SEARCH · Search NASA
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.
An overview is given of Landsat Thematic Mapper resampling technique, including a modification of the well-known cubic convolution interpolator (nearest neighbor interpolation) used to provide geometric correction for TM data. Post launch study has shown that the modified cubic convolution interpolator can selectively enhance or suppress frequency bands in the output image. This selectivity is demonstrated on TM Band 3 imagery.
Efforts in transferring computational work from the LRC computer to the IRIS Graphics Workstation at MSU are reported and the computation of a conservative solution of a simple hyperbolic equation on an overlapping grid is discussed. Several conclusions concerning computations on overlapping grids are apparent. Problems only occur when there is a major difference in grid spacing on the individual component grids. In the case of hyperbolic equations, it is necessary that both interpolation and extrapolation be applied at the grid boundaries. When interpolated values are used at outflow boundary points, excessive oscillations in the numerical solution may be the result. The same conclusions would be valid for more complicated systems of hyperbolic equations such as the Euler equations for inviscid flow. Some of the solution values would be extrapolated at the overlap boundary, the exact number depending on the number of characteristics pointing out of the overlap region. It is also possible that similar boundary conditions may be needed for some parabolic equations such as high Reynolds number viscous flow equations. Efforts were also expended on the development of three-dimensional conservative interpolation procedures. Finally, the investigation of grid smoothing procedures were initiated during this reporting period. It was decided that the first grid smoothing algorithms will be based on the concepts of variational grid generation.
A method of interpolating atmospheric soundings while reducing the errors associated with simple time interpolation was developed. The purpose of this was to provide a means to determine atmospheric stability at times between standard soundings and to relate changes in stability to intensity changes in an MCC. Four MCC cases were chosen for study with this method with four stability indices being included. The discussion centers on three aspects for each stability parameter examined: the stability field in the vicinity of the storm and its changes in structure and magnitude during the lifetime of the storm, the average stability within the storm boundary as a function of time and its relation to storm intensity, and the apparent flux of stability parameter into the storm as a consequence of low-level storm relative flow. It was found that the results differed among the four stability parameters, sometimes in a conflicting fashion. Thus, an interpolation of how the storm intensity is related to the changing environmental stability depends upon the particular index utilized. Some explanation for this problem is offered.
A velocity-pressure integrated, mixed interpolation, Galerkin finite element method for the Navier-Stokes equations is presented. In the method, the velocity variables are interpolated using complete quadratic shape functions, and the pressure is interpolated using linear shape functions which are defined on a triangular element for the two-dimensional case and on a tetrahedral element for the three-dimensional case. The triangular element and the tetrahedral element are contained inside the complete bi- and tri-quadratic elements for velocity variables for two and three dimensional cases, respectively, so that the pressure is discontinuous across the element boundaries. Example problems considered include: a cavity flow of Reynolds numbers 400 through 10,000; a laminar backward facing step flow; and a laminar flow in a square duct of strong curvature. The computational results compared favorably with the finite difference computational results and/or experimental data available. It was found that the present method can capture the delicate pressure driven recirculation zones, that the method did not yield any spurious pressure modes, and that the method requires fewer grid points than the finite difference methods to obtain comparable computational results.
Prony coefficients found by computer program, without trial and error. Computational method and computer program developed to exploit full potential of Prony's interpolation method in analysis of experimental data on relaxation modules of viscoelastic material. Prony interpolation curve chosen to give least-squares best fit to "B-spline" interpolation of experimental data.
Velocity-pressure integrated and consistent penalty finite element computations of high Reynolds number, laminar flows are presented. In both of the methods, the pressure has been interpolated using linear shape functions for a triangular element. The triangular element is contained inside the bi-quadratic isoparametric element. It has been reported previously that the pressure interpolation method, when used in the velocity-pressure integrated method, yielded accurate computational results for high Reynolds number flows. It is shown that use of the same pressure interpolation method in the consistent penalty finite element method yielded accurate velocity and pressure fields which were comparable to those obtained using the velocity-pressure integrated method. Accuracy of the two finite element methods has been demonstrated by comparing the computational results with available experimental data and/or fine-grid finite difference computational results. Advantages and disadvantages of the two methods are discussed on the basis of accuracy and convergence nature. Example problems considered include a lid-driven cavity flow for Reynolds number of 10,000, a laminar backward-facing step flow, a laminar flow through a nest of cylinders, and a channel flow with an internal blockage. A finite element computer program (NSFLOW/P) for the 2-D, incompressible Navier-Stokes equations is also presented.
Algebraic grid generation is the direct expression of a physical coordinate system as a function of a uniform grid in a rectangular computational coordinate system. Algebraic grid generation is based on mathematical interpolation and is presented in general terms of multivariate transfinite interpolation. The multisurface method and the two-boundary technique are described as univariate procedures that can be applied within the context of transfinite interpolation. A technique for grid clustering is described. Problems that are commonly encountered in three-dimensional grid generation are discussed and approaches for dealing with complex physical domains using multiple computational grid blocks are presented.
A velocity-pressure-integrated mixed-interpolation Galerkin finite-element computation of the Navier-Stokes equations using the grids is presented. The velocity variables are interpolated using complete quadratic shape functions, and the pressure was interpolated using linear shape functions defined on a triangular element which is contained inside the quadratic element for velocity variables. Comprehensive computational results for a cavity flow at Reynolds number Re = 400-10,000 and a laminar backward-facing step flow at Re = 100-900 are presented. Many high-Re flows involve convection-dominated motion as well as diffusion-dominated motion in the flow domain. The computational results for both of the fluid motions compared favorably with high-accuracy finite-difference computational results and/or experimental data.
