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All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

Deformation of supersymmetric and conformal quantum mechanics through affine transformations

Affine transformations (dilatations and translations) are used to define a deformation of one-dimensional N = 2 supersymmetric quantum mechanics. Resulting physical systems do not have conserved charges and degeneracies in the spectra. Instead, superpartner Hamiltonians are q-isospectral, i.e. the spectrum of one can be obtained from another (with possible exception of the lowest level) by q(sup 2)-factor scaling. This construction allows easily to rederive a special self-similar potential found by Shabat and to show that for the latter a q-deformed harmonic oscillator algebra of Biedenharn and Macfarlane serves as the spectrum generating algebra. A general class of potentials related to the quantum conformal algebra su(sub q)(1,1) is described. Further possibilities for q-deformation of known solvable potentials are outlined.

Spiridonov, Vyacheslav↗
NASA NTRS1982

Numerical grid generation; Proceedings of the Symposium on Numerical Generation of Curvilinear Coordinate Systems and Their Use in the Numerical Solution of Partial Differential Equations, Nashville, TN, April 13-16, 1982

General curvilinear coordinate systems are considered along with the error induced by coordinate systems, basic differential models for coordinate generation, elliptic grid generation, conformal grid generation, algebraic grid generation, orthogonal grid generation, patched coordinate systems, and solid mechanics applications of boundary fitted coordinate systems. Attention is given to coordinate system control and adaptive meshes, the application of body conforming curvilinear grids for finite difference solution of external flow, the use of solution adaptive grids in solving partial differential equations, adaptive gridding for finite difference solutions to heat and mass transfer problems, and the application of curvilinear coordinate generation techniques to the computation of internal flows. Other topics explored are related to the solution of nonlinear water wave problems using boundary-fitted coordinate systems, the numerical modeling of estuarine hydrodynamics on a boundary-fitted coordinate system, and conformal grid generation for multielement airfoils.

Thompson, J. F.↗
NASA NTRS1989

An algebraic homotopy method for generating quasi-three-dimensional grids for high-speed configurations

A fast and versatile procedure for algebraically generating boundary conforming computational grids for use with finite-volume Euler flow solvers is presented. A semi-analytic homotopic procedure is used to generate the grids. Grids generated in two-dimensional planes are stacked to produce quasi-three-dimensional grid systems. The body surface and outer boundary are described in terms of surface parameters. An interpolation scheme is used to blend between the body surface and the outer boundary in order to determine the field points. The method, albeit developed for analytically generated body geometries is equally applicable to other classes of geometries. The method can be used for both internal and external flow configurations, the only constraint being that the body geometries be specified in two-dimensional cross-sections stationed along the longitudinal axis of the configuration. Techniques for controlling various grid parameters, e.g., clustering and orthogonality are described. Techniques for treating problems arising in algebraic grid generation for geometries with sharp corners are addressed. A set of representative grid systems generated by this method is included. Results of flow computations using these grids are presented for validation of the effectiveness of the method.

Moitra, Anutosh↗
NASA NTRS1988

Numerical simulation of hypersonic flow over an aeroassist flight experiment vehicle

Solutions of wind-tunnel and entry-flight flow around the vehicle are obtained from the Navier-Stokes equations coupled with the chemical species continuity equations if needed. The time-iterative method employs several techniques: shock fitting, chemistry-split ADI and an algebraic grid in conformal spherical-polar space. Sensitivities of the results to numerical parameters and to frozen, equilibrium and finite rate reactions are investigated in the forebody computation. Quantitative results are obtained for the shock layer and the near wake for the entire vehicle corresponding to both ground test and flight conditions. Complex flow characteristics are analyzed on the basis of the complete flowfield over the aerobrake and simplified afterbodies. The method is stable and cost effective, and has yielded shock locations and wall pressure distributions which are in good agreement with wind-tunnel data.

