SEARCH · Engineering Papers

Results for “ITERATIVE METHODS”

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.

SourceResearch connectionFrom yearThrough year

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

At least 109 records · Page 6

All sources NASA NTRS DOE OSTI

NASA NTRS1989

Finite element solvers for incompressible fluid flows and heat transfer

Two different finite-element solvers for incompressible viscous flow, i.e., the mixed interpolation method and the SIMPLE-type iterative method, are compared and tested with some benchmark problems. The advantages of the SIMPLE-type iterative method are the decoupling of the governing equations and the use of equal-order interpolation functions for both velocity and pressure. Even though there is a significant difference between the two methods in terms of the pressure field, similar solutions are obtained for the velocity field.

Sohn, Jeong L.↗

NASA NTRS2019

Application of a Temperature-Dependent Load Prediction Method to a RUAG Six-Component Block-Type Balance

Temperature-dependent data of a RUAG six-component block-type balance was analyzed to assess the accuracy of two load prediction methods for temperature-dependent balance data. The supplied data was prepared for the analysis by splitting it into calibration and check load data subsets. The first calibration data subset was obtained at a temperature of 294 Kelvin. The second calibration data subset was obtained at a temperature of 315 Kelvin. A subset of 38 points was extracted from the second data set and used as check loads so that the accuracy of the two load prediction methods could be tested. First, the Iterative Method in combination with an extended independent and dependent variable set was used for the balance load prediction. This approach fits electrical outputs as a function of loads and the temperature and, afterwards, constructs a load iteration scheme from the regression coefficients so that loads can be predicted from outputs and the temperature during a wind tunnel test. The Non-Iterative Method was also used for the load prediction. This alternate method can more easily be implemented in a data system as loads are directly fitted as a function of electrical outputs and the temperature. Analysis results for the axial force are only discussed in the paper as similar results were obtained for the other five load components. Results for both methods clearly show that the cross-product term constructed from either a primary gage load or a primary gage output and the temperature explains the majority of the temperature-dependent part of the predicted balance load. This term models the temperature dependent nature of the gage sensitivity. Therefore, it is recommended to apply primary gage loadings at different temperatures during a balance calibration whenever temperature effects need to be described. These loadings will contain information about the temperature-dependent nature of the gage sensitivities that can be quantified by related cross-product terms in regression models of the data.

strain-gage balance↗

NASA NTRS2017

Wind Tunnel Strain-Gage Balance Calibration Data Analysis Using a Weighted Least Squares Approach

A new approach is presented that uses a weighted least squares fit to analyze wind tunnel strain-gage balance calibration data. The weighted least squares fit is specifically designed to increase the influence of single-component loadings during the regression analysis. The weighted least squares fit also reduces the impact of calibration load schedule asymmetries on the predicted primary sensitivities of the balance gages. A weighting factor between zero and one is assigned to each calibration data point that depends on a simple count of its intentionally loaded load components or gages. The greater the number of a data point's intentionally loaded load components or gages is, the smaller its weighting factor becomes. The proposed approach is applicable to both the Iterative and Non-Iterative Methods that are used for the analysis of strain-gage balance calibration data in the aerospace testing community. The Iterative Method uses a reasonable estimate of the tare corrected load set as input for the determination of the weighting factors. The Non-Iterative Method, on the other hand, uses gage output differences relative to the natural zeros as input for the determination of the weighting factors. Machine calibration data of a six-component force balance is used to illustrate benefits of the proposed weighted least squares fit. In addition, a detailed derivation of the PRESS residuals associated with a weighted least squares fit is given in the appendices of the paper as this information could not be found in the literature. These PRESS residuals may be needed to evaluate the predictive capabilities of the final regression models that result from a weighted least squares fit of the balance calibration data.

calibration analysis↗

NASA NTRS1981

Eigenvector determination by iterative optical methods

Three power algorithms are considered by which an iterative optical processor can be used to compute the eigenvalues and eigenvectors of a matrix. The algorithms are appropriate for three applications: (1) calculating the largest eigenvalue; (2) calculating the eigenvalues in order of decreasingly dominant eigenvalues; and (3) calculating the eigenvector whose eigenvalue is closest to a given value.

