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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 181 records · Page 10
All sourcesNASA NTRSDOE OSTI
NASA NTRS1995

Application of FEM to estimate complex permittivity of dielectric material at microwave frequency using waveguide measurements

A simple waveguide measurement technique is presented to determine the complex dielectric constant of a dielectric material. The dielectric sample is loaded in a shorted x-band rectangular waveguide. Using a network analyzer; the reflection coefficient of the shorted waveguide (loaded with sample) is measured. Using the Finite Element Method (FEM), the exact reflection coefficient of the shorted waveguide (loaded with sample) is determined as a function of the dielectric constant. Matching the measured value of the reflection coefficient with the reflection coefficient calculated using the FEM utilizing the Newton-Raphson Method, an estimate of the dielectric constant of a dielectric material is obtained. A comparison of estimated values of dielectric constant obtained from simple waveguide modal theory and the present approach is presented.

Deshpande, M. D.↗
NASA NTRS1994

Computation of iodine species concentrations in water

During an evaluation of the use of iodine as a water disinfectant and the development of methods for measuring various iodine species in water onboard Space Freedom, it became necessary to compute the concentration of the various species based on equilibrium principles alone. Of particular concern was the case when various amounts of iodine, iodide, strong acid, and strong base are added to water. Such solutions can be used to evaluate the performance of various monitoring methods being considered. The authors of this paper present an overview of aqueous iodine chemistry, a set of nonlinear equations which can be used to model the above case, and a computer program for solving this system of equations using the Newton-Raphson method. The program was validated by comparing results over a range of concentrations and pH values with those previously presented by Gottardi for a given pH. Use of this program indicated that there are multiple roots to many cases and selecting an appropriate initial guess is important. Comparison of program results with laboratory results for the case when only iodine is added to water indicates the program gives high pH values for the iodine concentrations normally used for water disinfection. Extending the model to include the effects of iodate formation results in the computer pH values being closer to those observed, but the model with iodate does not agree well for the case in which base is added in addition to iodine to raise the pH. Potential explanations include failure to obtain equilibrium conditions in the lab, inaccuracies in published values for the equilibrium constants, and inadequate model of iodine chemistry and/or the lack of adequate analytical methods for measuring the various iodine species in water.

Schultz, John R.↗
NASA NTRS1999

Computation of Steady and Unsteady Laminar Flames: Theory

In this paper we describe the numerical analysis underlying our efforts to develop an accurate and reliable code for simulating flame propagation using complex physical and chemical models. We discuss our spatial and temporal discretization schemes, which in our current implementations range in order from two to six. In space we use staggered meshes to define discrete divergence and gradient operators, allowing us to approximate complex diffusion operators while maintaining ellipticity. Our temporal discretization is based on the use of preconditioning to produce a highly efficient linearly implicit method with good stability properties. High order for time accurate simulations is obtained through the use of extrapolation or deferred correction procedures. We also discuss our techniques for computing stationary flames. The primary issue here is the automatic generation of initial approximations for the application of Newton's method. We use a novel time-stepping procedure, which allows the dynamic updating of the flame speed and forces the flame front towards a specified location. Numerical experiments are presented, primarily for the stationary flame problem. These illustrate the reliability of our techniques, and the dependence of the results on various code parameters.

Hagstrom, Thomas↗
NASA NTRS1993

Large-scale computation of incompressible viscous flow by least-squares finite element method

The least-squares finite element method (LSFEM) based on the velocity-pressure-vorticity formulation is applied to large-scale/three-dimensional steady incompressible Navier-Stokes problems. This method can accommodate equal-order interpolations and results in symmetric, positive definite algebraic system which can be solved effectively by simple iterative methods. The first-order velocity-Bernoulli function-vorticity formulation for incompressible viscous flows is also tested. For three-dimensional cases, an additional compatibility equation, i.e., the divergence of the vorticity vector should be zero, is included to make the first-order system elliptic. The simple substitution of the Newton's method is employed to linearize the partial differential equations, the LSFEM is used to obtain discretized equations, and the system of algebraic equations is solved using the Jacobi preconditioned conjugate gradient method which avoids formation of either element or global matrices (matrix-free) to achieve high efficiency. To show the validity of this scheme for large-scale computation, we give numerical results for 2D driven cavity problem at Re = 10000 with 408 x 400 bilinear elements. The flow in a 3D cavity is calculated at Re = 100, 400, and 1,000 with 50 x 50 x 50 trilinear elements. The Taylor-Goertler-like vortices are observed for Re = 1,000.

Jiang, Bo-Nan↗
NASA NTRS1991

Domain decomposition methods in computational fluid dynamics

The divide-and-conquer paradigm of iterative domain decomposition, or substructuring, has become a practical tool in computational fluid dynamic applications because of its flexibility in accommodating adaptive refinement through locally uniform (or quasi-uniform) grids, its ability to exploit multiple discretizations of the operator equations, and the modular pathway it provides towards parallelism. These features are illustrated on the classic model problem of flow over a backstep using Newton's method as the nonlinear iteration. Multiple discretizations (second-order in the operator and first-order in the preconditioner) and locally uniform mesh refinement pay dividends separately, and they can be combined synergistically. Sample performance results are included from an Intel iPSC/860 hypercube implementation.

