Bezier curves are an established tool in Computer Aided Geometric Design. One of the drawbacks of the Bezier method is that the curves often bear little resemblance to their control polygons. As a result, it becomes increasingly difficult to obtain anything but a rough outline of the desired shape. One possible solution is tomanipulate the curve itself instead of the control polygon. The standard cubic Bezier curve form has introduced into it two shape parameters, gamma 1 and 2. These...

Topics: NASA Technical Reports Server (NTRS), COMPUTER AIDED DESIGN, COMPUTER GRAPHICS, CURVES (GEOMETRY),...

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Apr 16, 2021
04/21

by
Elizabeth Denne (dennedesigns)

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A tumor may be modeled in spherical coordinates by rho=1+1/5 sin(mTheta)sin(nPhi). This model shows the case where m=8 and n=7. This model was designed by my WLU summer research student Ryan McDonnell ('17). Dave Pfaff helped him work out how to color the model in meshlab. (The pictures show the powder print before and after super-glue is added to strengthen the model.)

Topics: spherical_coordinates, Math, thingiverse, stl, Multivariable_Calc, tumor_model

To increase the effectiveness and efficiency of fiber-reinforced materials, the use of fibers in a curvilinear rather than the traditional straightline format is explored. The capacity of a laminated square plate with a central circular hole loaded in tension is investigated. The orientation of the fibers is chosen so that the fibers in a particular layer are aligned with the principle stress directions in that layer. Finite elements and an iteration scheme are used to find the fiber...

Topics: NASA Technical Reports Server (NTRS), COMPOSITE MATERIALS, FIBER COMPOSITES, FIBER ORIENTATION,...

A proposed three-degree-of-freedom (tilt/tip/piston) manipulator, suitable for aligning an optical or mechanical component, would offer several advantages over prior such manipulators: Unlike in some other manipulators, no actuator would support the weight of another actuator: All of the actuators would be mounted on a base. Hence, there would be less manipulated weight. The basic geometry of the manipulator would afford mechanical advantage: that is, actuator motions would be larger than the...

Topics: NASA Technical Reports Server (NTRS), ACTUATORS, MANIPULATORS, PISTONS, ATTITUDE (INCLINATION),...

Boundary and interface conditions are derived for high order finite difference methods applied to multidimensional linear problems in curvilinear coordinates. The boundary and interface conditions lead to conservative schemes and strict and strong stability provided that certain metric conditions are met.

Topics: NASA Technical Reports Server (NTRS), FINITE DIFFERENCE THEORY, SPHERICAL COORDINATES, NUMERICAL...

Conventional gravity and magnetic anomaly continuation invokes the standard Poisson boundary condition of a zero anomaly at an infinite vertical distance from the observation surface. This simple continuation is limited, however, where multiple altitude slices of the anomaly field have been observed. Increasingly, areas are becoming available constrained by multiple boundary conditions from surface, airborne, and satellite surveys. This paper describes the implementation of continuation with...

Topics: NASA Technical Reports Server (NTRS), GRAVITY ANOMALIES, MAGNETIC ANOMALIES, FOURIER...

Finite difference methods for composite grids were analyzed. It was observed that linear interpolation between grids would suffice only where low order accuracy was required. In the context of fluid flow, this would be in regions where the flow was essentially free stream. Higher order interpolation schemes were also investigated. The well known quadratic and cubic interpolating polynomials would increase the formal accuracy of the overall numerical algorithm. However, it can also be shown that...

Topics: NASA Technical Reports Server (NTRS), COMPUTATIONAL GRIDS, COORDINATE TRANSFORMATIONS, ELLIPTIC...

A set of higher-order boundary-layer equations is derived valid for three-dimensional compressible flows. The equations are written in a generalized curvilinear coordinate system, in which the surface coordinates are nonorthogonal; the third axis is restricted to be normal to the surface. Also, higher-order viscous terms which are retained depend on the surface curvature of the body. Thus, the equations are suitable for the calculation of the boundary layer about arbitrary vehicles. As a...

