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All sourcesNASA NTRSDOE OSTI
NASA NTRS1984

Computation of three-dimensional viscous flows using a space-marching method

A space-marching method, developed to compute three-dimensional flows for internal geometries, has been utilized to predict viscous flows through a curved duct and over a swept wing. The Navier-Stokes equations have been posed as an initial value problem by neglecting the streamwise viscous diffusion terms and by treating the pressure gradient as a known source term. The resulting equations have been solved by a non-iterative (single pass) algorithm at each streamwise step. The results are compared with earlier computations (based on iterative methods) and the experimental data. The agreement between the present predictions, the experimental data, and the earlier predictions is good for the cases computed. The computation time is only a fraction of the iterative methods.

Murthy, K. N. S.↗
NASA NTRS2005

Computation of Sound Propagation by Boundary Element Method

This report documents the development of a Boundary Element Method (BEM) code for the computation of sound propagation in uniform mean flows. The basic formulation and implementation follow the standard BEM methodology; the convective wave equation and the boundary conditions on the surfaces of the bodies in the flow are formulated into an integral equation and the method of collocation is used to discretize this equation into a matrix equation to be solved numerically. New features discussed here include the formulation of the additional terms due to the effects of the mean flow and the treatment of the numerical singularities in the implementation by the method of collocation. The effects of mean flows introduce terms in the integral equation that contain the gradients of the unknown, which is undesirable if the gradients are treated as additional unknowns, greatly increasing the sizes of the matrix equation, or if numerical differentiation is used to approximate the gradients, introducing numerical error in the computation. It is shown that these terms can be reformulated in terms of the unknown itself, making the integral equation very similar to the case without mean flows and simple for numerical implementation. To avoid asymptotic analysis in the treatment of numerical singularities in the method of collocation, as is conventionally done, we perform the surface integrations in the integral equation by using sub-triangles so that the field point never coincide with the evaluation points on the surfaces. This simplifies the formulation and greatly facilitates the implementation. To validate the method and the code, three canonic problems are studied. They are respectively the sound scattering by a sphere, the sound reflection by a plate in uniform mean flows and the sound propagation over a hump of irregular shape in uniform flows. The first two have analytical solutions and the third is solved by the method of Computational Aeroacoustics (CAA), all of which are used to compare the BEM solutions. The comparisons show very good agreements and validate the accuracy of the BEM approach implemented here.

Guo, Yueping↗
NASA NTRS1972

Optimization of a two stage light gas gun

Performance characteristics of the Texas A&M University light gas gun are presented along with a review of basic gun theory and popular prediction methods. A computer routine based on the simple isentropic compression method is discussed. Results from over 60 test shots are given which demonstrate an increase in gun muzzle velocity from 9.100 ft/sec. to 19,000 ft/sec. The data gathered indicated the Texas A&M light gas gun more closely resembles an isentropic compression gun rather than a shock compression gun.

Rynearson, R. J.↗
NASA NTRS1972

Simulation, Manual and Computerized (SMAC)

The guiding concept was to develop a simulation modeling method which can be quickly taught and learned, yet can be used to solve significant real world problems. SMAC consists of two manual simulation methods and one computer program. One of the manual methods is designed to impart an understanding of simulation; the other is designed to be a practical simulation method. The computer program will simulate queueing situations with up to five parallel servers or up to three series servers. The program is built around GASP 2A routines and retains the 8K capability of GASP.

Parker, M. W.↗
NASA NTRS1977

Methods of shield analysis for protection against electrons in space

It is anticipated that many future manned space operations will be radiation limited and that laminated wall structures and the use of new materials will be required to reduce radiation exposure. Methods for electron shield analysis are reviewed in light of anticipated needs in the space program. The most general method is still the Monte Carlo method, which is of limited usefulness for shield analysis due to excessive computer requirements. Methods based on energy deposition coefficients or energy transmission and reflection factors are quite accurate, but are currently limited to aluminum shield material. Analytical methods based on Mar's approximation for the electron transmission factor are relatively general and computer efficient but seriously underestimate shield requirements. A correction to methods using Mar's approximate transmission factor is derived herein and results in a slightly conservative estimate of shield requirements. Techniques for laminated shield design are still lacking.

