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NASA NTRS1982

Coordinate generation with precise controls over mesh properties

Powerful local controls have been developed for mesh generation with the class of multisurface coordinate transformations. The controls come from local piecewise linear interpolants, and the resulting coordinates have continuous first derivatives. At the boundaries, the mesh controls provide the capability of joining distinct coordinate systems together with continuous derivatives. Away from boundaries, a local region can be given a particular mesh form to model internal objects or to simplify a problem. Applications of the controls are illustrated with a sequence of two-dimensional examples. For simplicity, each is generated about a NACA0012 airfoil which is of unit length and with leading edge pointed in a negative x-direction.

Eiseman, P. R.↗

NASA NTRS1982

Marching grid generation using parabolic partial differential equations

The feasibility of using parabolic partial differential equations for grid generation is examined. Source terms in the form of a linear interpolation between the current grid and the outer boundary are used in generating a grid for a two-dimensional airfoil flow. Grid generation equations are derived by assuming that grid spacings are locally nonuniform on the computational domain. The grid spacing control method is described in detail, and the local orthogonality of the grid lines is discussed. An O-mesh and an H-mesh generated by the described method are shown.

Nakamura, S.↗

NASA NTRS1984

The influence of ocean surface temperature gradient and continentality on the Walker circulation. I - Prescribed tropical changes

A coarse mesh global climate model has been developed to assess ocean surface temperature (OST) gradient and continentality influences on the Walker circulation, which is characterized in the zonal plane by three pairs of clockwise and counterclockwise cells in the troposphere. The model response exhibits statistically significant changes in the intensity of the various cells and branches with small shifts in the east-west extent. The overall structure in the zonal plane for experiments with the coldest and with mean temperatures, however, remained unchanged. In an experiment involving the replacement of the South American continent by an ocean with OSTs linearly interpolated from the eastern Pacific to the western Atlantic, a dramatic change took place in the structure of the Walker circulation. It is concluded that both continentality and OST gradient are important Walker circulation forcing mechanisms.

Chervin, R. M.↗

NASA NTRS1986

Monochromatic calculations of atmospheric radiative transfer due to molecular line absorption

Sensitivity studies related to the effects of line cutoff, spectral resolution, and temperature and pressure interpolations in radiative transfer have been performed so that a data set of absorption coefficients for water vapor, CO2, and O3 may be created efficiently. Results show that computations of absorption coefficients are affected only slightly by cutting a line off at a wave number 190 times the Lorentz half width from the center, or equivalently, cutting off 0.33 percent of the line intensity from the wings. To achieve a relative cooling rate error smaller than 2 percent, it is sufficient to precompute the absorption coefficient at three temperatures (210, 250, and 290 K) and 19 pressures with Delta (log 10 p) = 0.2. The absorption coefficient at other conditions can be interpolated linearly with pressure and exponentially with a quadratic in temperature. For the spectral resolution the absorption coefficients can be adequately computed at 0.01, 0.002, 0.005, and 0.025/cm intervals in the thermal water vapor, the CO2 and O3 bands, and the solar water vapor bands, respectively, which limits the error to only a few percent in the cooling and heating rates. Using the precomputed absorption coefficients, repeated monochromatic calculations of atmospheric heating/cooling rates for radiation model developments and for comparison with less detailed calculations are no longer difficult.

Chou, M.-D.↗

NASA NTRS1987

High resolution upwind schemes for the three-dimensional incompressible Navier-Stokes equations

Based on flux-difference splitting, implicit high resolution schemes are constructed for efficient computations of steady-state solutions to the three-dimensional, incompressible Navier-Stokes equations in curvilinear coordinates. These schemes use first-order accurate Euler backward-time differencing and second-order central differencing for the viscous shear fluxes. Up to third-order accurate upwind differencing is achieved through a reconstruction of the solution from its cell averages. The reconstruction is accomplished by linear interpolation, where the node stencils are selected such that in regions of smooth solution the flow is highly resolved while spurious oscillations in regions of rapid changes in gradient are still suppressed. Fairly rapid convergence to steady-state solutions is attained with a completely vectorizable hybrid time-marching method. Flows around a sharp-edged delta wing are computed with the maximum accuracy of the upwind-differencing restricted to first-, second-, and third-order, to illustrate the effect of accuracy on the global and on the local vortical flow fields. The results are validated with experimental data.