Topics: NASA Technical Reports Server (NTRS), BOUNDARY LAYER EQUATIONS, COMPRESSIBLE FLOW, SPHERICAL...

This is a working paper in which a formulation is given for solving the boundary-layer equations in general body-fitted curvilinear coordinates while retaining the original Cartesian dependent variables. The solution procedure does not require that any of the coordinates be orthogonal, and much of the software developed for many Navier-Stokes schemes can be readily used. A limited number of calculations has been undertaken to validate the approach.

Topics: NASA Technical Reports Server (NTRS), BOUNDARY LAYERS, CARTESIAN COORDINATES, COMPUTATIONAL FLUID...

Direct numerical simulations (DNS) of the acoustic receptivity process on a semi-infinite flat plate with a modified-super-elliptic (MSE) leading edge are performed. The incompressible Navier-Stokes equations are solved in stream-function/vorticity form in a general curvilinear coordinate system. The steady basic-state solution is found by solving the governing equations using an alternating direction implicit (ADI) procedure which takes advantage of the parallelism present in line-splitting...

Topics: NASA Technical Reports Server (NTRS), ALTERNATING DIRECTION IMPLICIT METHODS, BOUNDARY LAYER FLOW,...

A Navier-Stokes code was developed for low thrust viscous nozzle flow field prediction. An implicit finite volume in an arbitrary curvilinear coordinate system lower-upper (LU) scheme is used to solve the governing Navier-Stokes equations and species transportation equations. Sample calculations of carbon dioxide nozzle flow are presented to verify the validity and efficiency of this code. The computer results are in reasonable agreement with the experimental data.

Topics: NASA Technical Reports Server (NTRS), FLOW DISTRIBUTION, FLUID DYNAMICS, LOW THRUST, NAVIER-STOKES...

The efficient multilevel adaptive method has been successfully applied to perform direct numerical simulations (DNS) of flow transition in 3-D channels and 3-D boundary layers with 2-D and 3-D isolated and distributed roughness in a curvilinear coordinate system. A fourth-order finite difference technique on stretched and staggered grids, a fully-implicit time marching scheme, a semi-coarsening multigrid method associated with line distributive relaxation scheme, and an improved outflow...

Topics: NASA Technical Reports Server (NTRS), BASE FLOW, BOUNDARY LAYER TRANSITION, CHANNEL FLOW,...

A general survey of grid generators is presented with a concern for understanding why grids are necessary, how they are applied, and how they are generated. After an examination of the need for meshes, the overall applications setting is established with a categorization of the various connectivity patterns. This is split between structured grids and unstructured meshes. Altogether, the categorization establishes the foundation upon which grid generation techniques are developed. The two...

Topics: NASA Technical Reports Server (NTRS), COMPUTATIONAL GRIDS, COMPUTER PROGRAMMING, GRID GENERATION...

Progress in the direct-inverse wing design method in curvilinear coordinates has been made. This includes the remedying of a spanwise oscillation problem and the assessment of grid skewness, viscous interaction, and the initial airfoil section on the final design. It was found that, in response to the spanwise oscillation problem that designing at every other spanwise station produced the best results for the cases presented, a smoothly varying grid is especially needed for the accurate design...

Topics: NASA Technical Reports Server (NTRS), AIRCRAFT DESIGN, AIRFOILS, COMPUTER PROGRAMS, TRANSONIC...

The issue of adopting the velocity components as dependent velocity variables for the Navier-Stokes flow computations is investigated. The viewpoint advocated is that a numerical algorithm should preferably honor both the physical conservation law in differential form and the geometric conservation law in discrete form. With the use of Cartesian velocity vector, the momentum equations in curvilinear coordinates can retain the full conservation-law form and satisfy the physical conservation...

Topics: NASA Technical Reports Server (NTRS), COMPUTATIONAL FLUID DYNAMICS, COMPUTATIONAL GRIDS,...