Li, C. P.↗
NASA NTRS1991

Non-isotropic turbulence effects on spray combustion

A numerical model for the prediction of local properties of statistically stationary spray-combusting flows is evaluated by comparison with experimental data. To appraise the relative performance of turbulence models, computations were carried out by the k-epsilon model and the algebraic stress model. The present numerical results show the qualitative agreement with experimental data. In terms of overall local flow properties, the algebraic stress model improves a degree of conformity to the experimental data due to its ability to introduce the nonisotropic turbulence effects. Two swirl numbers are considered to investigate the influence of swirl on the droplet evaporation and trajectories, and the effects of droplet/turbulence interactions in flow properties. It is found that the large swirl produces a higher evaporationn rate, and more intensive turbulent mixing and burning. The discrepancies observed in the results are attributed mainly to uncertainties in the initial spray size and velocity distributions, the droplet/wall impingement interaction, the combustion model with the fast chemistry and the turbulence models dealing with the strong streamline curvature and complex interactions between the dispersed droplets and the continuous gas-phase flows.

Kim, Y. M.↗
NASA NTRS1986

The computation of flow past an oblique wing using the thin-layer Navier-Stokes equations

Essential aspects are presented for computing flow past an oblique wing with the thin-layer Navier-Stokes equations. A new method is developed for generating a grid system around a realistic wing. This method utilizes a series of conformal transformations. The thin-shear-layer approximation and an algebraic eddy-viscosity turbulence model are used to simplify the Reynolds-averaged Navier-Stokes equations. An implicit, factored numerical scheme and the concept of pencil data structure are utilized. For the first time, some flow fields caused by the oblique wing in a supersonic free stream are discussed, emphasizing the separated vortex flows associated with such a wing.

Mehta, Unmeel↗
NASA NTRS2001

The Development of a Factorizable Multigrid Algorithm for Subsonic and Transonic Flow

The factorizable discretization of Sidilkover for the compressible Euler equations previously demonstrated for channel flows has been extended to external flows.The dissipation of the original scheme has been modified to maintain stability for moderately stretched grids. The discrete equations are solved by symmetric collective Gauss-Seidel relaxation and FAS multigrid. Unlike the earlier work ordering the grid vertices in the flow direction has been found to be unnecessary. Solutions for essential incompressible flow (Mach 0.01) and supercritical flows have obtained for a Karman-Trefftz airfoil with it conformally mapped grid,as well as a NACA 0012 on an algebraically generated grid. The current work demonstrates nearly 0(n) convergence for subsonic and slightly transonic flows.

Roberts, Thomas W.↗
NASA NTRS1995

Elliptic surface grid generation on minimal and parmetrized surfaces

An elliptic grid generation method is presented which generates excellent boundary conforming grids in domains in 2D physical space. The method is based on the composition of an algebraic and elliptic transformation. The composite mapping obeys the familiar Poisson grid generation system with control functions specified by the algebraic transformation. New expressions are given for the control functions. Grid orthogonality at the boundary is achieved by modification of the algebraic transformation. It is shown that grid generation on a minimal surface in 3D physical space is in fact equivalent to grid generation in a domain in 2D physical space. A second elliptic grid generation method is presented which generates excellent boundary conforming grids on smooth surfaces. It is assumed that the surfaces are parametrized and that the grid only depends on the shape of the surface and is independent of the parametrization. Concerning surface modeling, it is shown that bicubic Hermite interpolation is an excellent method to generate a smooth surface which is passing through a given discrete set of control points. In contrast to bicubic spline interpolation, there is extra freedom to model the tangent and twist vectors such that spurious oscillations are prevented.

Spekreijse, S. P.↗
NASA NTRS1995

Elliptic surface grid generation on minimal and parametrized surfaces

An elliptic grid generation method, which generates boundary conforming grids in a two dimensional physical space, is presented. The method is based on the composition of an algebraic and elliptic transformation. The composite mapping obeys the Poisson grid generation system with control functions specified by the algebraic transformation. It is shown that the grid generation on a minimal surface in a three dimensional space is equivalent to the grid generation in a two dimensional domain in physical space. A second elliptic grid generation method, which generates boundary conforming grids on smooth surfaces, is presented. Concerning surface modeling, it is shown that bicubic Hermit interpolation is an excellent method to generate a smooth surface crossing a discrete set of control points.

