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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 685 records · Page 38
All sourcesNASA NTRSDOE OSTI
NASA NTRS1992

More About Generating Three-Dimensional Grids About Anything

Report presents additional details of mathematical basis and potential applications of method of generating three-dimensional grids fitted to bodies having arbitrary, complicated shapes. Grids used in finite-difference or finite-volume computations of flows around bodies. Grid-generation method involves numerical solutions of Poisson's equations described in "Generating Three-Dimensional Grids About Anything" (ARC-12620).

Sorenson, Reese L.↗
NASA NTRS1996

A non-axisymmetric linearized supersonic wave drag analysis: Mathematical theory

A Mathematical theory is developed to perform the calculations necessary to determine the wave drag for slender bodies of non-circular cross section. The derivations presented in this report are based on extensions to supersonic linearized small perturbation theory. A numerical scheme is presented utilizing Fourier decomposition to compute the pressure coefficient on and about a slender body of arbitrary cross section.

Barnhart, Paul J.↗
NASA NTRS2001

Left ventricular endocardial surface detection based on real-time 3D echocardiographic data

OBJECTIVE: A new computerized semi-automatic method for left ventricular (LV) chamber segmentation is presented. METHODS: The LV is imaged by real-time three-dimensional echocardiography (RT3DE). The surface detection model, based on level set techniques, is applied to RT3DE data for image analysis. The modified level set partial differential equation we use is solved by applying numerical methods for conservation laws. The initial conditions are manually established on some slices of the entire volume. The solution obtained for each slice is a contour line corresponding with the boundary between LV cavity and LV endocardium. RESULTS: The mathematical model has been applied to sequences of frames of human hearts (volume range: 34-109 ml) imaged by 2D and reconstructed off-line and RT3DE data. Volume estimation obtained by this new semi-automatic method shows an excellent correlation with those obtained by manual tracing (r = 0.992). Dynamic change of LV volume during the cardiac cycle is also obtained. CONCLUSION: The volume estimation method is accurate; edge based segmentation, image completion and volume reconstruction can be accomplished. The visualization technique also allows to navigate into the reconstructed volume and to display any section of the volume.

Non-NASA Center↗
NASA NTRS1967

General purpose computer programs for numerically analyzing linear ac electrical and electronic circuits for steady-state conditions

Digital computer programs determine steady-state performance characteristics of active and passive linear circuits. The ac analysis program solves the basic circuit parameters. The compiler program solves these circuit parameters and in addition provides a more versatile program by allowing the user to perform mathematical and logical operations.

Egebrecht, R. A.↗
NASA NTRS1972

Detailed mathematical models of a radioisotope thermoelectric generator.

Two new models for the design and performance analysis of RTG's are outlined in this paper. The first model assumes a small-signal transient-type calculational sequence that permits the separation of steady-state operation of the generator from its dynamic behavior. The second model uses a numerical (finite difference) solution of the performance equations of the RTG. Both models enable the investigation of transient and steady-state performance of RTG's. Simplifying assumptions have been kept to a minimum in the new RTG models and these models enable the inclusion of generator end losses, axial temperature gradients and heat interchange between thermoelements and thermal insulation in RTG performance calculations in a self-consistent manner.

Dewinter, F.↗
NASA NTRS1999

Direct Numerical Simulation of Wetting and Spreading Behavior on Heterogeneous and Roughened Substrates

A method of calculation is presented that allows the simulation of the time-dependent three-dimensional motion of thin liquid layers on solid substrates for systems with finite equilibrium contact angles. The contact angle is a prescribed function of position on the substrate. Similar mathematical models are constructed for substrates with a pattern of roughness. Evolution equations are given, using the lubrication approximation, that include viscous, capillary and disjoining forces. Motion to and from dry substrate regions is made possible by use of a thin energetically-stable wetting layer. We simulate motion on heterogeneous substrates with periodic arrays of high contact-angle patches. Two different problems are treated for heterogenous substrates. The first is spontaneous motion driven only by wetting forces. If the contact-angle difference is sufficiently high, the droplet can find several different stable positions, depending on the previous history of the motion. A second simulation treats a forced cyclical motion. Energy dissipation per cycle for a heterogeneous substrate is found to be larger than for a uniform substrate with the same total energy. The Landau-Levich solution for plate removal from a liquid bath is extended to account for a pattern of roughness on the plate.

