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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.

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17 records

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NASA NTRS1993

MGGHAT: Elliptic PDE software with adaptive refinement, multigrid and high order finite elements

MGGHAT (MultiGrid Galerkin Hierarchical Adaptive Triangles) is a program for the solution of linear second order elliptic partial differential equations in two dimensional polygonal domains. This program is now available for public use. It is a finite element method with linear, quadratic or cubic elements over triangles. The adaptive refinement via newest vertex bisection and the multigrid iteration are both based on a hierarchical basis formulation. Visualization is available at run time through an X Window display, and a posteriori through output files that can be used as GNUPLOT input. In this paper, we describe the methods used by MGGHAT, define the problem domain for which it is appropriate, illustrate use of the program, show numerical and graphical examples, and explain how to obtain the software.

Mitchell, William F.↗

NASA NTRS1976

Symmetries in laminated composite plates

The different types of symmetry exhibited by laminated anisotropic fibrous composite plates are identified and contrasted with the symmetries of isotropic and homogeneous orthotropic plates. The effects of variations in the fiber orientation and the stacking sequence of the layers on the symmetries exhibited by composite plates are discussed. Both the linear and geometrically nonlinear responses of the plates are considered. A simple procedure is presented for exploiting the symmetries in the finite element analysis. Examples are given of square, skew and polygonal plates where use of symmetry concepts can significantly reduce the scope and cost of analysis.

Noor, A. K.↗

NASA NTRS2003

Small Scale Polygons and the History of Ground Ice on Mars

Recent progress on polygon modeling has focused on the diameter and surface relief that we expect of thermal-contraction polygons in martian permafrost. With this in mind, we developed a finite-element model of thermal-contraction-crack behavior in permafrost in a martian climate. This model was generated from a finite element code by Jay Melosh (called TECTON) originally developed for terrestrial and planetary crustal-deformation studies. We adapted this model to martian permafrost by including time (and temperature) dependent rheologies, boundary conditions, and isotropic thermal-contraction, as well as several small adaptations to a martian environment. We tested our model extensively, including comparison to an analytic solution of pre-fracture stress. We recently published an analysis of two potential sources of water for forming the recent gullies. In this work we first evaluated the potential for near-surface ground ice (in the top meter or so of soil) to melt under conditions of solar heating on sloped surfaces at high obliquity, utilizing both thermal and diffusion-based ground-ice-stability models; our results suggested that the ground ice will sublimate, and the ice table will recede to greater depths before the melting temperature can be reached. An exception can occur only for extremely salt-rich ice, depressing the freezing point.

Mellon, Michael T.↗

NASA NTRS1992

Origin of giant Martian polygons

Extensive areas of the Martian northern plains in Utopia and Acidalia planitiae are characterized by 'polygonal terrane'. Polygonal terrane consists of material cut by complex troughs defining a pattern resembling mudcracks, columnar joints, or frost-wedge polygons on earth. However, the Martian polygons are orders of magnitude larger than these potential earth analogues, leading to severe mechanical difficulties for genetic models based on simple analogy arguments. Plate-bending and finite element models indicate that shrinkage of desiccating sediment or cooling volcanics accompanied by differential compaction over buried topography can account for the stresses responsible for polygon troughs as well as the large size of the polygons. Although trough widths and depths relate primarily to shrinkage, the large scale of the polygonl pattern relates to the spacing between topographic elevations on the surface buried beneath polygonal terrane material. Geological relationships favor a sedimentary origin for polygonal terrane material, but our model is not dependent on the specific genesis. Our analysis also suggests that the polygons must have formed at a geologically rapid rate.

Mcgill, George E.↗

NASA NTRS1985

Isoparametric 3-D Finite Element Mesh Generation Using Interactive Computer Graphics

An isoparametric 3-D finite element mesh generator was developed with direct interface to an interactive geometric modeler program called POLYGON. POLYGON defines the model geometry in terms of boundaries and mesh regions for the mesh generator. The mesh generator controls the mesh flow through the 2-dimensional spans of regions by using the topological data and defines the connectivity between regions. The program is menu driven and the user has a control of element density and biasing through the spans and can also apply boundary conditions, loads interactively.

