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NASA NTRS1985

CAG12 - A CSCM based procedure for flow of an equilibrium chemically reacting gas

The Conservative Supra Characteristic Method (CSCM), an implicit upwind Navier-Stokes algorithm, is extended to the numerical simulation of flows in chemical equilibrium. The resulting computer code known as Chemistry and Gasdynamics Implicit - Version 2 (CAG12) is described. First-order accurate results are presented for inviscid and viscous Mach 20 flows of air past a hemisphere-cylinder. The solution procedure captures the bow shock in a chemically reacting gas, a technique that is needed for simulating high altitude, rarefied flows. In an initial effort to validate the code, the inviscid results are compared with published gasdynamic and chemistry solutions and satisfactorily agreement is obtained.

Green, M. J.↗

NASA NTRS1985

Theoretical and experimental comparison of vapor cavitation in dynamically loaded journal bearings

Vapor cavitation for a submerged journal bearing under dynamically loaded conditions was investigated. The observation of vapor cavitation in the laboratory was done by high-speed photography. It was found that vapor cavitation occurs when the tensile stress applied to the oil exceeded the tensile strength of the oil or the binding of the oil to the surface. The theoretical solution to the Reynolds equation is determined numerically using a moving boundary algorithm. This algorithm conserves mass throughout the computational domain including the region of cavitation and its boundaries. An alternating direction implicit (MDI) method is used to effect the time march. A rotor undergoing circular whirl was studied. Predicted cavitation behavior was analyzed by three-dimensional computer graphic movies. The formation, growth, and collapse of the bubble in response to the dynamic conditions is shown. For the same conditions of dynamic loading, the cavitation bubble was studied in the laboratory using high-speed photography.

Brewe, D. E.↗

NASA NTRS1983

User's manual for a TEACH computer program for the analysis of turbulent, swirling reacting flow in a research combustor

Described is a computer program for the analysis of the subsonic, swirling, reacting turbulent flow in an axisymmetric, bluff-body research combustor. The program features an improved finite-difference procedure designed to reduce the effects of numerical diffusion and a new algorithm for predicting the pressure distribution within the combustor. A research version of the computer program described in the report was supplied to United Technologies Research Center by Professor A. D. Gosman and his students, R. Benodeker and R. I. Issa, of Imperial College, London. The Imperial College staff also supplied much of the program documentation. Presented are a description of the mathematical model for flow within an axisymmetric bluff-body combustor, the development of the finite-difference procedure used to represent the system of equations, an outline of the algorithm for determining the static pressure distribution within the combustor, a description of the computer program including its input format, and the results for representative test cases.

Chiappetta, L. M.↗

NASA NTRS1986

Novel measurement techniques (development and analysis of silicon solar cells near 20% effciency)

Work in identifying, developing, and analyzing techniques for measuring bulk recombination rates, and surface recombination velocities and rates in all regions of high-efficiency silicon solar cells is presented. The accuracy of the previously developed DC measurement system was improved by adding blocked interference filters. The system was further automated by writing software that completely samples the unkown solar cell regions with data of numerous recombination velocity and lifetime pairs. The results can be displayed in three dimensions and the best fit can be found numerically using the simplex minimization algorithm. Also described is a theoretical methodology to analyze and compare existing dynamic measurement techniques.

Wolf, M.↗

NASA NTRS1987

Lanczos modes for reduced-order control of flexible structures

Lanczos mode models represent low-frequency forced response better than do normal mode models and can be developed for both continuous and finite element structural representations. It was recommended that Lanczos mode models for systems with multiple input and/or rigid body modes should be developed; numerical stability of the Lanczos algorithm should be assessed; and control system designs employing the Lanczos mode models should be attempted.

Craig, Roy R., Jr.↗

NASA NTRS1986

Linearized form of implicit TVD schemes for the multidimensional Euler and Navier-Stokes equations

Linearized alternating direction implicit (ADI) forms of a class of total variation diminishing (TVD) schemes for the Euler and Navier-Stokes equations have been developed. These schemes are based on the second-order-accurate TVD schemes for hyperbolic conservation laws developed by Harten (1983, 1984). They have the property of not generating spurious oscillations across shocks and contact discontinuities. In general, shocks can be captured within 1-2 grid points. These schemes are relatively simple to understand and easy to implement into a new or existing computer code. One can modify a standard three-point central-difference code by simply changing the conventional numerical dissipation term into the one designed for the TVD scheme. For steady-state applications, the only difference in computation is that the current schemes require a more elaborate dissipation term for the explicit operator; no extra computation is required for the implicit operator. Numerical experiments with the proposed algorithms on a variety of steady-state airfoil problems illustrate the versatility of the schemes.