Schwartz, Leonard W.↗
NASA NTRS1979

Two dimensional aerodynamic interference effects on oscillating airfoils with flaps in ventilated subsonic wind tunnels

The numerical computation of unsteady airloads acting upon thin airfoils with multiple leading and trailing-edge controls in two-dimensional ventilated subsonic wind tunnels is studied. The foundation of the computational method is strengthened with a new and more powerful mathematical existence and convergence theory for solving Cauchy singular integral equations of the first kind, and the method of convergence acceleration by extrapolation to the limit is introduced to analyze airfoils with flaps. New results are presented for steady and unsteady flow, including the effect of acoustic resonance between ventilated wind-tunnel walls and airfoils with oscillating flaps. The computer program TWODI is available for general use and a complete set of instructions is provided.

Fromme, J.↗
NASA NTRS1981

Ascent and eruption of basaltic magma on the earth and moon

The ascent and emplacement of basaltic magma on the earth and moon is modeled by the application of geological and physical observations and constraints. Relatively simple mathematical models of the motion of gas/liquid mixtures are shown to be adequate in the treatment of basaltic eruptions, provided that allowance is made for the coalescence of gas bubbles and that realistic geological and petrochemical constraints are applied to the numerical values of variables. Because gas exsolution from magmas on the earth and moon commonly occur at depths of less than 2 km, it is generally convenient to consider separately the rise of bubble-free magmatic liquid at depth in a planetary crust and the more complex motions occurring near the surface with gas exsolution.

Wilson, L.↗
NASA NTRS1983

Research on the control of large space structures

The research effort on the control of large space structures at the University of Houston has concentrated on the mathematical theory of finite-element models; identification of the mass, damping, and stiffness matrix; assignment of damping to structures; and decoupling of structure dynamics. The objective of the work has been and will continue to be the development of efficient numerical algorithms for analysis, control, and identification of large space structures. The major consideration in the development of the algorithms has been the large number of equations that must be handled by the algorithm as well as sensitivity of the algorithms to numerical errors.

Denman, E. D.↗
NASA NTRS1972

Computer program for investigating effects of nonlinear suspension-system elastic properties on parachute inflation loads and motions

A computer program is presented by which the effects of nonlinear suspension-system elastic characteristics on parachute inflation loads and motions can be investigated. A mathematical elastic model of suspension-system geometry is coupled to the planar equations of motion of a general vehicle and canopy. Canopy geometry and aerodynamic drag characteristics and suspension-system elastic properties are tabular inputs. The equations of motion are numerically integrated by use of an equivalent fifth-order Runge-Kutta technique.

Poole, L. R.↗
NASA NTRS1972

Further analytical study of hybrid rocket combustion

Analytical studies of the transient and steady-state combustion processes in a hybrid rocket system are discussed. The particular system chosen consists of a gaseous oxidizer flowing within a tube of solid fuel, resulting in a heterogeneous combustion. Finite rate chemical kinetics with appropriate reaction mechanisms were incorporated in the model. A temperature dependent Arrhenius type fuel surface regression rate equation was chosen for the current study. The governing mathematical equations employed for the reacting gas phase and for the solid phase are the general, two-dimensional, time-dependent conservation equations in a cylindrical coordinate system. Keeping the simplifying assumptions to a minimum, these basic equations were programmed for numerical computation, using two implicit finite-difference schemes, the Lax-Wendroff scheme for the gas phase, and, the Crank-Nicolson scheme for the solid phase.