Modern split component evaluations of the flux vector Jacobians are thoroughly analyzed for equilibrium-gas average-state determinations. It is shown that all such derivations satisfy a fundamental eigenvalue consistency theorem. A conservative-variable average state is then developed for arbitrary equilibrium-gas equations of state and curvilinear-coordinate fluxes. Original expressions for eigenvalues, sound speed, Mach number, and eigenvectors are then determined for a general average...

Topics: NASA Technical Reports Server (NTRS), COMPUTATIONAL FLUID DYNAMICS, EIGENVALUES, EIGENVECTORS,...

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295

Jul 26, 2010
07/10

by
NOBLE, JOHN M.; BASS, HENRY E.; RASPET, RICHAR

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ACOUSTIC MEASUREMENTS MADE IN THE ATMOSPHERE HAVE SHOWN SIGNIFICANT FLUCTUATIONS IN AMPLITUDE AND PHASE RESULTING FROM THE INTERACTION WITH TIME VARYING METEOROLOGICAL CONDITIONS. THE OBSERVED VARIATIONS APPEAR TO HAVE SHORT TERM AND LONG TERM (1 TO 5 MINUTES) VARIATIONS AT LEAST IN THE PHASE OF THE ACOUSTIC SIGNAL. ONE POSSIBLE WAY TO ACCOUNT FOR THIS LONG TERM VARIATION IS THE USE OF A LARGE SCALE WIND DRIVEN TURBULENCE MODEL. FROM A FOURIER ANALYSIS OF THE PHASE VARIATIONS, THE OUTER SCALES...

Topics: ALGORITHMS, SPHERICAL COORDINATES, STEADY FLOW, BACKWARD FACING STEPS, CAVITIES, CIRCULAR...

This paper discusses new boundary constraints for elliptic partial differential equations as used in grid generation problems in generalized curvilinear coordinate systems. These constraints, based on the principle of local conservation of thermal energy in the vicinity of the boundaries, are derived using the Green's Theorem. They uniquely determine the so called decay parameters in the source terms of these elliptic systems. These constraints' are designed for boundary clustered grids where...

Topics: NASA Technical Reports Server (NTRS), ELLIPTIC DIFFERENTIAL EQUATIONS, GRID GENERATION...

Consideration is being given to representing the magnetic field in the area 40 deg N to 83 deg N by means of functions in spherical coordinates. A solution to Laplace's equation for the magnetic potential over a restricted area was found, and programming and testing are currently being carried out. Magnetic anomaly modelling is proceeding. The program SPHERE, which was adapted to function correctly on the Cyber computer, is now operational, for deriving gravity and magnetic models in a...

Topics: NASA Technical Reports Server (NTRS), CANADA, DATA REDUCTION, GEOMAGNETISM, MAGNETIC SURVEYS,...

The Goertler instability of the laminar compressible boundary layer flows along concave surfaces is investigated. The linearized disturbance equations for the three-dimensional, counter-rotating streamwise vortices in two-dimensional boundary layers are presented in an orthogonal curvilinear coordinate. The basic approximation of the disturbance equations, that includes the effect of the growth of the boundary layer, is considered and solved numerically. The effect of compressibility on...

Topics: NASA Technical Reports Server (NTRS), BOUNDARY LAYER STABILITY, COMPRESSIBLE BOUNDARY LAYER,...

A method for generating three dimensional, finite difference grids about complicated geometries by using Poisson equations is developed. The inhomogenous terms are automatically chosen such that orthogonality and spacing restrictions at the body surface are satisfied. Spherical variables are used to avoid the axis singularity, and an alternating-direction-implicit (ADI) solution scheme is used to accelerate the computations. Computed results are presented that show the capability of the method....

Topics: NASA Technical Reports Server (NTRS), COMPUTATIONAL GRIDS, FLOW DISTRIBUTION, GRID GENERATION...