Yee, H. C.↗

NASA NTRS1987

Estimation of discontinuous coefficients in parabolic systems - Applications to reservoir simulation

Spline-based techniques for estimating spatially varying parameters that appear in parabolic distributed systems (typical of those found in reservoir simulation problems) are presented. In particular, the problem of determining discontinuous coefficients is discussed, estimating both the functional shape and points of discontinuity for such parameters. In addition, the ideas may also be applied to problems with unknown initial conditions and unknown parameters appearing in terms representing external forces. Convergence results and a summary of numerical performance of the resulting algorithms are given.

Lamm, Patricia K.↗

NASA NTRS1986

Performance comparisons on spatial lattice algorithm and direct matrix inverse method with application to adaptive arrays processing

Lattice algorithm has been employed in numerous adaptive filtering applications such as speech analysis/synthesis, noise canceling, spectral analysis, and channel equalization. In this paper the application to adaptive-array processing is discussed. The advantages are fast convergence rate as well as computational accuracy independent of the noise and interference conditions. The results produced by this technique are compared to those obtained by the direct matrix inverse method.

An, S. H.↗

NASA NTRS1986

Multigrid-sinc methods

A Galerkin method using Whittaker cardinal or 'sinc' functions as basis functions is described for the solution of boundary-value problems. When the solution is analytic in the interior of the domain, the error of approximation using 2N + 1 points is O(e exp /-gamma sq rt N/) even if derivatives of the solution are singular at the boundaries. A multigrid method with overall complexity O(N log N) is used to solve the discrete equations. This paper contains a description of the multigrid-sinc algorithm along with some preliminary numerical results for two-point boundary-value problems.

Schaffer, Steve↗

NASA NTRS1988

Single-grid spectral collocation for the Navier-Stokes equations

The aim of the paper is to study a collocation spectral method to approximate the Navier-Stokes equations: only one grid is used, which is built from the nodes of a Gauss-Lobatto quadrature formula, either of Legendre or of Chebyshev type. The convergence is proven for the Stokes problem provided with inhomogeneous Dirichlet conditions, then thoroughly analyzed for the Navier-Stokes equations. The practical implementation algorithm is presented, together with numerical results.

Bernardi, Christine↗

NASA NTRS1988

BEM for wave equation with boundary in arbitrary motion and applications to compressible potential aerodynamics of airplanes and helicopters

The wave equation for an object in arbitrary motion is investigated analytically using a BEM approach, and practical applications to potential flows of compressible fluids around aircraft wings and helicopter rotors are considered. The treatment accounts for arbitrary combined rotational and translational motion of the reference frame and for the wake motion. The numerical implementation as a computer algorithm is demonstrated on problems with prescribed and free wakes, the former in compressible flows and the latter for incompressible flows; results are presented graphically and briefly characterized.

Morino, Luigi↗

NASA NTRS1989

The design and application of upwind schemes on unstructured meshes

Solution and mesh generation algorithms for solving the Euler equations on unstructured meshes consisting of triangle and quadrilateral control volumes are presented. Cell-centered and mesh-vertex upwind finite-volume schemes are developed which utilize multi-dimensional monotone linear reconstruction procedures. These algorithms differ from existing algorithms (even on structured meshes). Numerical results in two dimensions are presented.

Barth, Timothy J.↗

NASA NTRS1989

The computation of generalized cross-validation functions through householder tridiagonalization with applications to the fitting of interaction spline models

An efficient algorithm for computing the generalized cross-validation function for the general cross-validated regularization/smoothing problem is provided. This algorithm is appropriate for problems where no natural structure is available, and the regularization/smoothing problem is solved (exactly) in a reproducing kernel Hilbert space. It is particularly appropriate for certain multivariate smoothing problems with irregularly spaced data, and certain remote sensing problems, such as those that occur in meteorology, where the sensors are arranged irregularly. The algorithm is applied to the fitting of interaction spline models with irregularly spaced data and two smoothing parameters; favorable timing results are presented. The algorithm may be extended to the computation of certain generalized maximum likelihood (GML) functions. Application of the GML algorithm to a problem in numerical weather forecasting, and to a broad class of hypothesis testing problems, is noted.