Wilson, J. W.↗
NASA NTRS1987

Estimation of geopotential from satellite-to-satellite range rate data: Numerical results

A technique for high-resolution geopotential field estimation by recovering the harmonic coefficients from satellite-to-satellite range rate data is presented and tested against both a controlled analytical simulation of a one-day satellite mission (maximum degree and order 8) and then against a Cowell method simulation of a 32-day mission (maximum degree and order 180). Innovations include: (1) a new frequency-domain observation equation based on kinetic energy perturbations which avoids much of the complication of the usual Keplerian element perturbation approaches; (2) a new method for computing the normalized inclination functions which unlike previous methods is both efficient and numerically stable even for large harmonic degrees and orders; (3) the application of a mass storage FFT to the entire mission range rate history; (4) the exploitation of newly discovered symmetries in the block diagonal observation matrix which reduce each block to the product of (a) a real diagonal matrix factor, (b) a real trapezoidal factor with half the number of rows as before, and (c) a complex diagonal factor; (5) a block-by-block least-squares solution of the observation equation by means of a custom-designed Givens orthogonal rotation method which is both numerically stable and tailored to the trapezoidal matrix structure for fast execution.

Thobe, Glenn E.↗
NASA NTRS1988

A global-local finite element method suitable for parallel computations

A global-local finite element analysis procedure is developed based on the fast convergent nature of FEM in displacement. A special scheme is used to utilize the global displacement solution as boundary conditions for local regions of interest. In the local region, a refined mesh is used for further stress analysis. This global-local procedure can be easily programmed in parallel on MIMD multi-processor computers for significant time savings. A Sequent Balance 21000 system is used for demonstrating the parallel programming.

Sun, C. T.↗
NASA NTRS1989

NASA Computational Fluid Dynamics Conference. Volume 1: Sessions 1-6

This publication is a collection of the presentations given at the NASA Computational Fluid Dynamics (CFD) Conference held at NASA Ames Research Center, Moffett Field, California, March 7-9, 1989. The objectives of the conference were to disseminate CFD research results to industry and university CFD researchers, to promote synergy among NASA CFD researchers, and to permit feedback from researchers outside of NASA on issues pacing the discipline of CFD. The focus of the conference was on the application of CFD technology but also included fundamental activities. The conference was sponsored by the Aerodynamics Division, Office of Aeronautics and Space Technology (OAST), NASA Headquarters, Washington, D.C. 20546. The conference consisted of twelve sessions of papers representative of CFD research conducted within NASA and three non-NASA panel sessions. For each panel session, the panel membership consisted of industry and university CFD researchers. A summary of the comments made during the panel sessions has been included in this publication. Volume 1 contains the papers given in Sessions I-VT. Volume 2 covers Sessions VII-XII.

Computational fluid dynamics↗
NASA NTRS1991

Computation of turbulent flow in a thin liquid layer of fluid involving a hydraulic jump

Numerically computed flow fields and free surface height distributions are presented for the flow of a thin layer of liquid adjacent to a solid horizontal surface that encounters a hydraulic jump. Two kinds of flow configurations are considered: two-dimensional plane flow and axisymmetric radial flow. The computations used a boundary-fitted moving grid method with a k-epsilon model for the closure of turbulence. The free surface height was determined by an optimization procedure which minimized the error in the pressure distribution on the free surface. It was also checked against an approximate procedure involving integration of the governing equations and use of the MacCormack predictor-corrector method. The computed film height also compared reasonably well with previous experiments. A region of recirculating flow was found to be present adjacent to the solid boundary near the location of the jump, which was caused by a rapid deceleration of the flow.

Rahman, M. M.↗
NASA NTRS1992

Consensus theoretic classification methods

Consensus theory is adopted as a means of classifying geographic data from multiple sources. The foundations and usefulness of different consensus theoretic methods are discussed in conjunction with pattern recognition. Weight selections for different data sources are considered and modeling of non-Gaussian data is investigated. The application of consensus theory in pattern recognition is tested on two data sets: 1) multisource remote sensing and geographic data and 2) very-high-dimensional remote sensing data. The results obtained using consensus theoretic methods are found to compare favorably with those obtained using well-known pattern recognition methods. The consensus theoretic methods can be applied in cases where the Gaussian maximum likelihood method cannot. Also, the consensus theoretic methods are computationally less demanding than the Gaussian maximum likelihood method and provide a means for weighting data sources differently.