The primary methodology during the grant period has been the use of micro or meso-scale simulations to address specific questions concerning magnetospheric processes related to the aurora and substorm morphology. This approach, while useful in providing some answers, has its limitations. Many of the problems relating to the magnetosphere are inherently global and kinetic. Effort during the last year of the grant period has increasingly focused on development of a global-scale hybrid code to...

Topics: NASA Technical Reports Server (NTRS), ATMOSPHERIC PHYSICS, AURORAL ARCS, COMPUTER PROGRAMS, EARTH...

The flow field is simulated on the surface of a given delta wing (Butler wing) at zero incident in a uniform stream. The simulation is done by integrating a set of flow field equations. This set of equations governs the unsteady, viscous, compressible, heat conducting flow of an ideal gas. The equations are written in curvilinear coordinates so that the wing surface is represented accurately. These equations are solved by the finite difference method, and results obtained for high-speed...

Topics: NASA Technical Reports Server (NTRS), COMPRESSIBLE FLOW, DELTA WINGS, FLOW DISTRIBUTION, HEAT...

A methodology for accurate and efficient simulation of unsteady, compressible flows is presented. The cornerstones of the methodology are a special discretization of the Navier-Stokes equations on structured body-fitted grid systems and an efficient solution-adaptive mesh refinement technique for structured grids. The discretization employs an explicit multidimensional upwind scheme for the inviscid fluxes and an implicit treatment of the viscous terms. The mesh refinement technique is based on...

Topics: NASA Technical Reports Server (NTRS), COMPRESSIBLE FLOW, COMPUTATIONAL FLUID DYNAMICS,...

We describe the use of LIDAR, or "laser radar," (LR) as a fast, accurate, and non-contact tool for the measurement of the radius of curvature (RoC) of large mirrors. We report the results of a demonstration of this concept using a commercial laser radar system. We measured the RoC of a 1.4m x 1m spherical mirror with a nominal RoC of 4.6 m with a manufacturing tolerance of 4600mm +/- 6mm. The prescription of the mirror is related to its role as ground support equipment used in the...

Topics: NASA Technical Reports Server (NTRS), OPTICAL RADAR, JAMES WEBB SPACE TELESCOPE, SPHERICAL...

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235

Jul 21, 2010
07/10

by
Luckring, J. M.; Hoffler, K. D.; Grantz, A. C

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A new version of the free vortex sheet formulation is presented which has greatly improved convergence characteristics for a broad range of geometries. The enhanced convergence properties were achieved largely with extended modeling capabilities of the leading edge vortex and the near field trailing wake. Results from the new code, designated FVS-1, are presented for a variety of configurations and flow conditions with emphasis on vortex flap applications.

Topics: CODING, NAVIER-STOKES EQUATION, COMPUTER PROGRAMS, EQUATIONS OF MOTION, INCOMPRESSIBLE FLOW,...

A three-dimensional numerical solver based on finite-difference solution of three-dimensional elastodynamic equations in generalized curvilinear coordinates has been developed and used to generate data such as radial and tangential stresses over various gear component geometries under rotation. The geometries considered are an annulus, a thin annular disk, and a thin solid disk. The solution is based on first principles and does not involve lumped parameter or distributed parameter systems...

Topics: NASA Technical Reports Server (NTRS), ELASTIC PROPERTIES, ELASTODYNAMICS, FINITE DIFFERENCE THEORY,...

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May 27, 2011
05/11

by
Benner, D. Chri

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This cooperative agreement has investigated a number of spectroscopic problems of interest to the Halogen Occultation Experiment (HALOE). The types of studies performed are in two parts, namely, those that involve the testing and characterization of correlation spectrometers and those that provide basic molecular spectroscopic information. In addition, some solar studies were performed with the calibration data returned by HALOE from orbit. In order to accomplish this a software package was...

Topics: FINITE VOLUME METHOD, REACTING FLOW, INVISCID FLOW, FINITE DIFFERENCE THEORY, DIFFERENTIAL...

