Search NASA⌕ Search

SEARCH · Search NASA

Results for “Integral solution”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
NASA NTRS2015

Identifying Key Issues and Potential Solutions for Integrated Arrival, Departure, Surface Operations by Surveying Stakeholder Preferences

NASA's Aeronautics Research Mission Directorate (ARMD) collaborates with the FAA and industry to provide concepts and technologies that enhance the transition to the next-generation air-traffic management system (NextGen). To facilitate this collaboration, ARMD has a series of Airspace Technology Demonstration (ATD) sub-projects that develop, demonstrate, and transitions NASA technologies and concepts for implementation in the National Airspace System (NAS). The second of these sub-projects, ATD-2, is focused on the potential benefits to NAS stakeholders of integrated arrival, departure, surface (IADS) operations. To determine the project objectives and assess the benefits of a potential solution, NASA surveyed NAS stakeholders to understand the existing issues in arrival, departure, and surface operations, and the perceived benefits of better integrating these operations. NASA surveyed a broad cross-section of stakeholders representing the airlines, airports, air-navigation service providers, and industry providers of NAS tools. The survey indicated that improving the predictability of flight times (schedules) could improve efficiency in arrival, departure, and surface operations. Stakeholders also mentioned the need for better strategic and tactical information on traffic constraints as well as better information sharing and a coupled collaborative planning process that allows stakeholders to coordinate IADS operations. To assess the impact of a potential solution, NASA sketched an initial departure scheduling concept and assessed its viability by surveying a select group of stakeholders for a second time. The objective of the departure scheduler was to enable flights to move continuously from gate to cruise with minimal interruption in a busy metroplex airspace environment using strategic and tactical scheduling enhanced by collaborative planning between airlines and service providers. The stakeholders agreed that this departure concept could improve schedule predictability and suggested several key attributes that were necessary to make the concept successful. The goals and objectives of the planned ATD-2 sub-project will incorporate the results of this stakeholder feedback.

integrated arrival/departure/surface operations↗
NASA NTRS1993

An integral equation solution for multistage turbomachinery design calculations

A method was developed to calculate flows in multistage turbomachinery. The method is an extension of quasi-three-dimensional blade-to-blade solution methods. Governing equations for steady compressible inviscid flow are linearized by introducing approximations. The linearized flow equations are solved using integral equation techniques. The flows through both stationary and rotating blade rows are determined in a single calculation. Multiple bodies can be modelled for each blade row, so that arbitrary blade counts can be analyzed. The method's benefits are its speed and versatility.

Mcfarland, Eric R.↗
NASA NTRS1977

A program for the solution of integral equations

The program, first written in REDUCE, was implemented in MACSYMA with several additional techniques which are explained. By utilizing many methods, the program can obtain closed-form and series solutions to a large class of linear and nonlinear problems. One of the techniques developed, reduction to a differential equation, has not previously appeared in the literature in the general form described.

Bogen, R. A.↗
NASA NTRS1996

Scalable Solutions to Integral Equation and Finite Element Simulations

The application of advanced computer architecture and software to a broad range of electromagnetic problems had allowed more accurate simulations of electrically larger and more complex components and systems...This paper overviews solutions to Maxwell's equations implicitly defined through systems of linear equations.

parallel↗
NASA NTRS1987

On the solution of integral equations with a generalized Cauchy kernel

A numerical technique is developed analytically to solve a class of singular integral equations occurring in mixed boundary-value problems for nonhomogeneous elastic media with discontinuities. The approach of Kaya and Erdogan (1987) is extended to treat equations with generalized Cauchy kernels, reformulating the boundary-value problems in terms of potentials as the unknown functions. The numerical implementation of the solution is discussed, and results for an epoxy-Al plate with a crack terminating at the interface and loading normal to the crack are presented in tables.

Kaya, A. C.↗
NASA NTRS1975

A three-dimensional viscoelastic model of a strike slip fault

An analytic approximation to the Green's function for the displacements due to a strike slip point source in an elastic layer over a viscoelastic half-space is developed. This approximate Green's function is useful because it can be analytically integrated over the fault surface. Comparison with a numerical integration of the exact solution integral indicates that the approximation is quite good. The approximate Green's function is integrated analytically to obtain the displacements due to a finite rectangular strike slip fault in an elastic layer over a viscoelastic half-space. Ground displacements and angle changes from a model survey net are computed to illustrate the viscoelastic relaxation which follows a fracture in the elastic region.

Rundle, J. B.↗
NASA NTRS1986

On the solution of integral equations with a generalized cauchy kernel

In this paper a certain class of singular integral equations that may arise from the mixed boundary value problems in nonhomogeneous materials is considered. The distinguishing feature of these equations is that in addition to the Cauchy singularity, the kernels contain terms that are singular only at the end points. In the form of the singular integral equations adopted, the density function is a potential or a displacement and consequently the kernel has strong singularities of the form (t-x) sup-2, x sup n-2 (t+x) sup n, (n or = 2, 0x,tb). The complex function theory is used to determine the fundamental function of the problem for the general case and a simple numerical technique is described to solve the integral equation. Two examples from the theory of elasticity are then considered to show the application of the technique.