Gu, Chong↗

NASA NTRS1989

On polynomial preconditioning for indefinite Hermitian matrices

The minimal residual method is studied combined with polynomial preconditioning for solving large linear systems (Ax = b) with indefinite Hermitian coefficient matrices (A). The standard approach for choosing the polynomial preconditioners leads to preconditioned systems which are positive definite. Here, a different strategy is studied which leaves the preconditioned coefficient matrix indefinite. More precisely, the polynomial preconditioner is designed to cluster the positive, resp. negative eigenvalues of A around 1, resp. around some negative constant. In particular, it is shown that such indefinite polynomial preconditioners can be obtained as the optimal solutions of a certain two parameter family of Chebyshev approximation problems. Some basic results are established for these approximation problems and a Remez type algorithm is sketched for their numerical solution. The problem of selecting the parameters such that the resulting indefinite polynomial preconditioners speeds up the convergence of minimal residual method optimally is also addressed. An approach is proposed based on the concept of asymptotic convergence factors. Finally, some numerical examples of indefinite polynomial preconditioners are given.

Freund, Roland W.↗

NASA NTRS1993

CDM analysis

The C Data Manager (CDM) is an advanced tool for creating an object-oriented database and for processing queries related to objects stored in that database. The CDM source code was purchased and will be modified over the course of the Arachnid project. In this report, the modified CDM is referred to as MCDM. Using MCDM, a detailed series of experiments was designed and conducted on a Sun Sparcstation. The primary results and analysis of the CDM experiment are provided in this report. The experiments involved creating the Long-form Faint Source Catalog (LFSC) database and then analyzing it with respect to following: (1) the relationships between the volume of data and the time required to create a database; (2) the storage requirements of the database files; and (3) the properties of query algorithms. The effort focused on defining, implementing, and analyzing seven experimental scenarios: (1) find all sources by right ascension--RA; (2) find all sources by declination--DEC; (3) find all sources in the right ascension interval--RA1, RA2; (4) find all sources in the declination interval--DEC1, DEC2; (5) find all sources in the rectangle defined by--RA1, RA2, DEC1, DEC2; (6) find all sources that meet certain compound conditions; and (7) analyze a variety of query algorithms. Throughout this document, the numerical results obtained from these scenarios are reported; conclusions are presented at the end of the document.

Larson, Robert E.↗

NASA NTRS1993

Additional support for the TDK/MABL computer program

An advanced version of the Two-Dimensional Kinetics (TDK) computer program was developed under contract and released to the propulsion community in early 1989. Exposure of the code to this community indicated a need for improvements in certain areas. In particular, the TDK code needed to be adapted to the special requirements imposed by the Space Transportation Main Engine (STME) development program. This engine utilizes injection of the gas generator exhaust into the primary nozzle by means of a set of slots. The subsequent mixing of this secondary stream with the primary stream with finite rate chemical reaction can have a major impact on the engine performance and the thermal protection of the nozzle wall. In attempting to calculate this reacting boundary layer problem, the Mass Addition Boundary Layer (MABL) module of TDK was found to be deficient in several respects. For example, when finite rate chemistry was used to determine gas properties, (MABL-K option) the program run times became excessive because extremely small step sizes were required to maintain numerical stability. A robust solution algorithm was required so that the MABL-K option could be viable as a rocket propulsion industry design tool. Solving this problem was a primary goal of the phase 1 work effort.

Nickerson, G. R.↗

NASA NTRS1992

Time-dependent cosmic ray shocks with injection - A progress report

The study presents preliminary results of a two-fluid hydrodynamical simulation of cosmic-ray-modified shock structure by extending the steady-state calculations of Zank et al. (1991) to the time-dependent case. The present simulations model diffusive shock acceleration of the energetic particle component at planar shocks. A new model for the injection of cosmic ray particles is presented. The quadratic artificial viscosity algorithm is found to be numerically unstable and therefore unusable for strong cosmic ray shocks. There is visible ringing and overshoot in the various profiles. A large enhancement in the fluid density appears downstream of the subshock. This 'overcompression' results from the upstream fluid being compressed in the precursor, then traversing a strong shock with compression ratio near the adiabatic limit of four.

Donohue, D. J.↗

NASA NTRS1990

Control/structure interaction conceptual design tool

The JPL Control/Structure Interaction Program is developing new analytical methods for designing micro-precision spacecraft with controlled structures. One of these, the Conceptual Design Tool, will illustrate innovative new approaches to the integration of multi-disciplinary analysis and design methods. The tool will be used to demonstrate homogeneity of presentation, uniform data representation across analytical methods, and integrated systems modeling. The tool differs from current 'integrated systems' that support design teams most notably in its support for the new CSI multi-disciplinary engineer. The design tool will utilize a three dimensional solid model of the spacecraft under design as the central data organization metaphor. Various analytical methods, such as finite element structural analysis, control system analysis, and mechanical configuration layout, will store and retrieve data from a hierarchical, object oriented data structure that supports assemblies of components with associated data and algorithms. In addition to managing numerical model data, the tool will assist the designer in organizing, stating, and tracking system requirements.

Briggs, Hugh C.↗