Kayrak, C.↗

NASA NTRS1996

Towards and FVE-FAC Method for Determining Thermocapillary Effects on Weld Pool Shape

Several practical materials processes, e.g., welding, float-zone purification, and Czochralski crystal growth, involve a pool of molten metal with a free surface, with strong temperature gradients along the surface. In some cases, the resulting thermocapillary flow is vigorous enough to convect heat toward the edges of the pool, increasing the driving force in a sort of positive feedback. In this work we examine this mechanism and its effect on the solid-liquid interface through a model problem: a half space of pure substance with concentrated axisymmetric surface heating, where surface tension is strong enough to keep the liquid free surface flat. The numerical method proposed for this problem utilizes a finite volume element (FVE) discretization in cylindrical coordinates. Because of the axisymmetric nature of the model problem, the control volumes used are torroidal prisms, formed by taking a polygonal cross-section in the (r, z) plane and sweeping it completely around the z-axis. Conservation of energy (in the solid), and conservation of energy, momentum, and mass (in the liquid) are enforced globally by integrating these quantities and enforcing conservation over each control volume. Judicious application of the Divergence Theorem and Stokes' Theorem, combined with a Crank-Nicolson time-stepping scheme leads to an implicit algebraic system to be solved at each time step. It is known that near the boundary of the pool, that is, near the solid-liquid interface, the full conduction-convection solution will require extremely fine length scales to resolve the physical behavior of the system. Furthermore, this boundary moves as a function of time. Accordingly, we develop the foundation of an adaptive refinement scheme based on the principles of Fast Adaptive Composite Grid methods (FAC). Implementation of the method and numerical results will appear in a later report.

Canright, David↗

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 NTRS1984

Application and enhancements of MOVIE.BYU

MOVIE.BYU (MOVIE.BRIGHAM YOUNG UNIVERSITY) is a system of programs for the display and manipulation of data representing mathematical, architectural, and topological models in which the geometry may be described in terms of panel (n-sided polygons) and solid elements or contour lines. The MOVIE.BYU system has been used in a series of applications of LaRC. One application has been the display, creation, and manipulation of finite element models in aeronautic/aerospace research. These models have been displayed on both vector and color raster devices, and the user has the option to modify color and shading parameters on these color raster devices. Another application involves the display of scalar functions (temperature, pressure, etc.) over the surface of a given model. This capability gives the researcher added flexibility in the analysis of the model and its accompanying data. Limited animation (frame-by-frame creation) has been another application of MOVIE.BYU in the modeling of kinematic processes in antenna structures.

Gates, R. L.↗

NASA NTRS1994

Buckling and vibration analysis of laminated panels using VICONOPT

The analysis aspects of the 23,000-line FORTRAN program VIPASA with constraints and optimization (VICONOPT) are described. Overall stiffness matrices assembled from the earlier exact vibration and instability of plate assemblies including shear and anisotropy (VIPASA) flat plate stiffnesses are optionally coupled by Langrangian multipliers to find critical buckling loads, or natural frequencies of undamped vibration, of prismatic assemblies of anisotropic flat plates with arbitrarily located point supports or simple transverse supporting frames. The longitudunal continuity of typical wing and fuselage panels is closely approximated because the solutions are for the infinitely long structure obtained by repeating a bay and its supports longitudinally. Any longitudinally invariant in-plane plate stresses are permitted, and very rapid solutions are guaranteed by numerous refinements, including multilevel substructuring and a method for repetitive cross sections that is exact for regular polygons used to represent cylinders. Modal displacements and stresses in or between plies of laminated plates are calculated and plotted, with values being recovered at all nodes of substructures. Comparison with usual approximate finite-element methods confirms that, for comparably converged solutions, VICONOPT is typically between 100 and 10(exp 4) times faster.