Hung, W. S. Y.↗
NASA NTRS1975

A nonlinear model for gas chromatograph systems

Fundamental engineering design techniques and concepts were studied for the optimization of a gas chromatograph-mass spectrometer chemical analysis system suitable for use on an unmanned, Martian roving vehicle. Previously developed mathematical models of the gas chromatograph are found to be inadequate for predicting peak heights and spreading for some experimental conditions and chemical systems. A modification to the existing equilibrium adsorption model is required; the Langmuir isotherm replaces the linear isotherm. The numerical technique of Crank-Nicolson was studied for use with the linear isotherm to determine the utility of the method. Modifications are made to the method eliminate unnecessary calculations which result in an overall reduction of the computation time of about 42 percent. The Langmuir isotherm is considered which takes into account the composition-dependent effects on the thermodynamic parameter, mRo.

Feinberg, M. P.↗
NASA NTRS1980

Scientific achievements from ten years of lunar laser ranging

In the 10 years since lunar laser ranging became a reality the need to analyze the observations has motivated improvements in several aspects of the mathematical model of earth-moon dynamics. Application of the data to improved estimates of the physical parameters of the earth-moon system has yielded significant astronomical, selenophysical, geophysical, and cosmological results. The scientific impact, both in improved theories and in numerical applications, is surveyed. The underlying physics and major difficulties are discussed, as well as the scientific results.

Mulholland, J. D.↗
NASA NTRS1992

Supercomputers Of The Future

Report evaluates supercomputer needs of five key disciplines: turbulence physics, aerodynamics, aerothermodynamics, chemistry, and mathematical modeling of human vision. Predicts these fields will require computer speed greater than 10(Sup 18) floating-point operations per second (FLOP's) and memory capacity greater than 10(Sup 15) words. Also, new parallel computer architectures and new structured numerical methods will make necessary speed and capacity available.

Peterson, Victor L.↗
NASA NTRS1993

Analyzing Impacts Of Meteoroids And Debris On Spacecraft

BUMPERII is modular computer program implementing numerical solution technique to calculate probability of no penetration (PNP) of spacecraft by orbiting artificial debris or impacts of meteoroids. Equation used to calculate PNP based on Poisson-distribution model applicable to similar analysis of smaller craft, but reflects more rigorous mathematical modeling of size, shape, orientation, and other characteristics of spacecraft that affect impacts, and necessary for PNP analysis of such larger structures as components of space station. Written in FORTRAN 77.

Bjorkman, Mike↗
NASA NTRS1993

The obliquity of Mars and 'climate friction'

A mathematical theory is presented which explains the increase of the mean obliquity of Mars over geologic time due to the so called 'climate friction' (i.e., the climatic changes associated with obliquity oscillations of Mars). The theory is compared with a 10 m.y. numerical integration of the equations performed for a hypothetically large amount of climate friction for two cases of the obliquity oscillations: (1) a single sinusoid and (2) a sum of three sinusoids. The theory and numerics agree for both cases within about 12 percent on the size of the secular increase in obliquity. One possible mechanism of climate friction investigated is 'postglacial rebound' on Mars. According to this theory, giant polar caps form when the obliquity is low, and slowly squeeze out an equatorial bulge. When the obliquity is high, the caps disappear, but the bulge takes some time to collapse, due to mantle viscosity, causing it to oscillate out of phase with the obliquity oscillations. This causes a secular increase in the average obliquity.

Rubincam, David P.↗
NASA NTRS1989

The Story of PI

The early history and the uses of the mathematical notation - pi - are presented through both film footage and computer animation in this 'Project Mathematics' series video. Pi comes from the first letter in the Greek word for perimeter. Archimedes, and early Greek mathematician, formulated the equations for the computation of a circle's area using pi and was the first person to seriously approximate pi numerically, although only to a few decimal places. By 1985, pi had been approximated to over one billion decimal places and was found to have no repeating pattern. One use of pi is the application of its approximation calculation as an analytical tool for determining the accuracy of supercomputers and software designs.

Apostol, Tom M.↗