Benediktsson, Jon A.↗
NASA NTRS1993

Analysis of multigrid methods on massively parallel computers: Architectural implications

We study the potential performance of multigrid algorithms running on massively parallel computers with the intent of discovering whether presently envisioned machines will provide an efficient platform for such algorithms. We consider the domain parallel version of the standard V cycle algorithm on model problems, discretized using finite difference techniques in two and three dimensions on block structured grids of size 10(exp 6) and 10(exp 9), respectively. Our models of parallel computation were developed to reflect the computing characteristics of the current generation of massively parallel multicomputers. These models are based on an interconnection network of 256 to 16,384 message passing, 'workstation size' processors executing in an SPMD mode. The first model accomplishes interprocessor communications through a multistage permutation network. The communication cost is a logarithmic function which is similar to the costs in a variety of different topologies. The second model allows single stage communication costs only. Both models were designed with information provided by machine developers and utilize implementation derived parameters. With the medium grain parallelism of the current generation and the high fixed cost of an interprocessor communication, our analysis suggests an efficient implementation requires the machine to support the efficient transmission of long messages, (up to 1000 words) or the high initiation cost of a communication must be significantly reduced through an alternative optimization technique. Furthermore, with variable length message capability, our analysis suggests the low diameter multistage networks provide little or no advantage over a simple single stage communications network.

Matheson, Lesley R.↗
NASA NTRS1993

Formal methods and digital systems validation for airborne systems

This report has been prepared to supplement a forthcoming chapter on formal methods in the FAA Digital Systems Validation Handbook. Its purpose is as follows: to outline the technical basis for formal methods in computer science; to explain the use of formal methods in the specification and verification of software and hardware requirements, designs, and implementations; to identify the benefits, weaknesses, and difficulties in applying these methods to digital systems used on board aircraft; and to suggest factors for consideration when formal methods are offered in support of certification. These latter factors assume the context for software development and assurance described in RTCA document DO-178B, 'Software Considerations in Airborne Systems and Equipment Certification,' Dec. 1992.

Rushby, John↗
NASA NTRS1997

Optimizing an Actuator Array for the Control of Multi-Frequency Noise in Aircraft Interiors

Techniques developed for selecting an optimized actuator array for interior noise reduction at a single frequency are extended to the multi-frequency case. Transfer functions for 64 actuators were obtained at 5 frequencies from ground testing the rear section of a fully trimmed DC-9 fuselage. A single loudspeaker facing the left side of the aircraft was the primary source. A combinatorial search procedure (tabu search) was employed to find optimum actuator subsets of from 2 to 16 actuators. Noise reduction predictions derived from the transfer functions were used as a basis for evaluating actuator subsets during optimization. Results indicate that it is necessary to constrain actuator forces during optimization. Unconstrained optimizations selected actuators which require unrealistically large forces. Two methods of constraint are evaluated. It is shown that a fast, but approximate, method yields results equivalent to an accurate, but computationally expensive, method.

Palumbo, D. L.↗
NASA NTRS2000

Transonic Flow Computations Using Nonlinear Potential Methods

This presentation describes the state of transonic flow simulation using nonlinear potential methods for external aerodynamic applications. The presentation begins with a review of the various potential equation forms (with emphasis on the full potential equation) and includes a discussion of pertinent mathematical characteristics and all derivation assumptions. Impact of the derivation assumptions on simulation accuracy, especially with respect to shock wave capture, is discussed. Key characteristics of all numerical algorithm types used for solving nonlinear potential equations, including steady, unsteady, space marching, and design methods, are described. Both spatial discretization and iteration scheme characteristics are examined. Numerical results for various aerodynamic applications are included throughout the presentation to highlight key discussion points. The presentation ends with concluding remarks and recommendations for future work. Overall. nonlinear potential solvers are efficient, highly developed and routinely used in the aerodynamic design environment for cruise conditions. Published by Elsevier Science Ltd. All rights reserved.

Holst, Terry L.↗
NASA NTRS2003

Mass Polarization Effect in He-like Ions: First and Second Order

In a paper with a similar title Yamanaka has calculated the mass polarization effect (to first order in mu/M for several low-lying states of the two-electron atoms and ions with atomic number Z from 2 to 10. Here we improve the previous results by using Hylleraas variational wave functions with up to 560 terms and extend the calculation to include some additional states and the Z=1ground state. In addition, we compute the second-order effect using the method of pseudostate summation. In one appendix another method of computation is discussed and used as a check, while the energies of the Z=1 ions are presented and discussed in a second appendix.

Bhatia, A. K.↗