC (Flux Interface Correction)--which we proposed recently. These methods are tested on two examples of a bidimensional elliptic problem. We compare, for V-cycle procedures, the asymptotic evolution of the global error evaluated by discrete norms, the corresponding local errors, and the convergence rates of these algorithms.

Khadra, Khodor↗
DOE OSTI2020

Development and Implementation of a CTF Code Verification Suite.

CTF is a thermal hydraulic subchannel code developed to predict light water reactor (LWR) core behavior. It is a version of Coolant Boiling in Rod Arrays (COBRA) developed by Oak Ridge National Laboratory (ORNL) and North Carolina State University (NCSU) and used in the Consortium for the Advanced Simulation of LWRs (CASL). Here, the existing CTF code verification matrix is expanded, which ensures that the code is a faithful representation of the underlying mathematical model. The suite of code verification tests are mapped to the underlying conservation equations of CTF and significant gaps are addressed. As such, five new problems are incorporated: isokinetic advection, conduction, pressure drop, convection, and pipe boiling. Convergence behavior and numerical errors are quantified for each of the tests and all tests converge at the correct rate to their corresponding analytic solution. A new verification utility that generalizes the code verification process is used to incorporate these problems into the CTF automated test suite.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
NASA NTRS1999

Solving Upwind-Biased Discretizations: Multigrid Solver Using Semicoarsening - 2

This paper studies a novel multigrid approach to the solution for a second order upwind biased discretization of the convection equation in two dimensions. This approach is based on semi-coarsening and well balanced explicit correction terms added to coarse-grid operators to maintain on coarse-grid the same cross-characteristic interaction as on the target (fine) grid. Colored relaxation schemes are used on all the levels allowing a very efficient parallel implementation. The results of the numerical tests can be summarized as follows: 1) The residual asymptotic convergence rate of the proposed V(0, 2) multigrid cycle is about 3 per cycle. This convergence rate far surpasses the theoretical limit (4/3) predicted for standard multigrid algorithms using full coarsening. The reported efficiency does not deteriorate with increasing the cycle, depth (number of levels) and/or refining the target-grid mesh spacing. 2) The full multi-grid algorithm (FMG) with two V(0, 2) cycles on the target grid and just one V(0, 2) cycle on all the coarse grids always provides an approximate solution with the algebraic error less than the discretization error. Estimates of the total work in the FMG algorithm are ranged between 18 and 30 minimal work units (depending on the target (discretizatioin). Thus, the overall efficiency of the FMG solver closely approaches (if does not achieve) the goal of the textbook multigrid efficiency. 3) A novel approach to deriving a discrete solution approximating the true continuous solution with a relative accuracy given in advance is developed. An adaptive multigrid algorithm (AMA) using comparison of the solutions on two successive target grids to estimate the accuracy of the current target-grid solution is defined. A desired relative accuracy is accepted as an input parameter. The final target grid on which this accuracy can be achieved is chosen automatically in the solution process. the actual relative accuracy of the discrete solution approximation obtained by AMA is always better than the required accuracy; the computational complexity of the AMA algorithm is (nearly) optimal (comparable with the complexity of the FMG algorithm applied to solve the problem on the optimally spaced target grid).

Diskin, Boris↗
NASA NTRS1974

Error in interpolation and choice of the range of discreteness in measurements in a hydrophysical field

Errors in interpolation and the choosing of the range of discreteness when making measurements in a hydrophysical field are discussed. Equations for optimum interpolating based on the theory of linear interpolation of stationary random sequences are presented; analogous equations are derived for the case of data collected at stations located at the apices of a right triangle.

Zudin, O. F.↗
DOE OSTI2021

Validation of SAS4A/SASSYS-1 for predicting steady-state single-phase natural circulation

The validation of system analysis codes for nuclear reactor systems is required for the development and application of these computational tools. Designed as a comprehensive system analysis code for advanced nuclear reactors, SAS4A/SASSYS-1 requires validation of its physics model for capturing single-phase natural circulation behavior. To support the validation of SAS4A/SASSYS-1, high-precision experiments are performed capturing steady-state single-phase natural circulation on a scaled facility with comprehensive instrumentation. In this work, dedicated tests are performed quantifying the critical modeling parameters, and a single-phase natural circulation benchmark dataset is obtained with well-documented uncertainty and comprehensive facility description. The validation is then performed against the dataset examining the capability of SAS4A/SASSYS-1 in simulating steady-state single-phase natural circulation. The experimental facility is modeled in the candidate code. Solution verification is performed using Richardson-extrapolation-based estimators which quantify and restrict numerical errors from discretization. Input uncertainty provided by the benchmark dataset is forward propagated through the candidate code, quantifying the output uncertainty in a Monte Carlo approach. The composition of the output uncertainty is also quantified through a variance-based sensitivity analysis. With the uncertainty quantified for each individual condition, a detailed comparison between the simulation results and experimental data is performed covering the whole dataset. The results show consistent agreement for all primary parameters. The current validation activity provides a valuable benchmark dataset for the validation of system analysis codes in capturing single-phase natural circulation and demonstrates satisfactory prediction capability of SAS4A/SASSYS1 for steady-state single-phase natural circulation.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2023