Velocity-pressure integrated and consistent penalty finite element computations of high Reynolds number laminar flows are presented. In both methods the pressure has been interpolated using linear shape functions for a triangular element which is contained inside the biquadratic flow element. It has been shown previously that the pressure interpolation method, when used in conjunction with the velocity-pressure integrated method, yields accurate computational results for high-Reynolds-number flows. It is shown in this paper that use of the same pressure interpolation method in the consistent penalty finite element method yields computational results which are comparable to those of the velocity-pressure integrated method for both the velocity and the pressure fields. Accuracy of the two finite element methods has been demonstrated by comparing the computational results with available experimental data and/or fine grid finite difference computational results. Advantages and disadvantages of the two finite element methods are discussed on the basis of accuracy and convergence nature. Example problems considered include a lid-driven cavity flow of Reynolds number 10000, a laminar backward-facing step flow and a laminar flow through a nest of cylinders.
A simple procedure was developed and applied for the grid generation around an airplane geometry. This approach is based on a transfinite interpolation with Lagrangian interpolation for the blending functions. A monotonic rational quadratic spline interpolation was employed for the grid distributions.
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.
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.
A simple procedure has been developed and applied for the grid generation around an airplane geometry. This approach is based on a transfinite interpolation with Lagrangian interpolation for the blending functions. A monotonic rational quadratic spline interpolation has been employed for the grid distributions.
An algorithm is described for learning image interpolation functions for sensor arrays whose sensor positions are somewhat disordered. The learning is based on failures of translation invariance, so it does not require knowledge of the images being presented to the visual system. Previously reported implementations of the method assumed the visual system to have precise knowledge of the translations. It is demonstrated that translation estimates computed from the imperfectly interpolated images can have enough accuracy to allow the learning process to converge to a correct interpolation.
An efficient computer program called GRID2D/3D has been developed to generate single and composite grid systems within geometrically complex two- and three-dimensional (2D and 3D) spatial domains that can deform with time. GRID2D/3D generates single grid systems by using algebraic grid generation methods based on transfinite interpolation. The distribution of grid points within the spatial domain is controlled by stretching functions and grid lines can intersect boundaries of the spatial domain orthogonally. GRID2D/3D generates composite grid systems by patching together two or more single grid systems. The patching can be discontinuous or continuous. For 2D spatial domains the boundary curves are constructed by using either cubic or tension spline interpolation. For 3D spatial domains the boundary surfaces are constructed by using a new technique, developed in this study, referred to as 3D bidirectional Hermite interpolation.
An essentially non-oscillatory reconstruction for functions defined on finite-element type meshes was designed. Two related problems are studied: the interpolation of possibly unsmooth multivariate functions on arbitrary meshes and the reconstruction of a function from its average in the control volumes surrounding the nodes of the mesh. Concerning the first problem, we have studied the behavior of the highest coefficients of the Lagrange interpolation function which may admit discontinuities of locally regular curves. This enables us to choose the best stencil for the interpolation. The choice of the smallest possible number of stencils is addressed. Concerning the reconstruction problem, because of the very nature of the mesh, the only method that may work is the so called reconstruction via deconvolution method. Unfortunately, it is well suited only for regular meshes as we show, but we also show how to overcome this difficulty. The global method has the expected order of accuracy but is conservative up to a high order quadrature formula only. Some numerical examples are given which demonstrate the efficiency of the method.
Most finite element schemes for solving the Navier-Stokes equations can be categorized into the Galerkin mixed method and the penalty method. The mixed method leads to a saddle-point problem. In order to guarantee the existence of a solution, the combination of velocity and pressure interpolations requires satisfaction of the Ladyzhenskaya Babuska Brezzi (LBB) consistency condition which precludes the use of equal order interpolations and many seemingly natural pairs of velocity and pressure elements. In a previous paper a least-squares finite element method based on the first order velocity-pressure-vorticity formulation for the Stokes problem was proposed. This method leads to a minimization problem. The choice of combination of elements is thus not subject to the LBB condition. The numerical experiments exhibit the optimal rate of convergence for all variables with equal order interpolations. A theoretical error analysis supports the numerical results. In this paper the least-squares finite element method is extended to solving the incompressible Navier-Stokes problem.
Knowledge of the three-dimensional world is essential for many guidance and navigation applications. A sequence of images from an electro-optical sensor can be processed using optical flow algorithms to provide a sparse set of ranges as a function of azimuth and elevation. A natural way to enhance the range map is by interpolation. However, this should be undertaken with care since interpolation assumes continuity of range. The range is continuous in certain parts of the image and can jump at object boundaries. In such situations, the ability to detect homogeneous object regions by scene segmentation can be used to determine regions in the range map that can be enhanced by interpolation. The use of scalar features derived from the spatial gray-level dependence matrix for texture segmentation is explored. Thresholding of histograms of scalar texture features is done for several images to select scalar features which result in a meaningful segmentation of the images. Next, the selected scalar features are used with a neural net to automate the segmentation procedure. Back-propagation is used to train the feed forward neural network. The generalization of the network approach to subsequent images in the sequence is examined. It is shown that the use of multiple scalar features as input to the neural network result in a superior segmentation when compared with a single scalar feature. It is also shown that the scalar features, which are not useful individually, result in a good segmentation when used together. The methodology is applied to both indoor and outdoor images.