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NASA NTRS1986

Constructing multicomponent phase diagrams by overlapping ZPF lines

A procedure is introduced which can be used to draw isothermal sections from a multicomponent phase diagram in a matter of minutes, regardless of the diagram complexity. In the proposed method, the zero phase fraction (ZPF) lines are drawn separately for all phases existing in the system; by overlapping these ZPF lines, the desired section is obtained. Two examples - with five components and eight components - are given to illustrate the method. Regarding the second example, it is noted that although the final diagram may be altered to create discontinuities in slope at intersection points, the diagram remains unchanged from a topological standpoint. Thus, the overlapping ZPF lines supply all the information needed to construct complex diagrams. Even if many more phases and components are involved, the final diagram can be drawn with equal facility.

Gupta, H.↗

NASA NTRS1986

Lidar telescope overlap function and effects of misalignment for unstable resonator transmitter and coherent receiver

Effects of lidar telescope overlap function modeling on the accuracy of aerosol backscatter measurements are discussed. The treatment pertains primarily to a lidar arrangement which combines high sensitivity and a large degree of geometrical signal compression but places stringent requirements on the accuracy of the overlap function modeling - coherent IR lidar with noncoaxial (side-by-side) transmit and receive telescopes. A model is presented which includes an unstable resonator transmitter and accommodates both coaxial and noncoaxial arrangements, and comparison is made to experimental results including effects of misalignment.

Ancellet, G. M.↗

NASA NTRS1988

Overlapping grids for flow field calculations

Many problems in computational fluid dynamics (CFD) involve the calculation of flow fields within or around complex geometric configurations. The flow solution is computed on a computational grid. The construction of the grid is one of the major difficulties in the application of CFD to the analysis of flow about actual aircraft configurations. Due to geometric complexity, the grid has to be constructed in simple subregions and then all of these subgrids have to be pieced together to form a complete grid for the entire flow field. The entire grid, which is called a composite grid because it is formed from many parts, may have common regions. In either case, the computation of the flow field, using any numerical algorithm, will require the transfer of information between individual subgrids. The transfer of information is more difficult with overlapping grids. Algorithms have been developed and tested for automating the transfer of information between two overlapping grids.

Mastin, Charles Wayne↗

NASA NTRS1989

An Investigation of the Overlap Between the Statistical Discrete Gust and the Power Spectral Density Analysis Methods

The results of a NASA investigation of a claimed Overlap between two gust response analysis methods: the Statistical Discrete Gust (SDG) Method and the Power Spectral Density (PSD) Method are presented. The claim is that the ratio of an SDG response to the corresponding PSD response is 10.4. Analytical results presented for several different airplanes at several different flight conditions indicate that such an Overlap does appear to exist. However, the claim was not met precisely: a scatter of up to about 10 percent about the 10.4 factor can be expected.

Perry, Boyd, III↗

NASA NTRS1988

A general explicit solution of the central overlap problem

The matrix of the normal equations of a central overlapping-plate solution with general models for frame parameters and the star parameters is inverted explicitly in terms of the inverses of the matrices in the isolated systems for the frame and star parameters. This makes it possible to calculate from explicit formulas the numerical estimates of the star and frame parameters which would follow from a rigorous overlapping-plate solution. Also, the covariance matrix of the adjustment parameters are calculated.

Eichhorn, Heinrich↗

NASA NTRS1989

An investigation of the 'Overlap' between the Statistical-Discrete-Gust and the Power-Spectral-Density analysis methods

This paper presents the results of a NASA investigation of a claimed 'Overlap' between two gust response analysis methods: the Statistical Discrete Gust (SDG) method and the Power Spectral Density (PSD) method. The claim is that the ratio of an SDG response to the corresponding PSD response is 10.4. Analytical results presented in this paper for several different airplanes at several different flight conditions indicate that such an 'Overlap' does appear to exist. However, the claim was not met precisely: a scatter of up to about 10 percent about the 10.4 factor can be expected.

Perry, Boyd, III↗

NASA NTRS1990

An overlapped grid method for multigrid, finite volume/difference flow solvers: MaGGiE

The objective is to develop a domain decomposition method via overlapping/embedding the component grids, which is to be used by upwind, multi-grid, finite volume solution algorithms. A computer code, given the name MaGGiE (Multi-Geometry Grid Embedder) is developed to meet this objective. MaGGiE takes independently generated component grids as input, and automatically constructs the composite mesh and interpolation data, which can be used by the finite volume solution methods with or without multigrid convergence acceleration. Six demonstrative examples showing various aspects of the overlap technique are presented and discussed. These cases are used for developing the procedure for overlapping grids of different topologies, and to evaluate the grid connection and interpolation data for finite volume calculations on a composite mesh. Time fluxes are transferred between mesh interfaces using a trilinear interpolation procedure. Conservation losses are minimal at the interfaces using this method. The multi-grid solution algorithm, using the coaser grid connections, improves the convergence time history as compared to the solution on composite mesh without multi-gridding.

