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At least 559 records · Page 31
All sourcesNASA NTRSDOE OSTI
NASA NTRS1992

On the numeric integration of dynamic attitude equations

We describe new types of numerical integration algorithms developed by the authors. The main aim of the algorithms is to numerically integrate differential equations which evolve on geometric objects, such as the rotation group. The algorithms provide iterates which lie on the prescribed geometric object, either exactly, or to some prescribed accuracy, independent of the order of the algorithm. This paper describes applications of these algorithms to the evolution of the attitude of a rigid body.

Crouch, P. E.↗
NASA NTRS1981

On the utility of finite element theory for computational fluid dynamics

An implicit finite element numerical solution algorithm is derived for the compressible Navier-Stokes equations expressed in generalized coordinates. The theoretical basis utilizes a Galerkin-Weighted Residuals formulation, and extremization of approximation error within the context of a multipole expansion. A von Neumann analysis for a simplified form indicates the algorithm fourth- to sixth-order phase accurate, with third-order dissipation for the elementary linear element construction. Performance is improved for the algorithm constructed using quadratic interpolation. Numerical experiments for shocked duct flows are employed to optimize the several algorithm parameters. Additional numerical solutions validate algorithm accuracy and utility for aerodynamics applications.

Baker, A. J.↗
NASA NTRS1998

A Polynomial Time, Numerically Stable Integer Relation Algorithm

Let x = (x1, x2...,xn be a vector of real numbers. X is said to possess an integer relation if there exist integers a(sub i) not all zero such that a1x1 + a2x2 + ... a(sub n)Xn = 0. Beginning in 1977 several algorithms (with proofs) have been discovered to recover the a(sub i) given x. The most efficient of these existing integer relation algorithms (in terms of run time and the precision required of the input) has the drawback of being very unstable numerically. It often requires a numeric precision level in the thousands of digits to reliably recover relations in modest-sized test problems. We present here a new algorithm for finding integer relations, which we have named the "PSLQ" algorithm. It is proved in this paper that the PSLQ algorithm terminates with a relation in a number of iterations that is bounded by a polynomial in it. Because this algorithm employs a numerically stable matrix reduction procedure, it is free from the numerical difficulties, that plague other integer relation algorithms. Furthermore, its stability admits an efficient implementation with lower run times oil average than other algorithms currently in Use. Finally, this stability can be used to prove that relation bounds obtained from computer runs using this algorithm are numerically accurate.

Ferguson, Helaman R. P.↗
NASA NTRS1993

Statistical computation of tolerance limits

Based on a new theory, two computer codes were developed specifically to calculate the exact statistical tolerance limits for normal distributions within unknown means and variances for the one-sided and two-sided cases for the tolerance factor, k. The quantity k is defined equivalently in terms of the noncentral t-distribution by the probability equation. Two of the four mathematical methods employ the theory developed for the numerical simulation. Several algorithms for numerically integrating and iteratively root-solving the working equations are written to augment the program simulation. The program codes generate some tables of k's associated with the varying values of the proportion and sample size for each given probability to show accuracy obtained for small sample sizes.

Wheeler, J. T.↗
NASA NTRS1976

Numerical comparison of discrete Kalman filter algorithms - Orbit determination case study

Numerical characteristics of various Kalman filter algorithms are illustrated with a realistic orbit determination study. The case study of this paper highlights the numerical deficiencies of the conventional and stabilized Kalman algorithms. Computational errors associated with these algorithms are found to be so large as to obscure important mismodeling effects and thus cause misleading estimates of filter accuracy. The positive result of this study is that the U-D covariance factorization algorithm has excellent numerical properties and is computationally efficient, having CPU costs that differ negligibly from the conventional Kalman costs. Accuracies of the U-D filter using single precision arithmetic consistently match the double precision reference results. Numerical stability of the U-D filter is further demonstrated by its insensitivity to variations in the a priori statistics.

Bierman, G. J.↗
NASA NTRS1988

Benchmark solutions for the galactic ion transport equations with spatial and energy coupling

In order to anticipate future space shielding requirements, NASA has initiated an effort to formulate computational methods to simulate radiation effects in space. As part of the program, numerical transport algorithms have been developed for the deterministic Boltzman equation describing galactic cosmic ray (GCR) interactions with matter. It thus becomes necessary to assess the accuracy of proposed deterministic algorithms. For this reason, analytical benchmark solutions to mathematically tractable galactic cosmic ray equations have recently been obtained. Even though these problems involve simplifying assumptions of the associated physics, they still contain the essential features of the basic transport processes. The solutions obtained are features of the basic transport processes. The solutions obtained are compared to results from numerical algorithms in order to ensure proper coding and to provide a measure of the accuracy of the numerical methods used in the algorithm. For the first time, mathematical methods have been applied to the galactic ion transport (GIT) equations in the straight ahead approximation with constant nuclear properties. The approach utilizes a Laplace transforms inversion yielding a closed form benchmark solution which is also computationally efficient.