Kennedy, David↗

NASA NTRS1996

Generating Voronoi Diagrams for Curved Shapes with Divide-and-Conquer

Voronoi diagrams have been used in many practical applications including solid modeling, Numerical Control machining, Finite Element mesh generation, etc. Investigating the properties of these diagrams is an active research topic with many fruitful results. Computational techniques for Voronoi diagrams, however, have been concentrated on low order elements, for points, lines, polygons, quadratic curves and surfaces. This paper presents a divide-and-conquer scheme computing the diagrams for planar shapes bounded by closed curves commonly encountered in Computer Aided Design. These curves include analytical curves and splines. The algorithm first divides the boundary curve into sections, delimited by curve points with the minimal curvatures. Bisector branches for these sections are then generated and merged recursively to obtain the final diagram. A detailed example in the paper shows the steps of the generation and merging of the bisectors. A simple analysis of the complexity of the algorithm is also presented.

Chou, Jin J.↗

NASA NTRS1981

International Conference on Numerical Methods in Fluid Dynamics, 7th, Stanford University, Stanford and Moffett Field, CA, June 23-27, 1980, Proceedings

Topics discussed include polygon transformations in fluid mechanics, computation of three-dimensional horseshoe vortex flow using the Navier-Stokes equations, an improved surface velocity method for transonic finite-volume solutions, transonic flow calculations with higher order finite elements, the numerical calculation of transonic axial turbomachinery flows, and the simultaneous solutions of inviscid flow and boundary layer at transonic speeds. Also considered are analytical solutions for the reflection of unsteady shock waves and relevant numerical tests, reformulation of the method of characteristics for multidimensional flows, direct numerical simulations of turbulent shear flows, the stability and separation of freely interacting boundary layers, computational models of convective motions at fluid interfaces, viscous transonic flow over airfoils, and mixed spectral/finite difference approximations for slightly viscous flows.

Reynolds, W. C.↗

NASA NTRS1997

Exact Integrations of Polynomials and Symmetric Quadrature Formulas over Arbitrary Polyhedral Grids

This paper is concerned with two important elements in the high-order accurate spatial discretization of finite volume equations over arbitrary grids. One element is the integration of basis functions over arbitrary domains, which is used in expressing various spatial integrals in terms of discrete unknowns. The other consists of quadrature approximations to those integrals. Only polynomial basis functions applied to polyhedral and polygonal grids are treated here. Non-triangular polygonal faces are subdivided into a union of planar triangular facets, and the resulting triangulated polyhedron is subdivided into a union of tetrahedra. The straight line segment, triangle, and tetrahedron are thus the fundamental shapes that are the building blocks for all integrations and quadrature approximations. Integrals of products up to the fifth order are derived in a unified manner for the three fundamental shapes in terms of the position vectors of vertices. Results are given both in terms of tensor products and products of Cartesian coordinates. The exact polynomial integrals are used to obtain symmetric quadrature approximations of any degree of precision up to five for arbitrary integrals over the three fundamental domains. Using a coordinate-free formulation, simple and rational procedures are developed to derive virtually all quadrature formulas, including some previously unpublished. Four symmetry groups of quadrature points are introduced to derive Gauss formulas, while their limiting forms are used to derive Lobatto formulas. Representative Gauss and Lobatto formulas are tabulated. The relative efficiency of their application to polyhedral and polygonal grids is detailed. The extension to higher degrees of precision is discussed.

Liu, Yen↗

NASA NTRS1980

Buckling of periodic structures

Equations are developed for the buckling of a general lattice structure that has repetitive geometry. Equilibrium at a typical node is expressed using finite element techniques, and the only assumption is that the response is periodic. By basing the stiffness matrix on the exact solution of the beam column equation, accurate results are obtained for complex buckling behavior that would require a very large system of equations using conventional techniques. The present method requires the eigenvalues of only a 6x6 determinant. The results are used to study the buckling of isogrid cylinders, three-element truss columns and polygonal rings. Details of the analysis including expressions for all terms in the governing stability determinant are given.

Anderson, M. S.↗

NASA NTRS1983

Vibration characteristics of hexagonal radial rib and hoop platforms

Experiment and analysis have been used to characterize the modes of vibration of planar radial rib and hoop hexagonal platforms. Finite element analysis correlated very well with experimental results. The sensitivity of mode shapes and frequencies to cable stiffness and initial tension is presented. Threshold values have been identified, above which changes in cable stiffness do not affect the first few platform vibration modes. Primary vibration modes of the radial rib platform involve beam bending. Vibration modes of the hoop platform exhibit both beam bending and frame bending and torsion. Results indicate for low order polygonal structures, the radial rib concept produced a higher fundamental frequency. For high order polygonal structures, the hoop concept has the potential to achieve a higher fundamental frequency than the radial rib concept.