Gropp, William D.↗
NASA NTRS1992

Domain decomposition methods in computational fluid dynamics

The divide-and-conquer paradigm of iterative domain decomposition, or substructuring, has become a practical tool in computational fluid dynamic applications because of its flexibility in accommodating adaptive refinement through locally uniform (or quasi-uniform) grids, its ability to exploit multiple discretizations of the operator equations, and the modular pathway it provides towards parallelism. These features are illustrated on the classic model problem of flow over a backstep using Newton's method as the nonlinear iteration. Multiple discretizations (second-order in the operator and first-order in the preconditioner) and locally uniform mesh refinement pay dividends separately, and they can be combined synergistically. Sample performance results are included from an Intel iPSC/860 hypercube implementation.

Gropp, William D.↗
NASA NTRS2014

First-Order Hyperbolic System Method for Time-Dependent Advection-Diffusion Problems

A time-dependent extension of the first-order hyperbolic system method for advection-diffusion problems is introduced. Diffusive/viscous terms are written and discretized as a hyperbolic system, which recovers the original equation in the steady state. The resulting scheme offers advantages over traditional schemes: a dramatic simplification in the discretization, high-order accuracy in the solution gradients, and orders-of-magnitude convergence acceleration. The hyperbolic advection-diffusion system is discretized by the second-order upwind residual-distribution scheme in a unified manner, and the system of implicit-residual-equations is solved by Newton's method over every physical time step. The numerical results are presented for linear and nonlinear advection-diffusion problems, demonstrating solutions and gradients produced to the same order of accuracy, with rapid convergence over each physical time step, typically less than five Newton iterations.

Mazaheri, Alireza↗
NASA NTRS1989

Globally convergent techniques in nonlinear Newton-Krylov

Some convergence theory is presented for nonlinear Krylov subspace methods. The basic idea of these methods is to use variants of Newton's iteration in conjunction with a Krylov subspace method for solving the Jacobian linear systems. These methods are variants of inexact Newton methods where the approximate Newton direction is taken from a subspace of small dimensions. The main focus is to analyze these methods when they are combined with global strategies such as linesearch techniques and model trust region algorithms. Most of the convergence results are formulated for projection onto general subspaces rather than just Krylov subspaces.

Brown, Peter N.↗
NASA NTRS1989

Advances in upwind relaxation methods

Numerical techniques for solving the compressible Euler and Navier-Stokes equations are discussed with an emphasis on characteristic-based schemes. Two popular approaches, flux difference splitting and flux vector splitting, are described in one-dimensional Cartesian coordinates and then extended to three-dimensional generalized coordinates. A technique for increasing the spatial accuracy is presented, followed by a discussion of numerical dissipation mechanisms. An introduction to the use of implicit time integration schemes for accelerating the convergence rate to steady-state solutions including Newton's method, relaxation strategies, and approximate factorization techniques and their implementation on a vector processor concludes the chapter.

Walters, R. W.↗
NASA NTRS2013

Design of a Variational Multiscale Method for Turbulent Compressible Flows

A spectral-element framework is presented for the simulation of subsonic compressible high-Reynolds-number flows. The focus of the work is maximizing the efficiency of the computational schemes to enable unsteady simulations with a large number of spatial and temporal degrees of freedom. A collocation scheme is combined with optimized computational kernels to provide a residual evaluation with computational cost independent of order of accuracy up to 16th order. The optimized residual routines are used to develop a low-memory implicit scheme based on a matrix-free Newton-Krylov method. A preconditioner based on the finite-difference diagonalized ADI scheme is developed which maintains the low memory of the matrix-free implicit solver, while providing improved convergence properties. Emphasis on low memory usage throughout the solver development is leveraged to implement a coupled space-time DG solver which may offer further efficiency gains through adaptivity in both space and time.

Design↗
NASA NTRS1989

Theory of wide-angle photometry from standard stars

Wide angle celestial structures, such as bright comet tails and nearby galaxies and clusters of galaxies, rely on photographic methods for quantified morphology and photometry, primarily because electronic devices with comparable resolution and sky coverage are beyond current technological capability. The problem of the photometry of extended structures and of how this problem may be overcome through calibration by photometric standard stars is examined. The perfect properties of the ideal field of view are stated in the guise of a radiometric paraxial approximation, in the hope that fields of view of actual telescopes will conform. Fundamental radiometric concepts are worked through before the issue of atmospheric attenuation is addressed. The independence of observed atmospheric extinction and surface brightness leads off the quest for formal solutions to the problem of surface photometry. Methods and problems of solution are discussed. The spectre is confronted in the spirit of standard stars and shown to be chimerical in that light, provided certain rituals are adopted. After a brief discussion of Baker-Sampson polynomials and the vexing issue of saturation, a pursuit is made of actual numbers to be expected in real cases. While the numbers crunched are gathered ex nihilo, they demonstrate the feasibility of Newton's method in the solution of this overdetermined, nonlinear, least square, multiparametric, photometric problem.

