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All sourcesNASA NTRSDOE OSTI
NASA NTRS1989

Applications of algebraic image operators to model-based vision

A highly structured and compact algebraic representation of grey-level images is expanded. Addition and multiplication are defined for the set of all grey-level images, which can then be described as polynomials of two variables. Utilizing this new algebraic structure, an innovative, efficient edge-detection scheme is devised. A robust method for linear feature extraction is developed by combining the techniques of a Hough transform and a line follower with this new edge detection scheme. The major advantage of this feature extractor is its general, object-independent nature. Target attributes, such as line segment lengths, intersections, angles of intersection, and endpoints are derived by the feature extraction algorithm and employed during model matching. The feature extractor and model matcher are being incorporated into a distributed robot-control system.

Lerner, Bao-Ting↗
NASA NTRS1991

A second order iteration procedure for correlation of analysis frequencies with test data

A second derivative frequency modification procedure is developed to iteratively change analysis modeling parameters for the more rapid convergence of analytically determined frequencies to those obtained by structural dynamic testing. A nonlinear system of algebraic equations in the modeling parameters is derived and a rapidly converging iterative method for their solution is presented. Numerical results obtained show that the higher order formulation and nonlinear predictor-corrector solution procedure yields results which are more rapidly convergent than those obtained using only the usual linear first-order parameter modification procedure. The proposed higher order theory also connverges in some cases when the ordinary linear theory does not.

Ojalvo, I. U.↗
NASA NTRS1993

An automatic multigrid method for the solution of sparse linear systems

An automatic version of the multigrid method for the solution of linear systems arising from the discretization of elliptic PDE's is presented. This version is based on the structure of the algebraic system solely, and does not use the original partial differential operator. Numerical experiments show that for the Poisson equation the rate of convergence of our method is equal to that of classical multigrid methods. Moreover, the method is robust in the sense that its high rate of convergence is conserved for other classes of problems: non-symmetric, hyperbolic (even with closed characteristics) and problems on non-uniform grids. No double discretization or special treatment of sub-domains (e.g. boundaries) is needed. When supplemented with a vector extrapolation method, high rates of convergence are achieved also for anisotropic and discontinuous problems and also for indefinite Helmholtz equations. A new double discretization strategy is proposed for finite and spectral element schemes and is found better than known strategies.

Shapira, Yair↗
NASA NTRS1997

Complementary Reliability-Based Decodings of Binary Linear Block Codes

This correspondence presents a hybrid reliability-based decoding algorithm which combines the reprocessing method based on the most reliable basis and a generalized Chase-type algebraic decoder based on the least reliable positions. It is shown that reprocessing with a simple additional algebraic decoding effort achieves significant coding gain. For long codes, the order of reprocessing required to achieve asymptotic optimum error performance is reduced by approximately 1/3. This significantly reduces the computational complexity, especially for long codes. Also, a more efficient criterion for stopping the decoding process is derived based on the knowledge of the algebraic decoding solution.

Fossorier, Marc P. C.↗
NASA NTRS1999

A Method to Solve Interior and Exterior Camera Calibration Parameters for Image Resection

An iterative method is presented to solve the internal and external camera calibration parameters, given model target points and their images from one or more camera locations. The direct linear transform formulation was used to obtain a guess for the iterative method, and herein lies one of the strengths of the present method. In all test cases, the method converged to the correct solution. In general, an overdetermined system of nonlinear equations is solved in the least-squares sense. The iterative method presented is based on Newton-Raphson for solving systems of nonlinear algebraic equations. The Jacobian is analytically derived and the pseudo-inverse of the Jacobian is obtained by singular value decomposition.

Samtaney, Ravi↗
NASA NTRS1983

Application of the implicit MacCormack scheme to the PNS equations

The two-dimensional parabolized Navier-Stokes equations are solved using MacCormack's (1981) implicit finite-difference scheme. It is shown that this method for solving the parabolized Navier-Stokes equations does not require the inversion of block tridiagonal systems of algebraic equations and allows the original explicit scheme to be employed in those regions where implicit treatment is not needed. The finite-difference algorithm is discussed and the computational results for two laminar test cases are presented. Results obtained using this method for the case of a flat plate boundary layer are compared with those obtained using the conventional Beam-Warming scheme, as well as those obtained from a boundary layer code. The computed results for a more severe test of the method, the hypersonic flow past a 15 deg compression corner, are found to compare favorably with experiment and a numerical solution of the complete Navier-Stokes equations.