Baysal, Oktay↗

NASA NTRS1991

Tables of square-law signal detection statistics for Hann spectra with 50 percent overlap

The Search for Extraterrestrial Intelligence, currently being planned by NASA, will require that an enormous amount of data be analyzed in real time by special purpose hardware. It is expected that overlapped Hann data windows will play an important role in this analysis. In order to understand the statistical implication of this approach, it has been necessary to compute detection statistics for overlapped Hann spectra. Tables of signal detection statistics are given for false alarm rates from 10(exp -14) to 10(exp -1) and signal detection probabilities from 0.50 to 0.99; the number of computed spectra ranges from 4 to 2000.

Deans, Stanley R.↗

NASA NTRS1992

On constructing three-dimensional overlapping grids with CMPGRD

Techniques for the construction of three-dimensional composite overlapping grids, using the grid construction program CMPGRD, are described. The overlapping approach can be used to generate grids for regions of complicated geometry. The grids can be constructed to be smooth and free from coordinate singularities. The ability to create smooth grids for complicated regions is an important first step towards the accurate numerical solution of partial differential equations. The creation of grids for surfaces defined by cross-sections such as an airplane wing is described. A method for integrating the patched surfaces generated by a computer aided design (CAD) package with the CMPGRD program is described. Additionally, the creation of grids in regions where surfaces intersect is described.

Henshaw, William D.↗

NASA NTRS1992

Application of the Chimera overlapped grid scheme to simulation of Space Shuttle ascent flows

Several issues relating to the application of Chimera overlapped grids to complex geometries and flowfields are discussed. These include the addition of geometric components with different grid topologies, gridding for intersecting pieces of geometry, and turbulence modeling in grid overlap regions. Sample results are presented for transonic flow about the Space Shuttle launch vehicle. Comparisons with wind tunnel and flight measured pressures are shown.

Buning, Pieter G.↗

NASA NTRS1994

Direct Replacement of Arbitrary Grid-Overlapping by Non-Structured Grid

A new approach that uses nonstructured mesh to replace the arbitrarily overlapped structured regions of embedded grids is presented. The present methodology uses the Chimera composite overlapping mesh system so that the physical domain of the flowfield is subdivided into regions which can accommodate easily-generated grid for complex configuration. In addition, a Delaunay triangulation technique generates nonstructured triangular mesh which wraps over the interconnecting region of embedded grids. It is designed that the present approach, termed DRAGON grid, has three important advantages: eliminating some difficulties of the Chimera scheme, such as the orphan points and/or bad quality of interpolation stencils; making grid communication in a fully conservative way; and implementation into three dimensions is straightforward. A computer code based on a time accurate, finite volume, high resolution scheme for solving the compressible Navier-Stokes equations has been further developed to include both the Chimera overset grid and the nonstructured mesh schemes. For steady state problems, the local time stepping accelerates convergence based on a Courant - Friedrichs - Leury (CFL) number near the local stability limit. Numerical tests on representative steady and unsteady supersonic inviscid flows with strong shock waves are demonstrated.

Kao, Kai-Hsiung↗

NASA NTRS1995

Adaptively-refined overlapping grids for the numerical solution of systems of hyperbolic conservation laws

Adaptive mesh refinement (AMR) in conjunction with higher-order upwind finite-difference methods have been used effectively on a variety of problems in two and three dimensions. In this paper we introduce an approach for resolving problems that involve complex geometries in which resolution of boundary geometry is important. The complex geometry is represented by using the method of overlapping grids, while local resolution is obtained by refining each component grid with the AMR algorithm, appropriately generalized for this situation. The CMPGRD algorithm introduced by Chesshire and Henshaw is used to automatically generate the overlapping grid structure for the underlying mesh.

Brislawn, Kristi D.↗

NASA NTRS1997

Sub-Plate Overlap Code Documentation

An expansion of the plate overlap method of astrometric data reduction to a single plate has been proposed and successfully tested. Each plate is (artificially) divided into sub-plates which can then be overlapped. This reduces the area of a 'plate' over which a plate model needs to accurately represent the relationship between measured coordinates and standard coordinates. Application is made to non-astrographic plates such as Schmidt plates and to wide-field astrographic plates. Indeed, the method is completely general and can be applied to any type of recording media.