Ganapol, Barry D.↗
NASA NTRS1973

Use of Polarization Lidar for Investigation of Meteorological Formations

This paper presents the results of theoretical and experimental, investigations of depolarization characteristics of different meteorological formations. Experimental investigations are carried out with a monostatic lidar. The ruby laser radiation is polarized in a vertical plane. The radiation reflected is accepted by a lens system of 150 rom in diameter and a viewing angle of 12' and further it is divided by Wollaston prism into the components polarized orthogonally. In this case the principal plane of the prism is exposed parallel with the laser polarization plane. Investigations show the degree of radiation polarization, reflected from water clouds, to be changed within 1/0.7 (seldom up to 0.6) depending on their density. In most cases a signal reflected from the cloud leading edge is polarized completely. The time shift is observed between polarized and crosspolarized components of a Fignal, reflected from a cloud, depending on the density of a meteorological object. While penetrating into the cloud depth a degree of polarization decreases up to 0.8-0.7, and the character of this decrease is different for various types of clouds. For crystal clouds the shift between the components of the reflected signal is not observed and the magnitude of polarization degree amounts to 0.1/0.3 in comparison with water clouds. The polarization degree of radiation reflected by fog is not less than 0.6, and that in the rains of average intensity (about 5 mm/h) is always about 1. The authors have suggested an algorithm of numerical solution of nonstationary transfer equation in the vector form to forecast the influence of multiple scattering effects on polarization characteristics of the lidar light signal. The method of statistical simulation (Monte-Carlo technique) forms the basis of the algorithm. Numerical estimates obtained for a model of stratocumulus at lambda = 0.6943 microns under boundary conditions close to the conditions of natural experiment being discussed proved to be in a good agreement with the results of observation. Specifically, Fig. 1 shows the profiles of polarization (p) versus depth (L) of the following drop formations: fog (curve 1) with horizontal meteorological visibility of 4 km two stratocumulus at a height of 1100 m with the attenuation factors delta = 0.01m(exp -1) (curve 2) and delta = 0.05m(exp -1) (curve 3). Curve 3 shows the results of numerical estimates and the value of their statistical error.

Balin, Yu. S.↗
NASA NTRS1995

Numerical magetohydrodynamics in astronphysics: Algorithm and tests for one-dimensional flow`

We describe a numerical code to solve the equations for ideal magnetohydrodynamics (MHD). It is based on an explicit finite difference scheme on an Eulerian grid, called the total variation diminishing (TVD) scheme, which is a second-order-accurate extension of the Roe-type upwind scheme. We also describe a non-linear Riemann solver for ideal MHD, which includes rarefractions as well as shocks. The numerical code and the Riemann solver have been used to test each other. Extensive tests encompassing all the possible ideal MHD structures with planar symmetries (i.e., one-dimensional flows) are presented. These include those for which the field structure is two dimensional (i.e., those flows often called '1 + 1/2 dimensional') as well as those for which the magnetic field plane rotates (i.e., those flows often called '1 + 1/2 + 1/2 dimensional'). Results indicate that the code can resolve strong fast, slow, and magnetosonic shocks within two to four cells, but more cells are required if shocks become weak. With proper steepening, we could resolve rotational discontinuities within three to five cells. However, without successful implementation of steepening, contact discontinuities are resolved with approximately 10 cells and tangential discountinuities are resolved with approximately 15 cells. Out tests confirm that slow compound structures with tow-dimensional magnetic fields are composed of intermediate shocks (so-called 2-4 intermediate shocks) followed by slow rarefaction waves. Finally, tests demostrate that in two-dimensional magnetohydrodynamics, fast compound structures, which are composed of intermediate shocks (so-called 1-3 intermediate shocks) preceeded by fast rarefaction waves, are also possible.

Ryu, Dongsu↗
NASA NTRS1990

Numerical Models For Control Of Robots

Algorithm develops numerical models of kinematics of robots for use in directing movements of robots. Based on empirical data. Predicts movements from previous measurements of actual movements. Replaces analytical or iterative models used commonly.

Waggener, Mary S.↗
NASA NTRS1991

Three-dimensional incompressible Navier-Stokes solver using lower-upper symmetric-Gauss-Seidel algorithm

A numerical method based on the pseudocompressibility concept is developed for solving the three-dimensional incompressible Navier-Stokes equations using the lower-upper symmetric-Gauss-Seidel implicit scheme. Very high efficiency is achieved in a new flow solver, INS3D-LU code, by accomplishing the complete vectorizability of the algorithm on oblique planes of sweep in three dimensions.