Hartwich, PETER-M.↗

NASA NTRS1988

Testing for periodicity of extinction

The statistical techniques used by Raup and Sepkoski (1984 and 1986) to identify a 26-Myr periodicity in the biological extinction record for the past 250 Myr are reexamined, responding in detail to the criticisms of Stigler and Wagner (1987). It is argued that evaluation of a much larger set of extinction data using a time scale with 51 sampling intervals supports the finding of periodicity. In a reply by Sigler and Wagner, the preference for a 26-Myr period is attributed to a numerical quirk in the Harland et al. (1982) time scale, in which the subinterval boundaries are not linear interpolations between the stage boundaries but have 25-Myr periodicity. It is stressed that the results of the stringent statistical tests imposed do not disprove periodicity but rather indicate that the evidence and analyses presented so far are inadequate.

Raup, David M.↗

NASA NTRS1985

Modal forced vibration analysis of aerodynamically excited turbosystems

Theoretical aspects of a new capability to determine the vibratory response of turbosystems subjected to aerodynamic excitation are presented. Turbosystems such as advanced turbopropellers with highly swept blades, and axial-flow compressors and turbines can be analyzed using this capability. The capability has been developed and implemented in the April 1984 release of the general purpose finite element program NASTRAN. The dynamic response problem is addressed in terms of the normal modal coordinates of these tuned rotating cyclic structures. Both rigid and flexible hubs/disks are considered. Coriolis and centripetal accelerations, as well as differential stiffness effects are included. Generally non-uniform steady inflow fields and uniform flow fields arbitrarily inclined at small angles with respect to the axis of rotation of the turbosystem are considered sources of aerodynamic excitation. The spatial non-uniformities are considered to be small deviations from a principally uniform inflow. Subsonic and supersonic relative inflows are addressed, with provision for linearly interpolating transonic airloads.

Elchuri, V.↗

NASA NTRS1985

NASTRAN supplemental documentation for modal forced vibration analysis of aerodynamically excited turbosystems

This report is a supplemental NASTRAN document for a new capability to determine the vibratory response of turbosystems subjected to aerodynamic excitation. Supplements of NASTRAN Theoretical, User's, Programmer's, and Demonstration Manuals are included. Turbosystems such as advanced turbopropellers with highly swept blades, and axial-flow compressors and turbines can be analyzed using this capability, which has been developed and implemented in the April 1984 release of the general purpose finite element program NASTRAN. The dynamic response problem is addressed in terms of the normal modal coordinates of these tuned rotating cyclic structures. Both rigid and flexible hubs/disks are considered. Coriolis and centripetal accelerations, as well as differential stiffness effects are included. Generally nonuniform steady inflow fields and uniform flow fields arbitrarily inclined at small angles with respect to the axis of rotation of the turbosystem are considered as the sources of aerodynamic excitation. The spatial nonuniformities are considered to be small deviations from a principally uniform inflow. Subsonic relative inflows are addressed, with provision for linearly interpolating transonic airloads.

Elchuri, V.↗

NASA NTRS1989

Context dependent anti-aliasing image reconstruction

Image Reconstruction has been mostly confined to context free linear processes; the traditional continuum interpretation of digital array data uses a linear interpolator with or without an enhancement filter. Here, anti-aliasing context dependent interpretation techniques are investigated for image reconstruction. Pattern classification is applied to each neighborhood to assign it a context class; a different interpolation/filter is applied to neighborhoods of differing context. It is shown how the context dependent interpolation is computed through ensemble average statistics using high resolution training imagery from which the lower resolution image array data is obtained (simulation). A quadratic least squares (LS) context-free image quality model is described from which the context dependent interpolation coefficients are derived. It is shown how ensembles of high-resolution images can be used to capture the a priori special character of different context classes. As a consequence, a priori information such as the translational invariance of edges along the edge direction, edge discontinuity, and the character of corners is captured and can be used to interpret image array data with greater spatial resolution than would be expected by the Nyquist limit. A Gibb-like artifact associated with this super-resolution is discussed. More realistic context dependent image quality models are needed and a suggestion is made for using a quality model which now is finding application in data compression.