Usher, Peter D.↗
NASA NTRS1979

Algebraic methods for the solution of some linear matrix equations

The characterization of polynomials whose zeros lie in certain algebraic domains (and the unification of the ideas of Hermite and Lyapunov) is the basis for developing finite algorithms for the solution of linear matrix equations. Particular attention is given to equations PA + A'P = Q (the Lyapunov equation) and P - A'PA = Q the (discrete Lyapunov equation). The Lyapunov equation appears in several areas of control theory such as stability theory, optimal control (evaluation of quadratic integrals), stochastic control (evaluation of covariance matrices) and in the solution of the algebraic Riccati equation using Newton's method.

Djaferis, T. E.↗
NASA NTRS2000

Computer-implemented method and apparatus for autonomous position determination using magnetic field data

A computer-implemented method and apparatus for determining position of a vehicle within 100 km autonomously from magnetic field measurements and attitude data without a priori knowledge of position. An inverted dipole solution of two possible position solutions for each measurement of magnetic field data are deterministically calculated by a program controlled processor solving the inverted first order spherical harmonic representation of the geomagnetic field for two unit position vectors 180 degrees apart and a vehicle distance from the center of the earth. Correction schemes such as a successive substitutions and a Newton-Raphson method are applied to each dipole. The two position solutions for each measurement are saved separately. Velocity vectors for the position solutions are calculated so that a total energy difference for each of the two resultant position paths is computed. The position path with the smaller absolute total energy difference is chosen as the true position path of the vehicle.

Ketchum, Eleanor A.↗
NASA NTRS1996

Practical Aspects of Krylov Subspace Iterative Methods in CFD

Implementation issues associated with the application of Krylov subspace iterative methods, such as Newton-GMRES, are presented within the framework of practical computational fluid dynamic (CFD) applications. This paper categorizes, evaluates, and contrasts the major ingredients (function evaluations, matrix-vector products, and preconditioners) of Newton-GMRES Krylov subspace methods in terms of their effect on the local linear and global nonlinear convergence, memory requirements, and accuracy. The discussion focuses on Newton-GMRES in both a structured multi-zone incompressible Navier-Stokes solver and an unstructured mesh finite-volume Navier-Stokes solver. Approximate versus exact matrix-vector products, effective preconditioners, and other pertinent issues are addressed.

Pulliam, Thomas H.↗
NASA NTRS1978

The exact numerical calculation of propeller noise

This paper presents a method for computing the acoustic pressure signature of a propeller due to blade thickness and steady surface pressure loading including the effect of forward motion. The tip helical speed is restricted to subsonic. The formulation is based on the Ffowcs Williams-Hawkings exact result concerning the sound generation by moving bodies. The blade surface is described in a helical coordinate system by the blade angles, positions of the leading and trailing edges along the local pitch helix, and the camber and thickness distributions along the chord. The retarded distance of the moving acoustic source on an element of surface area of the propeller blade is obtained numerically by Newton's method. The surface integration over the propeller blades is carried out in the helical coordinate system using a double Gauss-Legendre formula. Good agreement was found between analytic and experimental results, both in the time and frequency domains. Some samples showing the effects of propeller geometry and tip Mach number on the acoustic signature are included.

Woan, C. J.↗
NASA NTRS1994

Global Asymptotic Behavior of Iterative Implicit Schemes

The global asymptotic nonlinear behavior of some standard iterative procedures in solving nonlinear systems of algebraic equations arising from four implicit linear multistep methods (LMMs) in discretizing three models of 2 x 2 systems of first-order autonomous nonlinear ordinary differential equations (ODEs) is analyzed using the theory of dynamical systems. The iterative procedures include simple iteration and full and modified Newton iterations. The results are compared with standard Runge-Kutta explicit methods, a noniterative implicit procedure, and the Newton method of solving the steady part of the ODEs. Studies showed that aside from exhibiting spurious asymptotes, all of the four implicit LMMs can change the type and stability of the steady states of the differential equations (DEs). They also exhibit a drastic distortion but less shrinkage of the basin of attraction of the true solution than standard nonLMM explicit methods. The simple iteration procedure exhibits behavior which is similar to standard nonLMM explicit methods except that spurious steady-state numerical solutions cannot occur. The numerical basins of attraction of the noniterative implicit procedure mimic more closely the basins of attraction of the DEs and are more efficient than the three iterative implicit procedures for the four implicit LMMs. Contrary to popular belief, the initial data using the Newton method of solving the steady part of the DEs may not have to be close to the exact steady state for convergence. These results can be used as an explanation for possible causes and cures of slow convergence and nonconvergence of steady-state numerical solutions when using an implicit LMM time-dependent approach in computational fluid dynamics.

Yee, H. C.↗
NASA NTRS1967

Computer program for network synthesis by frequency response fit

Computer program synthesizes a passive network by minimizing the difference in desired and actual frequency response. The program solves for the critical points of the error function /weighted least squares fit between calculated and desired frequency response/ by the multivariable Newton-Raphson method with components constrained to an admissible region.

Green, S.↗