In aerospace computational fluid dynamics (CFD) calculations, the Delaunay triangulation of suitable quadrilateral meshes can lead to unsuitable triangulated meshes. Here, we present case studies which illustrate the limitations of using structured grid generation methods which produce points in a curvilinear coordinate system for subsequent triangulations for CFD applications. We discuss conditions under which meshes of quadrilateral elements may not produce a Delaunay triangulation suitable...

Topics: NASA Technical Reports Server (NTRS), COMPUTATIONAL FLUID DYNAMICS, GRID GENERATION (MATHEMATICS),...

A theoretical overview of the response coefficient method for heat conduction transients with time-dependent input forcing functions is presented with a number of illustrative applications. The method may be the most convenient and economical if the same problem is to be solved many times with different input-time histories or if the solution time is relatively long. The method is applicable to a wide variety of problems, including irregular geometries, position-dependent boundary conditions,...

Topics: NASA Technical Reports Server (NTRS), BOUNDARY CONDITIONS, CONDUCTIVE HEAT TRANSFER, DIFFERENTIAL...

Described are many algorithmic and computational aspects of upwind schemes and their second-order accurate formulations based on Total-Variation-Diminishing (TVD) approaches. An operational unification of the underlying first-order scheme is first presented encompassing Godunov's, Roe's, Osher's, and Split-Flux methods. For higher order versions, the preprocessing and postprocessing approaches to constructing TVD discretizations are considered. TVD formulations can be used to construct...

Topics: NASA Technical Reports Server (NTRS), ALGORITHMS, COMPUTATION, EULER EQUATIONS OF MOTION, TVD...

An approach to compute 3-D flows using two stream functions is presented. The method generates a boundary fitted grid as part of its solution. Commonly used two steps for computing the flow fields are combined into a single step in the present approach: (1) boundary fitted grid generation; and (2) solution of Navier-Stokes equations on the generated grid. The presented method can be used to directly compute 3-D viscous flows, or the potential flow approximation of this method can be used to...

Topics: NASA Technical Reports Server (NTRS), ALGORITHMS, FLOW DISTRIBUTION, GRID GENERATION (MATHEMATICS),...

A common requirement for all geodetic investigations is a well-defined coordinate system attached to the earth in some prescribed way, as well as a well-defined inertial coordinate system in which the motions of the terrestrial frame can be monitored. The paper deals with the problems encountered when establishing such coordinate systems and the transformations between them. In addition, problems related to the modeling of the deformable earth are discussed. This paper is an updated version of...

Topics: NASA Technical Reports Server (NTRS), COORDINATES, GEODETIC SURVEYS, INERTIAL REFERENCE SYSTEMS,...

The objective of this study is to investigate the complex three-dimensional flowfield of an oxygen safety pressure relieve valve during an incident, with a computational fluid dynamic (CFD) analysis. Specifically, the analysis will provide a flow pattern that would lead to the expansion of the eventual erosion pattern of the hardware, so as to combine it with other findings to piece together a most likely scenario for the investigation. The CFD model is a pressure based solver. An adaptive...

Topics: NASA Technical Reports Server (NTRS), COMPRESSIBLE FLOW, DAMAGE ASSESSMENT, EROSION, FIRES, FLOW...

This paper contains a collection of computational algorithms for determining geocentric ephemerides of Earth satellites, useful for both mission planning and data reduction applications. Special emphasis is placed on the computation of sidereal time, and on the determination of the geocentric coordinate of the center of the Sun, all to the accuracy found in the Astronomical Almanac. The report is completely self-contained in that no requirement is placed on any external source of information,...

Topics: NASA Technical Reports Server (NTRS), ARTIFICIAL SATELLITES, EPHEMERIDES, GEOCENTRIC COORDINATES,...

The finite volume approach in developing multi-dimensional, high-order accurate essentially non-oscillatory (ENO) schemes is considered. In particular, a two dimensional extension is proposed for the Euler equation of gas dynamics. This requires a spatial reconstruction operator that attains formal high order of accuracy in two dimensions by taking account of cross gradients. Given a set of cell averages in two spatial variables, polynomial interpolation of a two dimensional primitive function...