Beaudet, Paul R.↗

NASA NTRS1989

Semidiscrete Galerkin modelling of compressible viscous flow past a circular cone at incidence

A numerical study of the laminar and compressible boundary layer, about a circular cone in a supersonic free stream, is presented. It is thought that if accurate and efficient numerical schemes can be produced to solve the boundary layer equations, they can be joined to numerical codes that solve the inviscid outer flow. The combination of these numerical codes is competitive with the accurate, but computationally expensive, Navier-Stokes schemes. The primary goal is to develop a finite element method for the calculation of 3-D compressible laminar boundary layer about a yawed cone. The proposed method can, in principle, be extended to apply to the 3-D boundary layer of pointed bodies of arbitrary cross section. The 3-D boundary layer equations governing supersonic free stream flow about a cone are examined. The 3-D partial differential equations are reduced to 2-D integral equations by applying the Howarth, Mangler, Crocco transformations, a linear relation between viscosity, and a Blasius-type of similarity variable. This is equivalent to a Dorodnitsyn-type formulation. The reduced equations are independent of density and curvature effects, and resemble the weak form of the 2-D incompressible boundary layer equations in Cartesian coordinates. In addition the coordinate normal to the wall has been stretched, which reduces the gradients across the layer and provides high resolution near the surface. Utilizing the parabolic nature of the boundary layer equations, a finite element method is applied to the Dorodnitsyn formulation. The formulation is presented in a Petrov-Galerkin finite element form and discretized across the layer using linear interpolation functions. The finite element discretization yields a system of ordinary differential equations in the circumferential direction. The circumferential derivatives are solved by an implicit and noniterative finite difference marching scheme. Solutions are presented for a 15 deg half angle cone at angles of attack of 5 and 10 deg. The numerical solutions assume a laminar boundary layer with free stream Mach number of 7. Results include circumferential distribution of skin friction and surface heat transfer, and cross flow velocity distributions across the layer.

Meade, Andrew James, Jr.↗

NASA NTRS1991

Three dimensional unstructured multigrid for the Euler equations

The three-dimensional Euler equations are solved on unstructured tetrahedral meshes using a multigrid strategy. The driving algorithm consists of an explicit vertex-based finite-element scheme, which employs an edge-based data-structure to assemble the residuals. The multigrid approach employs a sequence of independently generated coarse and fine meshes to accelerate the convergence to steady-state of the fine grid solution. Variables, residuals and corrections are passed back and forth between the various grids of the sequence using linear interpolation. The addresses and weights for interpolation are determined in a preprocessing stage using an efficient graph traversal algorithm. The preprocessing operation is shown to require a negligible fraction of the CPU time required by the overall solution procedure, while gains in overall solution efficiencies greater than an order of magnitude are demonstrated on meshes containing up to 350,000 vertices. Solutions using globally regenerated fine meshes as well as adaptively refined meshes are given.

Mavriplis, D. J.↗

NASA NTRS1991

Digital cartography of Io

A high resolution controlled mosaic of the hemisphere of Io centered on longitude 310 degrees is produced. Digital cartographic techniques were employed. Approximately 80 Voyager 1 clear and blue filter frames were utilized. This mosaic was merged with low-resolution color images. This dataset is compared to the geologic map of this region. Passage of the Voyager spacecraft through the Io plasma torus during acquisition of the highest resolution images exposed the vidicon detectors to ionized radiation, resulting in dark-current buildup on the vidicon. Because the vidicon is scanned from top to bottom, more charge accumulated toward the bottom of the frames, and the additive error increases from top to bottom as a ramp function. This ramp function was removed by using a model. Photometric normalizations were applied using the Minnaert function. An attempt to use Hapke's photometric function revealed that this function does not adequately describe Io's limb darkening at emission angles greater than 80 degrees. In contrast, the Minnaert function accurately describes the limb darkening up to emission angles of about 89 degrees. The improved set of discrete camera angles derived from this effort will be used in conjunction with the space telemetry pointing history file (the IPPS file), corrected on 4 or 12 second intervals to derive a revised time history for the pointing of the Infrared Interferometric Spectrometer (IRIS). For IRIS observations acquired between camera shutterings, the IPPS file can be corrected by linear interpolation, provided that the spacecraft motions were continuous. Image areas corresponding to the fields of view of IRIS spectra acquired between camera shutterings will be extracted from the mosaic to place the IRIS observations and hotspot models into geologic context.