Spekreijse, S. P.↗
NASA NTRS2007

Reexamination of Ball-Race Conformity Effects on Ball Bearing Life

The analysis in this report considers the life of the ball set as well as the respective lives of the races to reassess the effect of ball-race conformity on ball bearing life. The related changes in ball bearing life are incorporated in life factors that can be used to modify the bearing predicted life using the Lundberg-Palmgren equations and the ANSI/ABMA and ISO Standards. Two simple algebraic relationships were established to calculate life factors LF(sub c) to determine the effect of inner- and outer-race conformity combinations on bearing L(sub 10) life for deepgroove and angular-contact ball bearings, respectively. Depending on the bearing type and series as well as conformity combinations, the calculated life for deep-groove ball bearings can be over 40 percent less than that calculated by the Lundberg-Palmgren equations. For angular-contact ball bearings, the life can vary between +16 and -39 percent from that calculated by the Lundberg-Palmgren equations. Comparing the two ball bearing types, the life factors LF(sub c) for the deep-groove bearings can be as much as 40 percent lower than that for angular-contact ball bearings.

Zaretsky, Erwin V.↗
NASA NTRS1990

Improved Coupled Fluid/Structural Dynamical Model

Improved algorithm developed for simulation of coupled motions of fluids and structures. Minimum requirement for correct simulation of damping is forces and velocities at interface compatible in models of structure and fluid at each time step. Improved algorithm, conforms to this requirement, involves fluid-transient model, structural modal/transient model, and an algebraic impedance/coupling subalgorithm. Use of this algorithm greatly improves computational stability.

Fenwick, James R.↗
NASA NTRS1992

GridMan: A grid manipulation system

GridMan is an interactive grid manipulation system. It operates on grids to produce new grids which conform to user demands. The input grids are not constrained to come from any particular source. They may be generated by algebraic methods, elliptic methods, hyperbolic methods, parabolic methods, or some combination of methods. The methods are included in the various available structured grid generation codes. These codes perform the basic assembly function for the various elements of the initial grid. For block structured grids, the assembly can be quite complex due to a large number of clock corners, edges, and faces for which various connections and orientations must be properly identified. The grid generation codes are distinguished among themselves by their balance between interactive and automatic actions and by their modest variations in control. The basic form of GridMan provides a much more substantial level of grid control and will take its input from any of the structured grid generation codes. The communication link to the outside codes is a data file which contains the grid or section of grid.

Eiseman, Peter R.↗
NASA NTRS1982

Boundary-fitted coordinate systems for numerical solution of partial differential equations - A review

A comprehensive review of methods of numerically generating curvilinear coordinate systems with coordinate lines coincident with all boundary segments is given. Some general mathematical framework and error analysis common to such coordinate systems is also included. The general categories of generating systems are those based on conformal mapping, orthogonal systems, nearly orthogonal systems, systems produced as the solution of elliptic and hyperbolic partial differential equations, and systems generated algebraically by interpolation among the boundaries. Also covered are the control of coordinate line spacing by functions embedded in the partial differential operators of the generating system and by subsequent stretching transformation. Dynamically adaptive coordinate systems, coupled with the physical solution, and time-dependent systems that follow moving boundaries are treated. References reporting experience using such coordinate systems are reviewed as well as those covering the system development.

Thompson, J. F.↗
NASA NTRS1993

Analysis of the Harrier forebody/inlet design using computational techniques

Under the support of this Cooperative Agreement, computations of transonic flow past the complex forebody/inlet configuration of the AV-8B Harrier II have been performed. The actual aircraft configuration was measured and its surface and surrounding domain were defined using computational structured grids. The thin-layer Navier-Stokes equations were used to model the flow along with the Chimera embedded multi-grid technique. A fully conservative, alternating direction implicit (ADI), approximately-factored, partially flux-split algorithm was employed to perform the computation. An existing code was altered to conform with the needs of the study, and some special engine face boundary conditions were developed. The algorithm incorporated the Chimera technique and an algebraic turbulence model in order to deal with the embedded multi-grids and viscous governing equations. Comparison with experimental data has yielded good agreement for the simplifications incorporated into the analysis. The aim of the present research was to provide a methodology for the numerical solution of complex, combined external/internal flows. This is the first time-dependent Navier-Stokes solution for a geometry in which the fuselage and inlet share a wall. The results indicate the methodology used here is a viable tool for transonic aircraft modeling.