Real-time evolution of Anderson impurity models via tensor network influence functionals

In this work, we present and analyze two tensor network-based influence functional approaches for simulating the real-time dynamics of quantum impurity models such as the Anderson model. Via comparison with recent numerically exact simulations, we show that such methods accurately capture the long-time nonequilibrium quench dynamics. The two parameters that must be controlled in these tensor network influence functional approaches are a time discretization (Trotter) error and a bond dimension (tensor network truncation) error. We show that the actual numerical uncertainties are controlled by an intricate interplay of these two approximations, which we demonstrate in different regimes. Our work opens the door to using these tensor network influence functional methods as general impurity solvers.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Validation of SAS4A/SASSYS-1 for Steady-State Single-Phase Natural Circulation

The development of numerical software for engineering applications requires the validation of the code against experimental benchmark datasets. To support the validation of SAS4A/SASSYS-1 in simulating the single-phase natural circulation within nuclear reactor systems, high-precision steady-state experiments are performed to capture single-phase natural circulation phenomena on an existing scaled facility with comprehensive instrumentation. Forced convection tests are designed precisely capturing the facility’s critical thermal-hydraulic parameters required for one-dimensional modeling, and a comprehensive single-phase natural circulation dataset is obtained with well-documented experimental uncertainty and facility description. Analysis and discussion based on the finalized dataset confirm the dataset’s ability in capturing dominant phenomena and address important physical interpretation of parameters. The dataset reported in this project provides a valuable benchmark resource for the validation of system analysis codes under single-phase natural circulation inside nuclear reactors. Validation of SAS4A/SASSYS-1 is then performed against the obtained benchmark dataset to confirm the capability of its physics model in simulating the steady-state single-phase natural circulation. The experimental facility is modeled in the candidate code. Solution verification is performed using Richardson-extrapolation-based estimators to quantify and restrict numerical errors from discretization. Numerical uncertainty originating from finite maximum pseudo-transient time is also quantified and restricted. Input uncertainty provided by the benchmark dataset is forward propagated through the candidate code, directly quantifying the simulation output in a Monte Carlo approach. The composition of the output uncertainty is further determined by the estimators of Sobol’ indices through a variance-based sensitivity analysis. With uncertainty quantified for each individual condition, detailed comparison between the simulation results and experimental data is performed covering the whole dataset, which shows consistent agreement for all important quantities. The validation activity reported in this project demonstrates that SAS4A/SASSYS-1 can predict the primary parameters with satisfactorily accuracy under steady-state single-phase natural circulation.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
NASA NTRS1980

A head-up display format for application to transport aircraft approach and landing

A head up display (HUD) format used in simulator studies of the application of HUD to the landing of civil transport aircraft is described in detail. The display features an indication of the aircraft's instantaneous flightpath that constitutes the primary controlled element. Discrete ILS error and altitude signals are scaled and positioned to provide precise guidance modes when tracked with the flightpath symbol. Consideration is given to both the availability and nonavailability of inertial velocity information in the aircraft.

Bray, R. S.↗
NASA NTRS1983

Analysis of Subpixel Registration Accuracy

Geometric and probabilistic models for subpixel accuracy are developed. The geometric models bound the error in offset estimation using the pixels in an observed digital straight line. One probabilistic model bounds the estimate of error offset for continuous images. The other model bounds the error for discrete images given that one is in the correct pixel.

Lavine, D.↗
NASA NTRS1983

Metric analysis and data validation across FORTRAN projects

The desire to predict the effort in developing or explaining the quality of software has led to the proposal of several metrics. As a step toward validating these metrics, the Software Engineering Laboratory (SEL) has analyzed the software science metrics, cyclomatic complexity, and various standard program measures for their relation to effort (including design through acceptance testing), development errors (both discrete and weighted according to the amount of time to locate and fix), and one another. The data investigated are collected from a project FORTRAN environment and examined across several projects at once, within individual projects and by reporting accuracy checks demonstrating the need to validate a database. When the data comes from individual programmers or certain validated projects, the metrics' correlations with actual effort seem to be strongest. For modules developed entirely by individual programmers, the validity ratios induce a statistically significant ordering of several of the metrics' correlations. When comparing the strongest correlations, neither software science's E metric cyclomatic complexity not source lines of code appears to relate convincingly better with effort than the others.

Basili, Victor R.↗
NASA NTRS1988

An error estimation procedure for plate bending elements

Procedures for identifying and eliminating errors inherent in individual finite elements and those due to the discretization of the continuum are presented. The elemental errors are identified through the use of an element formulation procedure based on physically interpretable strain gradient interpolation functions. The use of physically interpretable notation allows these errors to be eliminated using rational arguments. The discretization errors are identified by comparing the finite-element solution with a smoothed superconvergent solution. The errors thus identified are used to guide an adaptive mesh refinement procedure which produces improved results.