Belvin, W. K.↗

NASA NTRS1976

Calculation of subsonic and supersonic steady and unsteady aerodynamic forces using velocity potential aerodynamic elements

Expressions for calculation of subsonic and supersonic, steady and unsteady aerodynamic forces are derived, using the concept of aerodynamic elements applied to the downwash velocity potential method. Aerodynamic elements can be of arbitrary out of plane polygon shape, although numerical calculations are restricted to rectangular elements, and to the steady state case in the supersonic examples. It is suggested that the use of conforming, in place of rectangular elements, would give better results. Agreement with results for subsonic oscillating T tails is fair, but results do not converge as the number of collocation points is increased. This appears to be due to the form of expression used in the calculations. The methods derived are expected to facilitate automated flutter analysis on the computer. In particular, the aerodynamic element concept is consistent with finite element methods already used for structural analysis. The method is universal for the complete Mach number range, and, finally, the calculations can be arranged so that they do not have to be repeated completely for every reduced frequency.

Haviland, J. K.↗

NASA NTRS2017

JIGSAW-GEO (1.0): Locally Orthogonal Staggered Unstructured Grid Generation for General Circulation Modelling on the Sphere

An algorithm for the generation of non-uniform, locally orthogonal staggered unstructured spheroidal grids is described. This technique is designed to generate very high-quality staggered VoronoiDelaunay meshes appropriate for general circulation modelling on the sphere, including applications to atmospheric simulation, ocean-modelling and numerical weather prediction. Using a recently developed Frontal-Delaunay refinement technique, a method for the construction of high-quality unstructured spheroidal Delaunay triangulations is introduced. A locally orthogonal polygonal grid, derived from the associated Voronoi diagram, is computed as the staggered dual. It is shown that use of the Frontal-Delaunay refinement technique allows for the generation of very high-quality unstructured triangulations, satisfying a priori bounds on element size and shape. Grid quality is further improved through the application of hill-climbing-type optimisation techniques. Overall, the algorithm is shown to produce grids with very high element quality and smooth grading characteristics, while imposing relatively low computational expense. A selection of uniform and non-uniform spheroidal grids appropriate for high-resolution, multi-scale general circulation modelling are presented. These grids are shown to satisfy the geometric constraints associated with contemporary unstructured C-grid-type finite-volume models, including the Model for Prediction Across Scales (MPAS-O). The use of user-defined mesh-spacing functions to generate smoothly graded, non-uniform grids for multi-resolution-type studies is discussed in detail.

geophysical fluid dynamics↗

NASA NTRS1995

Adaptively Refined Euler and Navier-Stokes Solutions with a Cartesian-Cell Based Scheme

A Cartesian-cell based scheme with adaptive mesh refinement for solving the Euler and Navier-Stokes equations in two dimensions has been developed and tested. Grids about geometrically complicated bodies were generated automatically, by recursive subdivision of a single Cartesian cell encompassing the entire flow domain. Where the resulting cells intersect bodies, N-sided 'cut' cells were created using polygon-clipping algorithms. The grid was stored in a binary-tree data structure which provided a natural means of obtaining cell-to-cell connectivity and of carrying out solution-adaptive mesh refinement. The Euler and Navier-Stokes equations were solved on the resulting grids using an upwind, finite-volume formulation. The inviscid fluxes were found in an upwinded manner using a linear reconstruction of the cell primitives, providing the input states to an approximate Riemann solver. The viscous fluxes were formed using a Green-Gauss type of reconstruction upon a co-volume surrounding the cell interface. Data at the vertices of this co-volume were found in a linearly K-exact manner, which ensured linear K-exactness of the gradients. Adaptively-refined solutions for the inviscid flow about a four-element airfoil (test case 3) were compared to theory. Laminar, adaptively-refined solutions were compared to accepted computational, experimental and theoretical results.

Coirier, William J.↗