Mcewen, Alfred S.↗

NASA NTRS1992

Simulation model of a twin-tail, high performance airplane

The mathematical model and associated computer program to simulate a twin-tailed high performance fighter airplane (McDonnell Douglas F/A-18) are described. The simulation program is written in the Advanced Continuous Simulation Language. The simulation math model includes the nonlinear six degree-of-freedom rigid-body equations, an engine model, sensors, and first order actuators with rate and position limiting. A simplified form of the F/A-18 digital control laws (version 8.3.3) are implemented. The simulated control law includes only inner loop augmentation in the up and away flight mode. The aerodynamic forces and moments are calculated from a wind-tunnel-derived database using table look-ups with linear interpolation. The aerodynamic database has an angle-of-attack range of -10 to +90 and a sideslip range of -20 to +20 degrees. The effects of elastic deformation are incorporated in a quasi-static-elastic manner. Elastic degrees of freedom are not actively simulated. In the engine model, the throttle-commanded steady-state thrust level and the dynamic response characteristics of the engine are based on airflow rate as determined from a table look-up. Afterburner dynamics are switched in at a threshold based on the engine airflow and commanded thrust.

Buttrill, Carey S.↗

NASA NTRS1991

Application of artificial neural networks in nonlinear analysis of trusses

A method is developed to incorporate neural network model based upon the Backpropagation algorithm for material response into nonlinear elastic truss analysis using the initial stiffness method. Different network configurations are developed to assess the accuracy of neural network modeling of nonlinear material response. In addition to this, a scheme based upon linear interpolation for material data, is also implemented for comparison purposes. It is found that neural network approach can yield very accurate results if used with care. For the type of problems under consideration, it offers a viable alternative to other material modeling methods.

Alam, J.↗

NASA NTRS1993

Rapid exploration of curvilinear grids using direct volume rendering

Fast techniques for direct volume rendering over curvilinear grids of hexahedral cells are developed. This type of 3D grid is common in computational fluid dynamics and finite element analysis. Four new projection methods are presented and compared with each other and with previous methods for tetrahedral grids and rectilinear grids. All four methods use polygon-rendering hardware for speed. A simplified algorithm for visibility ordering, which is based on a combination of breadth-first and depth-first searches, is described. A new multi-pass blending method is described that reduces visual artifacts that are introduced by linear interpolation in hardware where exponential interpolation is needed. Multi-pass blending is of equal interest to hardware-oriented projection methods used on rectilinear grids. Visualization tools that permit rapid data banding and cycling through transfer functions, as well as region restrictions, are described.

Vangelder, Allen↗

NASA NTRS1993

Grid adaption using Chimera composite overlapping meshes

The objective of this paper is to perform grid adaptation using composite over-lapping meshes in regions of large gradient to capture the salient features accurately during computation. The Chimera grid scheme, a multiple overset mesh technique, is used in combination with a Navier-Stokes solver. The numerical solution is first converged to a steady state based on an initial coarse mesh. Solution-adaptive enhancement is then performed by using a secondary fine grid system which oversets on top of the base grid in the high-gradient region, but without requiring the mesh boundaries to join in any special way. Communications through boundary interfaces between those separated grids are carried out using tri-linear interpolation. Applications to the Euler equations for shock reflections and to a shock wave/boundary layer interaction problem are tested. With the present method, the salient features are well resolved.

Kao, Kai-Hsiung↗

NASA NTRS1993

De-Dopplerization of aircraft acoustic signals

A de-Dopplerization scheme is devised and applied to both a tonal noise source, a XV-15 aircraft, and a broadband noise source, a F-18 aircraft. The procedure is developed from the conservation equations of fluid mechanics and is described in the paper. The corrected time history is constructed by using linear interpolation in the measured time history. This was made possible by knowing the position history of the aircraft provided by radar and/or laser tracking. The XV-15 data established that the scheme can accurately account for Doppler frequency shifts. The F-18 data confirms what has been noted in prediction models and static tests pertaining to broadband shock associated noise. That is, the peak frequency increases and the peaks broaden toward the jet axis. Another issue addressed in the study is the influence of correcting for spherical spreading and Doppler amplitude on the spectral shape and overall sound pressure levels of the source. Results from this investigation confirm that the dominant noise source in high-speed jets is due to turbulent mixing.

Kelly, Jeffrey J.↗

NASA NTRS1993

Grid adaptation using Chimera composite overlapping meshes

Kao, Kai-Hsiung↗