Kaya, A. C.↗
NASA NTRS1986

On the solution of integral equations with a generalized cauchy kernal

A certain class of singular integral equations that may arise from the mixed boundary value problems in nonhonogeneous materials is considered. The distinguishing feature of these equations is that in addition to the Cauchy singularity, the kernels contain terms that are singular only at the end points. In the form of the singular integral equations adopted, the density function is a potential or a displacement and consequently the kernal has strong singularities of the form (t-x)(-2), x(n-2) (t+x)(n), (n is = or 2, 0 x, t b). The complex function theory is used to determine the fundamental function of the problem for the general case and a simple numerical technique is described to solve the integral equation. Two examples from the theory of elasticity are then considered to show the application of the technique.

Kaya, A. C.↗
NASA NTRS1993

An Improved Solution for Integrated Array Optics in Quasi-Optical mm and Submm Receivers: the Hybrid Antenna

The hybrid antenna discussed here is defined as a dielectric lens-antenna as a special case of an extended hemi-spherical dielectric lens that is operated in the diffraction limited regime. It is a modified version of the planar antenna on a lens scheme developed by Rutledge. The dielectric lens-antenna is fed by a planar-structure antenna, which is mounted on the flat side of the dielectric lens-antenna using it as a substrate, and the combination is termed a hybrid antenna. Beam pattern and aperture efficiency measurements were made at millimeter and submillimeter wavelengths as a function of extension of the hemi- spherical lens and different lens sizes. An optimum extension distance is found experimentally and numerically for which excellent beam patterns and simultaneously high aperture efficiencies can be achieved. At 115 GHz the aperture efficiency was measured to be (76 4 +/- 6) % for a diffraction limited beam with sidelobes below -17 dB. Results of a single hybrid antenna with an integrated Superconductor-Insulator-Superconductor (SIS) detector and a broad-band matching structure at submillimeter wavelengths are presented. The hybrid antenna is diffraction limited, space efficient in an array due to its high aperture efficiency, and is easily mass produced, thus being well suited for focal plane heterodyne receiver arrays.

Buttgenbach, Thomas H.↗
NASA NTRS2021

Systems Engineering and Assurance Modeling (SEAM): A Web-Based Solution for Integrated Mission Assurance

We present an overview of the Systems Engineering and Assurance Modeling (SEAM) platform, a web-browser-based tool which is designed to help engineers evaluate the radiation vulnerabilities and develop an assurance approach for electronic parts in space systems. The SEAM framework consists of three interconnected modeling tools, a SysML compatible system description tool, a Goal Structuring Notation (GSN) visual argument tool, and Bayesian Net and Fault Tree extraction and export tools. The SysML and GSN sections also have a coverage check application that ensures that every radiation fault identified on the SysML side is also addressed in the assurance case in GSN. The SEAM platform works on space systems of any degree of radiation hardness but is especially helpful for assessing radiation performance in systems with commercial-off-the-shelf (COTS) electronic components.

SEAM↗
NASA NTRS1989

Solution of steady and unsteady transonic-vortex flows using Euler and full-potential equations

Two methods are presented for inviscid transonic flows: unsteady Euler equations in a rotating frame of reference for transonic-vortex flows and integral solution of full-potential equation with and without embedded Euler domains for transonic airfoil flows. The computational results covered: steady and unsteady conical vortex flows; 3-D steady transonic vortex flow; and transonic airfoil flows. The results are in good agreement with other computational results and experimental data. The rotating frame of reference solution is potentially efficient as compared with the space fixed reference formulation with dynamic gridding. The integral equation solution with embedded Euler domain is computationally efficient and as accurate as the Euler equations.

Kandil, Osama A.↗
NASA NTRS2008

Regionalized Lunar South Pole Surface Navigation System Analysis

Apollo missions utilized Earth-based assets for navigation because the landings took place at lunar locations in constant view from the Earth. The new exploration campaign to the lunar south pole region will have limited Earth visibility, but the extent to which a navigation system comprised solely of Earth-based tracking stations will provide adequate navigation solutions in this region is unknown. This report presents a dilution-of-precision (DoP)-based, stationary surface navigation analysis of the performance of multiple lunar satellite constellations, Earth-based deep space network assets, and combinations thereof. Results show that kinematic and integrated solutions cannot be provided by the Earth-based deep space network stations. Also, the stationary surface navigation system needs to be operated either as a two-way navigation system or as a one-way navigation system with local terrain information, while the position solution is integrated over a short duration of time with navigation signals being provided by a lunar satellite constellation.

Welch, Bryan W.↗