Dow, John O.↗
NASA NTRS1978

Directional errors of movements and their correction in a discrete tracking task

Subjects can correct their own errors of movement more quickly than they can react to external stimuli by using three general categories of feedback: (1) knowledge of results, primarily visually mediated; (2) proprioceptive or kinaesthetic such as from muscle spindles and joint receptors, and (3) corollary discharge or efference copy within the central nervous system. The effects of these feedbacks on simple reaction time, choice reaction time, and error correction time were studied in four normal human subjects. The movement used was plantarflexion and dorsiflexion of the ankle joint. The feedback loops were modified, by changing the sign of the visual display to alter the subject's perception of results, and by applying vibration at 100 Hz simultaneously to both the agonist and antagonist muscles of the ankle joint. The central processing was interfered with when the subjects were given moderate doses of alcohol (blood alcohol concentration levels of up to 0.07%). Vibration and alcohol increase both the simple and choice reaction times but not the error correction time.

Jaeger, R. J.↗
NASA NTRS1982

Numerical analysis of Weyl's method for integrating boundary layer equations

A fast method for accurate numerical integration of Blasius equation is proposed. It is based on the limit interchange in Weyl's fixed point method formulated as an iterated limit process. Each inner limit represents convergence to a discrete solution. It is shown that the error in a discrete solution admits asymptotic expansion in even powers of step size. An extrapolation process is set up to operate on a sequence of discrete solutions to reach the outer limit. Finally, this method is extended to related boundary layer equations.

Najfeld, I.↗
NASA NTRS2004

Textbook Multigrid Efficiency for Leading Edge Stagnation

A multigrid solver is defined as having textbook multigrid efficiency (TME) if the solutions to the governing system of equations are attained in a computational work which is a small (less than 10) multiple of the operation count in evaluating the discrete residuals. TME in solving the incompressible inviscid fluid equations is demonstrated for leading- edge stagnation flows. The contributions of this paper include (1) a special formulation of the boundary conditions near stagnation allowing convergence of the Newton iterations on coarse grids, (2) the boundary relaxation technique to facilitate relaxation and residual restriction near the boundaries, (3) a modified relaxation scheme to prevent initial error amplification, and (4) new general analysis techniques for multigrid solvers. Convergence of algebraic errors below the level of discretization errors is attained by a full multigrid (FMG) solver with one full approximation scheme (F.4S) cycle per grid. Asymptotic convergence rates of the F.4S cycles for the full system of flow equations are very fast, approaching those for scalar elliptic equations.

Diskin, Boris↗
NASA NTRS2004

Textbook Multigrid Efficiency for Leading Edge Stagnation

A multigrid solver is defined as having textbook multigrid efficiency (TME) if the solutions to the governing system of equations are attained in a computational work which is a small (less than 10) multiple of the operation count in evaluating the discrete residuals. TME in solving the incompressible inviscid fluid equations is demonstrated for leading-edge stagnation flows. The contributions of this paper include (1) a special formulation of the boundary conditions near stagnation allowing convergence of the Newton iterations on coarse grids, (2) the boundary relaxation technique to facilitate relaxation and residual restriction near the boundaries, (3) a modified relaxation scheme to prevent initial error amplification, and (4) new general analysis techniques for multigrid solvers. Convergence of algebraic errors below the level of discretization errors is attained by a full multigrid (FMG) solver with one full approximation scheme (FAS) cycle per grid. Asymptotic convergence rates of the FAS cycles for the full system of flow equations are very fast, approaching those for scalar elliptic equations.

Diskin, Boris↗
NASA NTRS2000

Residual Distribution Schemes for Conservation Laws Via Adaptive Quadrature

This paper considers a family of nonconservative numerical discretizations for conservation laws which retains the correct weak solution behavior in the limit of mesh refinement whenever sufficient order numerical quadrature is used. Our analysis of 2-D discretizations in nonconservative form follows the 1-D analysis of Hou and Le Floch. For a specific family of nonconservative discretizations, it is shown under mild assumptions that the error arising from non-conservation is strictly smaller than the discretization error in the scheme. In the limit of mesh refinement under the same assumptions, solutions are shown to satisfy an entropy inequality. Using results from this analysis, a variant of the "N" (Narrow) residual distribution scheme of van der Weide and Deconinck is developed for first-order systems of conservation laws. The modified form of the N-scheme supplants the usual exact single-state mean-value linearization of flux divergence, typically used for the Euler equations of gasdynamics, by an equivalent integral form on simplex interiors. This integral form is then numerically approximated using an adaptive quadrature procedure. This renders the scheme nonconservative in the sense described earlier so that correct weak solutions are still obtained in the limit of mesh refinement. Consequently, we then show that the modified form of the N-scheme can be easily applied to general (non-simplicial) element shapes and general systems of first-order conservation laws equipped with an entropy inequality where exact mean-value linearization of the flux divergence is not readily obtained, e.g. magnetohydrodynamics, the Euler equations with certain forms of chemistry, etc. Numerical examples of subsonic, transonic and supersonic flows containing discontinuities together with multi-level mesh refinement are provided to verify the analysis.

Barth, Timothy↗