SEARCH · Engineering Papers

Results for “Iteration method”

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 991 records · Page 55

All sources NASA NTRS DOE OSTI

NASA NTRS1992

Application of vector-valued rational approximations to the matrix eigenvalue problem and connections with Krylov subspace methods

Let F(z) be a vectored-valued function F: C approaches C sup N, which is analytic at z=0 and meromorphic in a neighborhood of z=0, and let its Maclaurin series be given. We use vector-valued rational approximation procedures for F(z) that are based on its Maclaurin series in conjunction with power iterations to develop bona fide generalizations of the power method for an arbitrary N X N matrix that may be diagonalizable or not. These generalizations can be used to obtain simultaneously several of the largest distinct eigenvalues and the corresponding invariant subspaces, and present a detailed convergence theory for them. In addition, it is shown that the generalized power methods of this work are equivalent to some Krylov subspace methods, among them the methods of Arnoldi and Lanczos. Thus, the theory provides a set of completely new results and constructions for these Krylov subspace methods. This theory suggests at the same time a new mode of usage for these Krylov subspace methods that were observed to possess computational advantages over their common mode of usage.

Sidi, Avram↗

NASA NTRS1987

Design of transonic airfoils and wings using a hybrid design algorithm

A method has been developed for designing airfoils and wings at transonic speeds. It utilizes a hybrid design algorithm in an iterative predictor/corrector approach, alternating between analysis code and a design module. This method has been successfully applied to a variety of airfoil and wing design problems, including both transport and highly-swept fighter wing configurations. An efficient approach to viscous airfoild design and the effect of including static aeroelastic deflections in the wing design process are also illustrated.

Campbell, Richard L.↗

NASA NTRS1981

Computational methods of robust controller design for aerodynamic flutter suppression

The development of Riccati iteration, a tool for the design and analysis of linear control systems is examined. First, Riccati iteration is applied to the problem of pole placement and order reduction in two-time scale control systems. Order reduction, yielding a good approximation to the original system, is demonstrated using a 16th order linear model of a turbofan engine. Next, a numerical method for solving the Riccati equation is presented and demonstrated for a set of eighth order random examples. A literature review of robust controller design methods follows which includes a number of methods for reducing the trajectory and performance index sensitivity in linear regulators. Lastly, robust controller design for large parameter variations is discussed.

Anderson, L. R.↗

NASA NTRSDate not supplied

Towards Robust and Accurate Implicit Gradient Methods for Second- and Third-Order Nodal-Gradient Cell-Centered Finite-Volume Discretizations on Tetrahedral Grids

In this paper, we introduce implicit gradient methods as alternatives to conventional least-squares gradient methods for second- and third-order nodal-gradient cell-centered finite-volume discretizations, where solutions are stored at cells but gradients are stored at nodes. Because of the unique configuration of solutions and gradients, implicit gradient systems developed for the node-centered edge-based discretization method can be directly applied once the numerical solutions are interpolated from cells to nodes with sufficient accuracy. The resulting defect-correction solver can be loosely coupled with a flow-equation solver, and at convergence, solutions and gradients that satisfy the corresponding residual equations are obtained. Each iteration is relatively cheap compared with least-squares methods involving hundreds of neighbors. Numerical results are presented for accuracy verification studies and some simple but realistic flow problems.

Computational Fluid Dynamics↗

NASA NTRS1982

Noniterative grid generation using parabolic difference equations for fuselage-wing flow calculations

A fast method for generating three-dimensional grids for fuselage-wing transonic flow calculations using parabolic difference equations is described. No iterative scheme is used in the three-dimensional sense; grids are generated from one grid surface to the next starting from the fuselage surface. The computational procedure is similar to the iterative solution of the two-dimensional heat conduction equation. The proposed method is at least 10 times faster than the elliptic grid generation method and has much smaller memory requirements. Results are presented for a fuselage and wing of NACA-0012 section and thickness ratio of 10 percent. Although only H-grids are demonstrated, the present technique should be applicable to C-grids and O-grids in three dimensions.

Nakamura, S.↗

NASA NTRS2017

Gravity-Assist Trajectories to the Ice Giants: An Automated Method to Catalog Mass-or Time-Optimal Solutions

This work presents an automated method of calculating mass (or time) optimal gravity-assist trajectories without a priori knowledge of the flyby-body combination. Since gravity assists are particularly crucial for reaching the outer Solar System, we use the Ice Giants, Uranus and Neptune, as example destinations for this work. Catalogs are also provided that list the most attractive trajectories found over launch dates ranging from 2024 to 2038. The tool developed to implement this method, called the Python EMTG Automated Trade Study Application (PEATSA), iteratively runs the Evolutionary Mission Trajectory Generator (EMTG), a NASA Goddard Space Flight Center in-house trajectory optimization tool. EMTG finds gravity-assist trajectories with impulsive maneuvers using a multiple-shooting structure along with stochastic methods (such as monotonic basin hopping) and may be run with or without an initial guess provided. PEATSA runs instances of EMTG in parallel over a grid of launch dates. After each set of runs completes, the best results within a neighborhood of launch dates are used to seed all other cases in that neighborhood---allowing the solutions across the range of launch dates to improve over each iteration. The results here are compared against trajectories found using a grid-search technique, and PEATSA is found to outperform the grid-search results for most launch years considered.