Vijaya Kumar, B. V. K.↗

NASA NTRS1975

Radiation pattern synthesis of planar antennas using the iterative sampling method

A synthesis method is presented for determining an excitation of an arbitrary (but fixed) planar source configuration. The desired radiation pattern is specified over all or part of the visible region. It may have multiple and/or shaped main beams with low sidelobes. The iterative sampling method is used to find an excitation of the source which yields a radiation pattern that approximates the desired pattern to within a specified tolerance. In this paper the method is used to calculate excitations for line sources, linear arrays (equally and unequally spaced), rectangular apertures, rectangular arrays (arbitrary spacing grid), and circular apertures. Examples using these sources to form patterns with shaped main beams, multiple main beams, shaped sidelobe levels, and combinations thereof are given.

Stutzman, W. L.↗

NASA NTRS2020

Assessment of Temperature-Dependent Regression Model Terms of a RUAG Six-Component Block-Type Balance

A metric called the percent contribution was applied to regression models of temperature-dependent calibration data of a RUAG six-component block-type balance in order to assess the influence of temperature-dependent regression model terms on the balance load prediction. Regression models were examined that are needed if either the Iterative or the Non-Iterative Method is used for the load prediction. Computed values of the percent contribution confirmed that the cross-product term defined by a primary load and the temperature difference is the most influential temperature-dependent term of the regression model of a primary output that the Iterative Method needs. Similarly, the analysis showed that the cross-product term defined by a primary output and the temperature difference is the most influential temperature-dependent term of the regression model of a primary load that the Non-Iterative Method needs. Computed results support conclusions that were reported in an earlier theoretical study. This study asserted that the cross-product term defined by a primary load or output and the temperature difference models the temperature-dependent shift of the gage sensitivity. The influence of other temperature-dependent terms used in the regression models of the calibration data of RUAG's balance was negligible. This observation may be explained by the fact that RUAG's block-type balances have highly linear characteristics. Overall, the percent contribution has proven itself to be a reliable and easy-to-implement metric that may also be used for the assessment of the influence of temperature-dependent regression model terms on the load prediction of a six-component strain-gage balance.

Ulbrich, N.↗

NASA NTRS1989

Upwind relaxation methods for the Navier-Stokes equations using inner iterations

A supersonic and subsonic test problem is solved using an upwind line relaxation algorithm for the Navier-Stokes equations which employs inner iterations. In the supersonic test case, the inner iteration method was found to require only about 65 percent of the CPU time which was required by the most efficient line relaxation method without inner iterations. In the subsonic test case, poor matrix conditioning resulted in less efficiency than line relaxation methods employing a more conventional CPU-saving strategy.

Taylor, Arthur C., III↗

NASA NTRS2012

Discrete fourier transform (DFT) analysis for applications using iterative transform methods

According to various embodiments, a method is provided for determining aberration data for an optical system. The method comprises collecting a data signal, and generating a pre-transformation algorithm. The data is pre-transformed by multiplying the data with the pre-transformation algorithm. A discrete Fourier transform of the pre-transformed data is performed in an iterative loop. The method further comprises back-transforming the data to generate aberration data.

Dean, Bruce H.↗

DOE OSTI2022

Low-synch Gram–Schmidt with delayed reorthogonalization for Krylov solvers

The parallel strong-scaling of iterative methods is often determined by the number of global reductions at each iteration. Low-synch Gram-Schmidt algorithms are applied here to the Arnoldi algorithm to reduce the number of global reductions and therefore to improve the parallel strong-scaling of iterative solvers for nonsymmetric matrices such as the GMRES and the Krylov-Schur iterative methods. In the Arnoldi context, the factorization is "left-looking" and processes one column at a time. Among the methods for generating an orthogonal basis for the Arnoldi algorithm, the classical Gram-Schmidt algorithm, with reorthogonalization (CGS2) requires three global reductions per iteration. A new variant of CGS2 that requires only one reduction per iteration is presented and applied to the Arnoldi algorithm. Delayed CGS2 (DCGS2) employs the minimum number of global reductions per iteration (one) for a one-column at-a-time algorithm. The main idea behind the new algorithm is to group global reductions by rearranging the order of operations. DCGS2 must be carefully integrated into an Arnoldi expansion or a GMRES solver. Numerical stability experiments assess robustness for Krylov-Schur eigenvalue computations. Performance experiments on the ORNL Summit supercomputer then establish the superiority of DCGS2 over CGS2.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1989

