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NASA NTRS2020

Multigrid Preconditioning for a Space-Time Spectral-Element Discontinuous-Galerkin Solver

In this work we examine a multigrid preconditioning approach in the context of a high- order tensor-product discontinuous-Galerkin spectral-element solver. We couple multigrid ideas together with memory lean and efficient tensor-product preconditioned matrix-free smoothers. Block ILU(0)-preconditioned GMRES smoothers are employed on the coarsest spaces. The performance is evaluated on nonlinear problems arising from unsteady scale- resolving solutions of the Navier-Stokes equations: separated low-Mach unsteady ow over an airfoil from laminar to turbulent ow. A reduction in the number of ne space iterations is observed, which proves the efficiency of the approach in terms of preconditioning the linear systems, however this gain was not reflected in the CPU time. Finally, the preconditioner is successfully applied to problems characterized by stiff source terms such as the set of RANS equations, where the simple tensor product preconditioner fails. Theoretical justification about the findings is reported and future work is outlined.

Franciolini, Matteo↗

NASA NTRS1999

Plane Smoothers for Multiblock Grids: Computational Aspects

Standard multigrid methods are not well suited for problems with anisotropic discrete operators, which can occur, for example, on grids that are stretched in order to resolve a boundary layer. One of the most efficient approaches to yield robust methods is the combination of standard coarsening with alternating-direction plane relaxation in the three dimensions. However, this approach may be difficult to implement in codes with multiblock structured grids because there may be no natural definition of global lines or planes. This inherent obstacle limits the range of an implicit smoother to only the portion of the computational domain in the current block. This report studies in detail, both numerically and analytically, the behavior of blockwise plane smoothers in order to provide guidance to engineers who use block-structured grids. The results obtained so far show alternating-direction plane smoothers to be very robust, even on multiblock grids. In common computational fluid dynamics multiblock simulations, where the number of subdomains crossed by the line of a strong anisotropy is low (up to four), textbook multigrid convergence rates can be obtained with a small overlap of cells between neighboring blocks.

Llorente, Ignacio M.↗

NASA NTRS2015

Geology of Pluto and Charon Overview

Pluto's surface was found to be remarkably diverse in terms of its range of landforms, terrain ages, and inferred geological processes. There is a latitudinal zonation of albedo. The conspicuous bright albedo heart-shaped feature informally named Tombaugh Regio is comprised of several terrain types. Most striking is Texas-sized Sputnik Planum, which is apparently level, has no observable craters, and is divided by polygons and ovoids bounded by shallow troughs. Small smooth hills are seen in some of the polygon-bounding troughs. These hills could either be extruded or exposed by erosion. Sputnik Planum polygon/ovoid formation hypotheses range from convection to contraction, but convection is currently favored. There is evidence of flow of plains material around obstacles. Mountains, especially those seen south of Sputnik Planum, exhibit too much relief to be made of CH4, CO, or N2, and thus are probably composed of H2O-ice basement material. The north contact of Sputnik Planum abuts a scarp, above which is heavily modified cratered terrain. Pluto's large moon Charon is generally heavily to moderately cratered. There is a mysterious structure in the arctic. Charon's surface is crossed by an extensive system of rift faults and graben. Some regions are smoother and less cratered, reminiscent of lunar maria. On such a plain are large isolated block mountains surrounded by moats. At this conference we will present highlights of the latest observations and analysis. This work was supported by NASA's New Horizons project

Sputnik Planum↗

NASA NTRS2003

Production of Near-Mirror Surface Quality by Precision Grinding

Mechanical components such as gears and bearings operate with the working surfaces in intimate contact with a mating part. The performance of such components will be influenced by the quality of the working surface. In general, a smoother surface will perform better than a rougher surface since the lubrication conditions are improved. For example, surfaces with a special near-mirror quality finish of low roughness performed better than ground surfaces when tested using a block-on-ring arrangement. Bearings with near-mirror quality have been tested and analyzed; lower running torques were measured and improved fatigue life was anticipated. Experiments have been done to evaluate the performance of gears with improved, low roughness surface finishing. The measured performance improvements include an increased scuffing (scoring) load capacity by a factor of 1.6, a 30-percent reduction of gear tooth running friction, and longer fatigue lives by a factor of about four. One can also anticipate that near-mirror quality surface finishing could improve the performance of other mechanical components such as mechanical seals and heavily loaded journal bearings. Given these demonstrated benefits, capable and economical methods for the production of mechanical components with near-mirror quality surfaces are desired. One could propose the production of near-mirror quality surfaces by several methods such as abrasive polishing, chemical assisted polishing, or grinding. Production of the surfaces by grinding offers the possibility to control the macro-geometry (form), waviness, and surface texture with one process. The present study was carried out to investigate the possibility of producing near-mirror quality surfaces by grinding. The present study makes use of a specially designed grinding machine spindle to improve the surface quality relative to the quality produced when using a spindle of conventional design.

Dimofte, Florin↗

NASA NTRS1997

Multi-Scale Fractal Analysis of Image Texture and Pattern

Fractals embody important ideas of self-similarity, in which the spatial behavior or appearance of a system is largely scale-independent. Self-similarity is a property of curves or surfaces where each part is indistinguishable from the whole. The fractal dimension D of remote sensing data yields quantitative insight on the spatial complexity and information content contained within these data. Analyses of Normalized Difference Vegetation Index (NDVI) images of homogeneous land covers near Huntsville, Alabama revealed that the fractal dimension of an image of an agricultural land cover indicates greater complexity as pixel size increases, a forested land cover gradually grows smoother, and an urban image remains roughly self-similar over the range of pixel sizes analyzed(l0 to 80 meters). The forested scene behaves as one would expect-larger pixel sizes decrease the complexity of the image as individual clumps of trees are averaged into larger blocks. The increased complexity of the agricultural image with increasing pixel size results from the loss of homogeneous groups of pixels in the large fields to mixed pixels composed of varying combinations of NDVI values that correspond to roads and vegetation. The same process occur's in the urban image to some extent, but the lack of large, homogeneous areas in the high resolution NDVI image means the initially high D value is maintained as pixel size increases. The slope of the fractal dimension-resolution relationship provides indications of how image classification or feature identification will be affected by changes in sensor resolution.

Emerson, Charles W.↗