Lawrence, S. L.↗
NASA NTRS1993

Development of computational methods for heavy lift launch vehicles

The research effort has been focused on the development of an advanced flow solver for complex viscous turbulent flows with shock waves. The three-dimensional Euler and full/thin-layer Reynolds-averaged Navier-Stokes equations for compressible flows are solved on structured hexahedral grids. The Baldwin-Lomax algebraic turbulence model is used for closure. The space discretization is based on a cell-centered finite-volume method augmented by a variety of numerical dissipation models with optional total variation diminishing limiters. The governing equations are integrated in time by an implicit method based on lower-upper factorization and symmetric Gauss-Seidel relaxation. The algorithm is vectorized on diagonal planes of sweep using two-dimensional indices in three dimensions. A new computer program named CENS3D has been developed for viscous turbulent flows with discontinuities. Details of the code are described in Appendix A and Appendix B. With the developments of the numerical algorithm and dissipation model, the simulation of three-dimensional viscous compressible flows has become more efficient and accurate. The results of the research are expected to yield a direct impact on the design process of future liquid fueled launch systems.

Yoon, Seokkwan↗
NASA NTRS1993

Application of symbolic and algebraic manipulation software in solving applied mechanics problems

As its name implies, symbolic and algebraic manipulation is an operational tool which not only can retain symbols throughout computations but also can express results in terms of symbols. This report starts with a history of symbolic and algebraic manipulators and a review of the literatures. With the help of selected examples, the capabilities of symbolic and algebraic manipulators are demonstrated. These applications to problems of applied mechanics are then presented. They are the application of automatic formulation to applied mechanics problems, application to a materially nonlinear problem (rigid-plastic ring compression) by finite element method (FEM) and application to plate problems by FEM. The advantages and difficulties, contributions, education, and perspectives of symbolic and algebraic manipulation are discussed. It is well known that there exist some fundamental difficulties in symbolic and algebraic manipulation, such as internal swelling and mathematical limitation. A remedy for these difficulties is proposed, and the three applications mentioned are solved successfully. For example, the closed from solution of stiffness matrix of four-node isoparametrical quadrilateral element for 2-D elasticity problem was not available before. Due to the work presented, the automatic construction of it becomes feasible. In addition, a new advantage of the application of symbolic and algebraic manipulation found is believed to be crucial in improving the efficiency of program execution in the future. This will substantially shorten the response time of a system. It is very significant for certain systems, such as missile and high speed aircraft systems, in which time plays an important role.

Tsai, Wen-Lang↗
NASA NTRS1984

Advanced reliability method for fatigue analysis

When design factors are considered as random variables and the failure condition cannot be expressed by a closed form algebraic inequality, computations of risk (or probability of failure) may become extremely difficult or very inefficient. This study suggests using a simple and easily constructed second degree polynomial to approximate the complicated limit state in the neighborhood of the design point; a computer analysis relates the design variables at selected points. Then a fast probability integration technique (i.e., the Rackwitz-Fiessler algorithm) can be used to estimate risk. The capability of the proposed method is demonstrated in an example of a low cycle fatigue problem for which a computer analysis is required to perform local strain analysis to relate the design variables. A comparison of the performance of this method is made with a far more costly Monte Carlo solution. Agreement of the proposed method with Monte Carlo is considered to be good.

Wu, Y.-T.↗
NASA NTRS1984

Comparison of numerical techniques for integration of stiff ordinary differential equations arising in combustion chemistry

The efficiency and accuracy of several algorithms recently developed for the efficient numerical integration of stiff ordinary differential equations are compared. The methods examined include two general-purpose codes, EPISODE and LSODE, and three codes (CHEMEQ, CREK1D, and GCKP84) developed specifically to integrate chemical kinetic rate equations. The codes are applied to two test problems drawn from combustion kinetics. The comparisons show that LSODE is the fastest code currently available for the integration of combustion kinetic rate equations. An important finding is that an interactive solution of the algebraic energy conservation equation to compute the temperature does not result in significant errors. In addition, this method is more efficient than evaluating the temperature by integrating its time derivative. Significant reductions in computational work are realized by updating the rate constants (k = at(supra N) N exp(-E/RT) only when the temperature change exceeds an amount delta T that is problem dependent. An approximate expression for the automatic evaluation of delta T is derived and is shown to result in increased efficiency.

Radhakrishnan, K.↗
NASA NTRS2001

A Hybrid Numerical Method for Turbulent Mixing Layers

A hybrid method has been developed for simulations of compressible turbulent mixing layers. Such mixing layers dominate the flows in exhaust systems of modern day aircraft and also those of hypersonic vehicles currently under development. The method configurations in which a dominant structural feature provides an unsteady mechanism to drive the turbulent development in the mixing layer. The hybrid method uses a Reynolds-averaged Navier-Stokes (RANS) procedure to calculate wall bounded regions entering a mixing section, and a Large Eddy Simulation (LES) procedure to calculate the mixing dominated regions. A numerical technique was developed to enable the use of the hybrid RANS-LES method on stretched, non-Cartesian grids. Closure for the RANS equations was obtained using the Cebeci-Smith algebraic turbulence model in conjunction with the wall-function approach of Ota and Goldberg. The wall-function approach enabled a continuous computational grid from the RANS regions to the LES region. The LES equations were closed using the Smagorinsky subgrid scale model. The hybrid RANS-LES method is applied to a benchmark compressible mixing layer experiment. Preliminary two dimensional calculations are used to investigate the effects of axial grid density and boundary conditions. Vortex shedding from the base region of a splitter plate separating the upstream flows was observed to eventually transition to turbulence. The location of the transition, however, was much further downstream than indicated by experiments. Actual LES calculations, performed in three spatial directions, also indicated vortex shedding, but the transition to turbulence was found to occur much closer to the beginning of the mixing section. which is in agreement with experimental observations. These calculations demonstrated that LES simulations must be performed in three dimensions. Comparisons of time-averaged axial velocities and turbulence intensities indicated reasonable agreement with experimental data.