Taff, L. G.↗

NASA NTRS1998

A Parallel Non-Overlapping Domain-Decomposition Algorithm for Compressible Fluid Flow Problems on Triangulated Domains

This paper considers an algebraic preconditioning algorithm for hyperbolic-elliptic fluid flow problems. The algorithm is based on a parallel non-overlapping Schur complement domain-decomposition technique for triangulated domains. In the Schur complement technique, the triangulation is first partitioned into a number of non-overlapping subdomains and interfaces. This suggests a reordering of triangulation vertices which separates subdomain and interface solution unknowns. The reordering induces a natural 2 x 2 block partitioning of the discretization matrix. Exact LU factorization of this block system yields a Schur complement matrix which couples subdomains and the interface together. The remaining sections of this paper present a family of approximate techniques for both constructing and applying the Schur complement as a domain-decomposition preconditioner. The approximate Schur complement serves as an algebraic coarse space operator, thus avoiding the known difficulties associated with the direct formation of a coarse space discretization. In developing Schur complement approximations, particular attention has been given to improving sequential and parallel efficiency of implementations without significantly degrading the quality of the preconditioner. A computer code based on these developments has been tested on the IBM SP2 using MPI message passing protocol. A number of 2-D calculations are presented for both scalar advection-diffusion equations as well as the Euler equations governing compressible fluid flow to demonstrate performance of the preconditioning algorithm.

Barth, Timothy J.↗

NASA NTRS1994

Time-Accurate Incompressible Navier-Stokes Computations with Overlapped Moving Grids

MIT flapping foil experiment was used as a validation case to evaluate the current incompressible Navier-Stokes approach with overlapped grid schemes. Steady-state calculations were carried out for overlapped and patched grids. The grid dependency, turbulence model effects, and the effect of order of differencing were investigated. Numerical results were compared against experimental data. The resulting procedure were applied to unsteady flapping foil calculations. Two upstream NACA 0025 foils perform high-frequency synchronized motion and generate unsteady flow conditions to the downstream larger stationary foil. Comparison between unsteady experimental data and numerical results from two different moving boundary procedures will be presented.

Kiris, Cetin↗

NASA NTRS2002

Termination of String Rewriting Rules that have One Pair of Overlaps

This paper presents a partial solution to the long standing open problem of termination of one-rule string rewriting. Overlaps between the two sides of the rule play a central role in existing termination criteria. We characterize termination of all one-rule string rewriting systems that have one such overlap at either end. This both completes a result of Kurth and generalizes a result of Shikishima-Tsuji et al.

Geser, Alfons↗

NASA NTRS2003

Investigation of Overlap Correction Techniques for the Micro-Pulse Lidar NETwork (MPLNET)

The Micro-Pulse Lidar NETwork (MPLNET) uses elastic-scattering lidars stationed at sites around the globe to produce aerosol and cloud vertical profiles on a continuous year-round basis. Processing of MPLNET data requires a correction for the lidar overlap function in the 0-6 km range, to take into account the loss in near-field receiver efficiency. This correction is normally determined from recording horizontal profiles that require a approximately 10 km clear line-of-sight and homogenous atmospheric conditions, limiting the practicality in which successful corrections can be obtained. An alternative overlap correction method using a secondary receiver is considered that eliminates the need for horizontal measurements. A review of both methods is presented, including a discussion of signal uncertainties.

Berkoff, T. A.↗

NASA NTRS2006

Properties of CIRRUS Overlapping Clouds as Deduced from the GOES-12 Imagery Data

Understanding the impact of cirrus clouds on modifying both the solar reflected and terrestrial emitted radiations is crucial for climate studies. Unlike most boundary layer stratus and stratocumulus clouds that have a net cooling effect on the climate, high-level thin cirrus clouds can have a warming effect on our climate. Many research efforts have been devoted to retrieving cirrus cloud properties due to their ubiquitous presence. However, using satellite observations to detect and/or retrieve cirrus cloud properties faces two major challenges. First, they are often semitransparent at visible to infrared wavelengths; and secondly, they often occur over a lower cloud system. The overlapping of high-level cirrus and low-level stratus cloud poses a difficulty in determining the individual cloud top altitudes and optical properties, especially when the signals from cirrus clouds are overwhelmed by the signals of stratus clouds. Moreover, the operational satellite retrieval algorithms, which often assume only single layer cloud in the development of cloud retrieval techniques, cannot resolve the cloud overlapping situation properly. The new geostationary satellites, starting with the Twelfth Geostationary Operational Environmental Satellite (GOES-12), are providing a new suite of imager bands that have replaced the conventional 12-micron channel with a 13.3-micron CO2 absorption channel. The replacement of the 13.3-micron channel allows for the application of a CO2-slicing retrieval technique (Chahine et al. 1974; Smith and Platt 1978), which is one of the important passive satellite methods for remote sensing the altitudes of mid to high-level clouds. Using the CO2- slicing technique is more effective in detecting semitransparent cirrus clouds than using the conventional infrared-window method.

Chang, Fu-Lung↗