Chow, Chuen-Yen↗
NASA NTRS1989

The implementation of the graphics of program EAGLE: A numerical grid generation code on NASA Langley SNS computer system

Program EAGLE (Eglin Arbitrary Geometry Implicit Euler) Numerical Grid Generation System is a composite (multi-block) algebraic or elliptic grid generation system designed to discretize the domain in and/or around any arbitrarily shaped three dimensional regions. This system combines a boundary conforming surface generation scheme and includes plotting routines designed to take full advantage of the DISSPLA Graphics Package (Version 9.0). Program EAGLE is written to compile and execute efficiently on any Cray machine with or without solid state disk (SSD) devices. Also, the code uses namelist inputs which are supported by all Cray machines using the FORTRAN compiler CFT77. The namelist inputs makes it easier for the user to understand the inputs and operation of Program EAGLE. EAGLE's numerical grid generator is constructed in the following form: main program, EGG (executive routine); subroutine SURFAC (surface generation routine); subroutine GRID (grid generation routine); and subroutine GRDPLOT (grid plotting routines). The EAGLE code was modified to use on the NASA-LaRC SNS computer (Cray 2S) system. During the modification a conversion program was developed for the output data of EAGLE's subroutine GRID to permit the data to be graphically displayed by IRIS workstations, using Plot3D. The code of program EAGLE was modified to make operational subroutine GRDPLOT (using DI-3000 Graphics Software Packages) on the NASA-LaRC SNS Computer System. How to implement graphically, the output data of subroutine GRID was determined on any NASA-LaRC graphics terminal that has access to the SNS Computer System DI-300 Graphics Software Packages. A Quick Reference User Guide was developed for the use of program EAGLE on the NASA-LaRC SNS Computer System. One or more application program(s) was illustrated using program EAGLE on the NASA LaRC SNS Computer System, with emphasis on graphics illustrations.

Houston, Johnny L.↗
NASA NTRS1996

There aren't Non-Standard Solutions for the Braid Group Representations of the QYBE Associated with 10-D Representations of SU(4)

It is well known that the quantum Yang-Baxter equations (QYBE) play an important role in various theoretical and mathematical physics, such as completely integrable system in (1 + 1)-dimensions, exactly solvable models in statistical mechanics, the quantum inverse scattering method and the conformal field theories in 2-dimensions. Recently, much remarkable progress has been made in constructing the solutions of the QYBE associated with the representations of lie algebras. It is shown that for some cases except the standard solutions, there also exist new solutions, but the others have not non-standard solutions. In this paper by employing the weight conservation and the diagrammatic techniques we show that the solution associated with the 10-D representations of SU (4) are standard alone.

Yijun, Huang↗
NASA NTRS1983

Numerical solution of the Navier-Stokes equations for arbitrary 2-dimensional multi-element airfoils

Numerical solutions of the Navier-Stokes equations, with an algebraic turbulence model, for time-dependent two dimensional flow about multi-element airfoils were developed. Fundamental to these solutions was the use of numerically-generated boundary-conforming curvilinear coordinate systems to allow bodies of arbitrary shape to be treated. A general two dimensional grid generation code for multiple-body configuration was written as a part of this project and made available through the COSMIC code library.

Thompson, J. F.↗
NASA NTRS1993

Improved Blending-Function Algebraic Generation Of Grids

Method of algebraic generation of grids used in computing flows incorporates blending-function techniques to obtain high degree of orthogonality of each grid on its bounding surfaces and to blend grid smoothly, making it conform to all boundaries. Demonstrated in two dimensions, and applied in continuing development of software for real-time interactive generation of three-dimensional grids with color graphical displays. Software used routinely in generating grids for computing flows of practical interest.

Ching-Chung Luh, Raymond↗