Hughes, Kyle M.↗

NASA NTRS2017

Gravity-Assist Trajectories to the Ice Giants: An Automated Method to Catalog Mass- Or Time-Optimal Solutions

This work presents an automated method of calculating mass (or time) optimal gravity-assist trajectories without a priori knowledge of the flyby-body combination. Since gravity assists are particularly crucial for reaching the outer Solar System, we use the Ice Giants, Uranus and Neptune, as example destinations for this work. Catalogs are also provided that list the most attractive trajectories found over launch dates ranging from 2024 to 2038. The tool developed to implement this method, called the Python EMTG Automated Trade Study Application (PEATSA), iteratively runs the Evolutionary Mission Trajectory Generator (EMTG), a NASA Goddard Space Flight Center in-house trajectory optimization tool. EMTG finds gravity-assist trajectories with impulsive maneuvers using a multiple-shooting structure along with stochastic methods (such as monotonic basin hopping) and may be run with or without an initial guess provided. PEATSA runs instances of EMTG in parallel over a grid of launch dates. After each set of runs completes, the best results within a neighborhood of launch dates are used to seed all other cases in that neighborhood-allowing the solutions across the range of launch dates to improve over each iteration. The results here are compared against trajectories found using a grid-search technique, and PEATSA is found to outperform the grid-search results for most launch years considered.

Hughes, Kyle M.↗

NASA NTRS1999

Time-of-Arrival Lightning Location Retrieval Using an Oblate Spheroidal Earth Model

The problem of retrieving lightning ground strike location on an oblate spheroidal Earth using a network of 4 or more time-of-arrival sensors is considered. A recently developed analytic method for obtaining such retrievals on a spherical Earth surface is perturbed resulting in an iterative procedure to get correction terms. The perturbation procedure consists of applying a vector Newton's method to eqs. relating the distances from the lightning location to each sensor along a geodesic and the times of arrival of the wave produced by the lightning source at each sensor.

Solakiewicz, Richard↗

NASA NTRS1987

Automated design of controlled diffusion blades

A numerical automation procedure has been developed to be used in conjunction with an inverse hodograph method for the design of controlled diffusion blades. With this procedure a cascade of airfoils with a prescribed solidity, inlet Mach number, inlet air flow angle, and air flow turning can be produced automatically. The trailing edge thickness of the airfoil, an important quantity in inverse methods, is also prescribed. The automation procedure consists of a multidimensional Newton iteration in which the objective design conditions are achieved by acting on the hodograph input parameters of the underlying inverse code. The method, although more general in scope, is applied in this paper to the design of axial flow compressor blade sections, and a wide range of examples is presented.

Sanz, Jose M.↗

NASA NTRS1988

Automated design of controlled-diffusion blades

Sanz, J. M.↗

NASA NTRS1976

Calculations of the Electron Energy Distribution Function in a Uranium Plasma by Analytic and Monte Carlo Techniques

Electron energy distribution functions were calculated in a U235 plasma at 1 atmosphere for various plasma temperatures and neutron fluxes. The distributions are assumed to be a summation of a high energy tail and a Maxwellian distribution. The sources of energetic electrons considered are the fission-fragment induced ionization of uranium and the electron induced ionization of uranium. The calculation of the high energy tail is reduced to an electron slowing down calculation, from the most energetic source to the energy where the electron is assumed to be incorporated into the Maxwellian distribution. The pertinent collisional processes are electron-electron scattering and electron induced ionization and excitation of uranium. Two distinct methods were employed in the calculation of the distributions. One method is based upon the assumption of continuous slowing and yields a distribution inversely proportional to the stopping power. An iteration scheme is utilized to include the secondary electron avalanche. In the other method, a governing equation is derived without assuming continuous electron slowing. This equation is solved by a Monte Carlo technique.

Bathke, C. G.↗

NASA NTRS1976

A quadrilateral vortex method applied to configurations with high circulation

A quadrilateral vortex-lattice method is briefly described for calculating the potential flow aerodynamic characteristics of high-lift configurations. It incorporates an iterative scheme for calculating the deformation of forcefree wakes, including wakes from side edges. The method is applicable to multiple lifting surfaces with part-span flaps deflected, and can include ground effect and wind-tunnel interference. Numerical results, presented for a number of high-lift configurations, demonstrate rapid convergence of the iterative technique. The results are in good agreement with available experimental data.