Georgiadis, Nicholas J.↗
NASA NTRS1975

Computation of separated transonic turbulent flows

The two-dimensional Reynolds-averaged compressible Navier-Stokes equations are solved using MacCormack's second-order-accurate explicit finite difference method to simulate the separated transonic turbulent flow field over an airfoil. Four different algebraic eddy viscosity models are tested for viability to achieve turbulence closure for the class of flows considered. These models range from an unmodified boundary-layer mixing-length model to a relaxation model incorporating special considerations for the separation bubble region. Results of this study indicate the necessity for special attention to the separated flow region and suggest limits of applicability of algebraic turbulence models to these separated flow fields.

Deiwert, G. S.↗
NASA NTRS1982

Subsonic 3-D surface panel method for rapid analysis of multiple geometry perturbations

For any baseline aircraft configuration, a matrix of partial derivatives of surface velocity potential with respect to geometry coordinates is calculated. Linear extrapolation is then used to analyze the subcritical potential flow corresponding to a series of arbitrary small geometry perturbations. Each perturbation analysis is more than an order of magnitude more efficient than a conventional panel method solution because no influence coefficients are calculated and no large system of linear algebraic equations is solved. Wing and wing-fuselage examples are presented to demonstrate that the predicted pressure distributions are nearly exact for large changes to wing camber, thickness, and leading edge radius.

Bristow, D. R.↗
NASA NTRS1984

Analytical characterization of AOTV perigee aerothermodynamic regime

In preliminary design studies of AOTV (Aeroassisted Orbital Transfer Vehicle) configurations, it is desirable to have a simple analytical method for characterizing the aerothermodynamic regime at skip trajectory perigee as a function of vehicle L/D and m/CDA (ballistic coefficient). The present study derives an approximate perigee solution from the generalized equations of motion. For a prescribed entry velocity vector, the solution determines a Zeta function (proportional to density divided by m/CDA) at perigee as a parametric function of the exit velocity vector and (constant) L/D. The perigee Zeta function then determines perigee density (or altitude) as a parametric function of m/CDA. The solution allows the following classic aerothermodynamic parameters to be determined at perigee as parametric functions of m/CDA, L/D, and the exit velocity vector: Reynolds Number (viscous effects), Mach Number (compressibility effects), Knudsen Number (rarefaction effects), sphere and disk bow shock standoff distance, Damkohler Number (relaxation effects), viscous correlation parameter (viscid-inviscid interactions), and Stanton Number (convective heat transfer). Results of the analysis are given for low L/D and mid L/D AOTV configurations on return from geosynchronous and L5 orbits. It is concluded the method successfully provides preliminary estimates of the aerothermodynamic parameters through the use of simple algebraic equations and plots.

Desautel, D.↗
NASA NTRS1986

Analysis of Scramjet Inlets

NASCRIN analyzes two-dimensional flow fields in supersonic combustion ramjet (scramjet) inlets. Solves two-dimensional Euler or Navier-Strokes equations in conservative form by unsplit, explicit, two-step finitedifference method. More recent explicit/implicit, two-step scheme also incorporated for viscous flow analysis. Algebraic, two-layer eddy-viscosity model used for turbulent flow calculations.

Kumar, A.↗
NASA NTRS1985

On the electromagnetic scattering from infinite rectangular conducting grids

The study and development of two numerical techniques for the analysis of electromagnetic scattering from a rectangular wire mesh are described. Both techniques follow from one basic formulation and they are both solved in the spectral domain. These techniques were developed as a result of an investigation towards more efficient numerical computation for mesh scattering. These techniques are efficient for the following reasons: (a1) make use of the Fast Fourier Transform; (b2) they avoid any convolution problems by converting integrodifferential equations into algebraic equations; and (c3) they do not require inversions of any matrices. The first method, the SIT or Spectral Iteration Technique, is applied for regions where the spacing between wires is not less than two wavelengths. The second method, the SDCG or Spectral Domain Conjugate Gradient approach, can be used for any spacing between adjacent wires. A study of electromagnetic wave properties, such as reflection coefficient, induced currents and aperture fields, as functions of frequency, angle of incidence, polarization and thickness of wires is presented. Examples and comparisons or results with other methods are also included to support the validity of the new algorithms.

Christodoulou, C.↗