Development of parallel algorithms for electrical power management in space applications

The application of parallel techniques for electrical power system analysis is discussed. The Newton-Raphson method of load flow analysis was used along with the decomposition-coordination technique to perform load flow analysis. The decomposition-coordination technique enables tasks to be performed in parallel by partitioning the electrical power system into independent local problems. Each independent local problem represents a portion of the total electrical power system on which a loan flow analysis can be performed. The load flow analysis is performed on these partitioned elements by using the Newton-Raphson load flow method. These independent local problems will produce results for voltage and power which can then be passed to the coordinator portion of the solution procedure. The coordinator problem uses the results of the local problems to determine if any correction is needed on the local problems. The coordinator problem is also solved by an iterative method much like the local problem. The iterative method for the coordination problem will also be the Newton-Raphson method. Therefore, each iteration at the coordination level will result in new values for the local problems. The local problems will have to be solved again along with the coordinator problem until some convergence conditions are met.

Berry, Frederick C.↗

NASA NTRS2001

Microgravity Diode Laser Spectroscopy Measurements in a Reacting Vortex Ring

The technique of Diode Laser Spectroscopy (DLS) with wavelength modulation is utilized to measure the concentration of methane in reacting vortex rings under microgravity conditions. From the measured concentration of methane, other major species such as water, carbon dioxide, nitrogen, and oxygen can be easily computed under the assumption of equilibrium chemistry with an iterative method called ITAC (Iterative Temperature with Assumed Chemistry). The conserved scalar approach in modelling the coupling between fluid dynamics and combustion is utilized to represent the unknown variables in terms of the mixture fraction and scalar dissipation rate in conjunction with ITAC. Post-processing of the DLS and the method used to compute the species concentration are discussed. From the flame luminosity results, ring circulation appears to increase the fuel consumption rate inside the reacting vortex ring and the flame height for cases with similar fuel volumes but different ring circulations. The concentrations of methane, water, and carbon dioxide agree well with available results from numerical simulations.

Chen, Shin-Juh↗

DOE OSTI2024

A simulation study of the ability to detect power distribution perturbations in the texas A&M TRIGA reactor with self-powered neutron detectors

Given the variety of ways that nuclear reactor core power may be perturbed, reactor operators and developers are keen on understanding the accuracy and convergence time during which perturbations in reactor power distribution may be synthesized (i.e., inferred) from an array of in-core radiation detectors. A simulation study was conducted as described herein using a highly detailed model of the Texas A&M Training, Research, Isotopes, General Atomics Reactor, in which an array of self-powered neutron detectors (SPNDs) was considered for input to the power synthesis methodology. The core power synthesis is conducted using a point-based iterative method with an iterative loop built in to ensure working equation consistency. The forward problem of SPND response to simulated perturbations in reactor power was solved for Gaussian peak-type perturbations in the reactor power distribution. These perturbations varied in variance, amplitude, and core location to assess their impact on synthesis error and to determine the number of iterations required for convergence. A relation between the unique resolvability limit and perturbation width was identified such that the maximum synthesis error increased rapidly when the peak width went beneath this limit (a width approximating half the reactor’s fuel pin-to-pin pitch); this resolvability limit is specific to the SPND configuration and fuel segmentation considered herein. The synthesis error increased linearly with perturbation peak amplitude, whereas the convergence time increased nonlinearly. Perturbations located closer to the center of the core were synthesized more accurately, albeit with a higher number of required iterations. These findings provide a qualitative and quantitative understanding of the accuracy and speed at which different types of spatial power perturbations can be resolved in light-water reactors.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2021

Linear convergence of accelerated conditional gradient algorithms in spaces of measures

A class of generalized conditional gradient algorithms for the solution of optimization problem in spaces of Radon measures is presented. The method iteratively inserts additional Dirac-delta functions and optimizes the corresponding coefficients. Under general assumptions, a sub-linear [see formula in PDF] rate in the objective functional is obtained, which is sharp in most cases. To improve efficiency, one can fully resolve the finite-dimensional subproblems occurring in each iteration of the method. We provide an analysis for the resulting procedure: under a structural assumption on the optimal solution, a linear [see formula in PDF] convergence rate is obtained locally.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