Maskew, B.↗

NASA NTRS1986

Application of viscous-inviscid interaction methods to transonic turbulent flows

Two different viscous-inviscid interaction schemes were developed for the analysis of steady, turbulent, transonic, separated flows over axisymmetric bodies. The viscous and inviscid solutions are coupled through the displacement concept using a transpiration velocity approach. In the semi-inverse interaction scheme, the viscous and inviscid equations are solved in an explicitly separate manner and the displacement thickness distribution is iteratively updated by a simple coupling algorithm. In the simultaneous interaction method, local solutions of viscous and inviscid equations are treated simultaneously, and the displacement thickness is treated as an unknown and is obtained as a part of the solution through a global iteration procedure. The inviscid flow region is described by a direct finite-difference solution of a velocity potential equation in conservative form. The potential equation is solved on a numerically generated mesh by an approximate factorization (AF2) scheme in the semi-inverse interaction method and by a successive line overrelaxation (SLOR) scheme in the simultaneous interaction method. The boundary-layer equations are used for the viscous flow region. The continuity and momentum equations are solved inversely in a coupled manner using a fully implicit finite-difference scheme.

Lee, D.↗

NASA NTRS1986

Combined, nonlinear aerodynamic and structural method for the aeroelastic design of a three-dimensional wing in supersonic flow

An iterative procedure for the static aeroelastic design of a flexible wing at supersonic speeds has been developed. The procedure combines a nonlinear, full-potential solver (NCOREL) with an equivalent plate structural analysis method. The NCOREL method yields significantly improved aerodynamic estimates compared to linear theory. The equivalent plate structural analysis method demonstrates an order of magnitude reduction in computer memory and execution time compared to finite-element methods. A highly swept wing is analyzed at high lift using this aeroelastic procedure. The results indicate that the wing deforms favorably due to aerodynamic loading and, consequently, that the inviscid drag levels do not vary at the required lift coefficient although the angle of attack varies significantly. A sensitivity analysis of the type required for optimization studies was also performed with the aeroelastic design procedure.

Pittman, J. L.↗

NASA NTRS2004

Cirrus Clouds Optical, Microphysical and Radiative Properties Observed During Crystal-Face Experiment: I. A Radar-Lidar Retrieval System

A method of retrieving cloud microphysical properties using combined observations from both cloud radar and lidar is introduced. This retrieval makes use of an improvement to the traditional optimal estimation retrieval method, whereby a series of corrections are applied to the state vector during the search for an iterative solution. This allows faster convergence to a solution and is less processor intensive. The method is first applied to a synthetic cloud t o demonstrate its validity, and it is shown that the retrieval reliably reproduces vertical profiles of ice water content. The retrieval method is then applied to radar and lidar observations from the CRYSTAL-FACE experiment, and vertical profiles of ice crystal diameter, number concentration, and ice water content are retrieved for a cirrus cloud layers observed one day of that experiment. The validity of the relationship between visible extinction coefficient and radar reflectivity was examined. While synthetic tests showed such a functional relationship, the measured data only partially supported such a conclusion. This is due to errors in the forward model (as explained above) as well as errors in the data sets, including possible mismatch between lidar and radar profiles or errors in the optical depth. Empirical relationships between number concentrations and mean particle diameter were also examined. The results indicate that a distinct and robust relationship exists between these retrieved quantities and it is argued that such a relationship is more than an artifact of the retrieval process offering insight into the nature of the microphysical processes taking place in cirrus.

Mitrescu, C.↗

NASA NTRS1973

Application of the method local potential to the analysis of turbulent shear flows

It has been found that, in general, the local potential cannot be employed to obtain approximate solutions for the various correlations of turbulent properties which appear in the time averaged form of the conservation equations. Although the method of local potential is equivalent to the Galerkin method when the self-consistent condition is applied, the local potential can also be applied as an iterative algorithm in place of using the selfconsistent condition. This procedure offers an alternative to the Galerkin method and may be useful in obtaining approximate solutions for the total turbulent velocity. In addition, for certain simple turbulent shear flows the iterative algorithm may permit approximate, but non-empirical, solutions by modeling only the mean velocity and the Reynolds stress.

Reed, T. D.↗

NASA NTRS1975

A triangular thin shell finite element: Nonlinear analysis

Aspects of the formulation of a triangular thin shell finite element which pertain to geometrically nonlinear (small strain, finite displacement) behavior are described. The procedure for solution of the resulting nonlinear algebraic equations combines a one-step incremental (tangent stiffness) approach with one iteration in the Newton-Raphson mode. A method is presented which permits a rational estimation of step size in this procedure. Limit points are calculated by means of a superposition scheme coupled to the incremental side of the solution procedure while bifurcation points are calculated through a process of interpolation of the determinants of the tangent-stiffness matrix. Numerical results are obtained for a flat plate and two curved shell problems and are compared with alternative solutions.

Thomas, G. R.↗

NASA NTRS1975

Transonic airfoil flowfield analysis using Cartesian coordinates

A numerical technique for analyzing transonic airfoils is presented. The method employs the basic features of Jameson's iterative solution for the full potential equation, except that Cartesian coordinates are used rather than a grid which fits the airfoil, such as the conformal circle-plane or 'sheared parabolic' coordinates which were used previously. Comparison with previous results shows that it is not necessary to match the computational grid to the airfoil surface, and that accurate results can be obtained with a Cartesian grid for lifting supercritical airfoils.

Carlson, L. A.↗