Topics: NASA Technical Reports Server (NTRS), BOUNDARY CONDITIONS, BOUNDARY VALUE PROBLEMS, ESSENTIALLY...

The Attitude Profile Design (APD) Program was designed to be used as a stand-alone addition to the Simplex Computation of Optimum Orbital Trajectories (SCOOT). The program uses information from a SCOOT output file and the user defined attitude profile to produce time histories of attitude, angular body rates, and accelerations. The APD program is written in standard FORTRAN77 and should be portable to any machine that has an appropriate compiler. The input and output are through formatted...

Topics: NASA Technical Reports Server (NTRS), ATTITUDE (INCLINATION), COMPUTER PROGRAMS, POINTING CONTROL...

A modification of an implicit approximate-factorization finite-difference algorithm applied to the two-dimensional Euler and Navier-Stokes equations in general curvilinear coordinates is presented for supersonic freestream flow about and through inlets. The modification transforms the coupled system of equations Into an uncoupled diagonal form which requires less computation work. For steady-state applications the resulting diagonal algorithm retains the stability and accuracy characteristics...

Topics: NASA Technical Reports Server (NTRS), TWO DIMENSIONAL MODELS, INLET FLOW, COMPUTERIZED SIMULATION,...

Introduction: When describing human motion, biomechanists generally report joint angles in terms of Euler angle rotation sequences. However, there are known limitations in using this method to describe complex motions such as the shoulder joint during a baseball pitch. Euler angle notation uses a series of three rotations about an axis where each rotation is dependent upon the preceding rotation. As such, the Euler angles need to be regarded as a set to get accurate angle information....

Topics: NASA Technical Reports Server (NTRS), MOBILITY, SPHERICAL COORDINATES, BIODYNAMICS, EULER EQUATIONS...

The current work is initiated in an effort to obtain an efficient, accurate, and robust algorithm for the numerical solution of the incompressible Navier-Stokes equations in two- and three-dimensional generalized curvilinear coordinates for both steady-state and time-dependent flow problems. This is accomplished with the use of the method of artificial compressibility and a high-order flux-difference splitting technique for the differencing of the convective terms. Time accuracy is obtained in...

Topics: NASA Technical Reports Server (NTRS), ALGORITHMS, COMPRESSIBILITY, DUCTED FLOW, INCOMPRESSIBLE...

A numerical simulation of the incompressible viscous flow through a prosthetic tilting disk heart valve is presented in order to demonstrate the current capability to model unsteady flows with moving boundaries. Both steady state and unsteady flow calculations are done by solving the incompressible Navier-Stokes equations in 3-D generalized curvilinear coordinates. In order to handle the moving boundary problems, the chimera grid embedding scheme which decomposes a complex computational domain...

Topics: NASA Technical Reports Server (NTRS), BLOOD FLOW, BOUNDARY VALUE PROBLEMS, COMPUTERIZED SIMULATION,...

Computer simulation studies of two frequency domain adaptive beamforming algorithms for planar arrays are presented. The algorithms are modified complex LMS adaptive algorithms that can process an arbitrary number of harmonics. The algorithms provide estimates of the spherical coordinates (i.e., range, depression angle, and bearing angle) of multiple broadband targets in both the near-field and far-field. Computer simulation results comparing the average estimation error for range, depression...

Topics: Target localization in spherical coordinates, Sonar signal processing, Frequency domain adaptive...

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May 23, 2011
05/11

by
Mazuruk, K.; Su, Ching-Hua; Sha, Yi-Gao; Lehoczky, S. L

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An oscillating-cup viscometer was developed to measure viscosity of molten HgZnTe ternary semiconductor alloys. Data were collected for the pseudobinary Hg(0.84)Zn(0.16)Te melt between 770 and 850 C. The kinematic viscosity was found to vary from approximately 1.1 to 1.4 x 10(sup -3)sq cm/s. A slow relaxation phenomena was also observed for temperatures from the melting point of 770 to approx. 800 C. Possible mechanisms for this effect are discussed.