NASA NTRS1985

Fast and optimal solution to the Rankine-Hugoniot problem

A new, definitive, reliable and fast iterative method is described for determining the geometrical properties of a shock (i.e., theta sub Bn, yields N, V sub s and M sub A), the conservation constants and the self-consistent asymptotic magnetofluid variables, that uses the three dimensional magnetic field and plasma observations. The method is well conditioned and reliable at all theta sub Bn angles regardless of the shock strength or geometry. Explicit proof of uniqueness of the shock geometry solution by either analytical or graphical methods is given. The method is applied to synthetic and real shocks, including a bow shock event and the results are then compared with those determined by preaveraging methods and other iterative schemes. A complete analysis of the confidence region and error bounds of the solution is also presented.

Vinas, A. F.↗

NASA NTRS1986

Fast and optimal solution to the 'Rankine-Hugoniot problem'

Vinas, A. F.↗

NASA NTRS1974

Solution of an eigenvalue problem for the Laplace operator on a spherical surface

Methods for obtaining approximate solutions for the fundamental eigenvalue of the Laplace-Beltrami operator (also referred to as the membrane eigenvalue problem for the vibration equation) on the unit spherical surface are developed. Two specific types of spherical surface domains are considered: (1) the interior of a spherical triangle, i.e., the region bounded by arcs of three great circles, and (2) the exterior of a great circle arc extending for less than pi radians on the sphere (a spherical surface with a slit). In both cases, zero boundary conditions are imposed. In order to solve the resulting second-order elliptic partial differential equations in two independent variables, a finite difference approximation is derived. The symmetric (generally five-point) finite difference equations that develop are written in matrix form and then solved by the iterative method of point successive overrelaxation. Upon convergence of this iterative method, the fundamental eigenvalue is approximated by iteration utilizing the power method as applied to the finite Rayleigh quotient.

Walden, H.↗

NASA NTRS1984

Finite-difference fluid dynamics computer mathematical models for the design and interpretation of experiments for space flight

Numerical methods are used to design a spherical baroclinic flow model experiment of the large scale atmosphere flow for Spacelab. The dielectric simulation of radial gravity is only dominant in a low gravity environment. Computer codes are developed to study the processes at work in crystal growing systems which are also candidates for space flight. Crystalline materials rarely achieve their potential properties because of imperfections and component concentration variations. Thermosolutal convection in the liquid melt can be the cause of these imperfections. Such convection is suppressed in a low gravity environment. Two and three dimensional finite difference codes are being used for this work. Nonuniform meshes and implicit iterative methods are used. The iterative method for steady solutions is based on time stepping but has the options of different time steps for velocity and temperature and of a time step varying smoothly with position according to specified powers of the mesh spacings. This allows for more rapid convergence. The code being developed for the crystal growth studies allows for growth of the crystal as the solid-liquid interface. The moving interface is followed using finite differences; shape variations are permitted. For convenience in applying finite differences in the solid and liquid, a time dependent coordinate transformation is used to make this interface a coordinate surface.

Roberts, G. O.↗

NASA NTRS1992

An incremental strategy for calculating consistent discrete CFD sensitivity derivatives

In this preliminary study involving advanced computational fluid dynamic (CFD) codes, an incremental formulation, also known as the 'delta' or 'correction' form, is presented for solving the very large sparse systems of linear equations which are associated with aerodynamic sensitivity analysis. For typical problems in 2D, a direct solution method can be applied to these linear equations which are associated with aerodynamic sensitivity analysis. For typical problems in 2D, a direct solution method can be applied to these linear equations in either the standard or the incremental form, in which case the two are equivalent. Iterative methods appear to be needed for future 3D applications; however, because direct solver methods require much more computer memory than is currently available. Iterative methods for solving these equations in the standard form result in certain difficulties, such as ill-conditioning of the coefficient matrix, which can be overcome when these equations are cast in the incremental form; these and other benefits are discussed. The methodology is successfully implemented and tested in 2D using an upwind, cell-centered, finite volume formulation applied to the thin-layer Navier-Stokes equations. Results are presented for two laminar sample problems: (1) transonic flow through a double-throat nozzle; and (2) flow over an isolated airfoil.

Korivi, Vamshi Mohan↗