Yoon, Seokkwan↗
NASA NTRS1989

Three-dimensional simulation of underexpanded plumes using upwind algorithms

Different numerical techniques have been examined for simulating the underexpanded plumes in supersonic flows. The results revealed that the monotone differentiable limiter is superior to the TVD (total variation diminishing) minmod limiter when the MUSCL (monotonic upstream schemes for conservation laws) approach is used for Roe's upwind scheme. Roe's upwind scheme is found to be superior to the central difference scheme not only for capturing shock waves, but also for capturing shear flows.

Obayashi, Shigeru↗
NASA NTRS1987

An Adaptive Numeric Predictor-corrector Guidance Algorithm for Atmospheric Entry Vehicles

An adaptive numeric predictor-corrector guidance is developed for atmospheric entry vehicles which utilize lift to achieve maximum footprint capability. Applicability of the guidance design to vehicles with a wide range of performance capabilities is desired so as to reduce the need for algorithm redesign with each new vehicle. Adaptability is desired to minimize mission-specific analysis and planning. The guidance algorithm motivation and design are presented. Performance is assessed for application of the algorithm to the NASA Entry Research Vehicle (ERV). The dispersions the guidance must be designed to handle are presented. The achievable operational footprint for expected worst-case dispersions is presented. The algorithm performs excellently for the expected dispersions and captures most of the achievable footprint.

Spratlin, Kenneth Milton↗
NASA NTRS2010

Faster and More Accurate Transport Procedures for HZETRN

Several aspects of code verification are examined for HZETRN. First, a detailed derivation of the numerical marching algorithms is given. Next, a new numerical method for light particle transport is presented, and improvements to the heavy ion transport algorithm are discussed. A summary of various coding errors is also given, and the impact of these errors on exposure quantities is shown. Finally, a coupled convergence study is conducted. From this study, it is shown that past efforts in quantifying the numerical error in HZETRN were hindered by single precision calculations and computational resources. It is also determined that almost all of the discretization error in HZETRN is caused by charged target fragments below 50 AMeV. Total discretization errors are given for the old and new algorithms, and the improved accuracy of the new numerical methods is demonstrated. Run time comparisons are given for three applications in which HZETRN is commonly used. The new algorithms are found to be almost 100 times faster for solar particle event simulations and almost 10 times faster for galactic cosmic ray simulations.

Slaba, Tony C.↗
DOE OSTI2026

Computing an Optimal Entanglement Path with Throughput and Fidelity Considerations

Entanglement distribution is a core function of quantum networks essential for operations including teleportation, distributed quantum sensing, and multisite computation. Entanglement throughput and fidelity are two critical performance measures that depend on the quantum transmission along the links and swapping operations at the repeaters along the path. We study the problem of computing a end-to-end entanglement path that satisfies both fidelity and throughput requirements, leveraging qubit buffers at the nodes and considering the sequential swapping order. We show that the general problem of simultaneously satisfying both metrics to be NP-hard, and develop an algorithm to maximize throughput subject to a given fidelity threshold. We introduce the concepts of entanglement probability distribution and path domination and exploit them in the design of our algorithm. Extensive numerical results show that our algorithm can find optimal solutions in networks with thousands of nodes in less than a second. We also describe practical and possible implementation aspects of this algorithm in terms of devices and architecture support.

Xue, Guoliang [Arizona State University]↗
NASA NTRS1992

Comparison Of Two Viscous-Flow Computer Codes

Two viscous-flow computer codes compared by applying them to five test cases of steady-state transonic viscous flows about transonic airfoils. Two codes were: FLOMG, which solves Navier-Stokes differential equations of flow by implementing explicit, Runge-Kutta, finite-volume, multigrid numerical-integration algorithm; and ARC2D, which implements implicit, finite-difference, approximate-factorization, eigenvector-diagonalization numerical-integration algorithm.

Maksymiuk, C. M.↗
NASA NTRS2017

Application of a Fully Numerical Guidance to Mars Aerocapture

An advanced guidance algorithm, Fully Numerical Predictor-corrector Aerocapture Guidance (FNPAG), has been developed to perform aerocapture maneuvers in an optimal manner. It is a model-based, numerical guidance that benefits from requiring few adjustments across a variety of different hypersonic vehicle lift-to-drag ratios, ballistic co-efficients, and atmospheric entry conditions. In this paper, FNPAG is first applied to the Mars Rigid Vehicle (MRV) mid lift-to-drag ratio concept. Then the study is generalized to a design map of potential Mars aerocapture missions and vehicles, ranging from the scale and requirements of recent robotic to potential human and precursor missions. The design map results show the versatility of FNPAG and provide insight for the design of Mars aerocapture vehicles and atmospheric entry conditions to achieve desired performance.

Matz, Daniel A.↗