Topics: FLOW DISTRIBUTION, AUGMENTATION, HEAT TRANSFER, DUCTS, MATHEMATICAL MODELS, SECONDARY FLOW, FINITE...

Commonly used one dimensional geoid models predict that the isostatic geoid anomaly over old ocean basins for the boundary layer thermal model of the lithosphere is a factor of two greater than that for the plate model. Calculations presented, using the spherical analogues of the plate and boundary layer thermal models, show that for the actual global distribution of plate ages, one dimensional models are not accurate and a spherical, fully three dimensional treatment is necessary. The maximum...

Topics: NASA Technical Reports Server (NTRS), GEOIDS, OCEAN BOTTOM, PLATES (TECTONICS), SPHERICAL...

The overall objective of this research program is to obtain a better understanding of the interaction between the solar wind and the interstellar medium through the use of numerical solutions of the time-dependent magnetohydrodynamic (MHD) equations. The simulated results have been compared with observations where possible and with the results from previous analytic and numerical studies. The primary accomplishment of this project has been the development of codes for 2-D models in both...

Topics: NASA Technical Reports Server (NTRS), SOLAR WIND, INTERSTELLAR MATTER, TWO DIMENSIONAL MODELS,...

A comprehensive approach to the lithospheric analysis of potential field anomalies in the spherical domain is provided. It has widespread application in the analysis and design of satellite gravity and magnetic surveys for geological investigation.

Topics: NASA Technical Reports Server (NTRS), EARTH GRAVITATION, GEOMAGNETISM, LITHOSPHERE, MAGNETIC...

A numerical model which simulates geophysical fluid flow in a wide range of problems is described in detail, and comparisons of some of the model's results are made with previous experimental and numerical studies. The model is based upon the Boussinesq Navier-Stokes equations in spherical coordinates, which can be reduced to a cylindrical system when latitudinal walls are used near the pole and the ratio of latitudinal length to the radius of the sphere is small. The equations are approximated...

Topics: NASA Technical Reports Server (NTRS), COMPUTERIZED SIMULATION, FINITE DIFFERENCE THEORY, FLUID...

The flow field is simulated on the surface of a Butler wing in a uniform stream. Results are presented for the Mach number 3.5 and Reynolds number of 2,000,000. The simulation is done by integrating the viscous Navier-Stokes equations. These equations govern the unsteady, viscous, compressible and heat conducting flow of an ideal gas. The equations are written in curvilinear coordinates so that the wing surface is represented accurately. O-type and H-type grids have been used for this study,...

Topics: NASA Technical Reports Server (NTRS), AERODYNAMIC CONFIGURATIONS, AIRFOILS, COMPUTATIONAL FLUID...

No model of distribution of meteor substance is known to explain the observed diurnal and annual variations of meteor rates, if that distribution is assumed to be constant during the year. Differences between the results of observations and the prediction of diurnal variation rates leads to the conclusion that the density of the orbits of meteor bodies changes with the motion of the Earth along its orbit. The distributions of the flux density over the celestial sphere are obtained by the method...

Topics: NASA Technical Reports Server (NTRS), ANNUAL VARIATIONS, DIURNAL VARIATIONS, FLUX DENSITY,...

Presented is a re-derivation of the eddy viscous dissipation tensor commonly used in present oceanographic general circulation models. When isotropy is imposed, the currently-used form of the tensor fails to return to the laplacian operator. In this paper, the source of this error is identified in a consistent derivation of the tensor in both rectangular and earth spherical coordinates, and the correct form of the eddy viscous tensor is presented.

Topics: NASA Technical Reports Server (NTRS), DISSIPATION, EDDY VISCOSITY, OCEAN CURRENTS, OCEAN MODELS,...