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Viewgraphs on Cartesian-cell based grid generation and adaptive mesh refinement are presented. Topics covered include: grid generation; cell cutting; data structures; flow solver formulation; adaptive mesh refinement; and viscous flow.
A new algorithm for controlling the quality of multiply-refined tetrahedral meshes is presented in this paper. The basic dynamic mesh adaption procedure allows localized grid refinement and coarsening to efficiently capture aerodynamic flow features in computational fluid dynamics problems; however, repeated application of the procedure may significantly deteriorate the quality of the mesh. Results presented show the effectiveness of this mesh quality algorithm and its potential in the area of helicopter aerodynamics and acoustics.
Three transition interpolation schemes for use in h-or r-refinement have been analyzed in terms of accuracy, implementation ease and extendability. They include blending-function interpolation, displacement averaging, and strain matching at discrete points along the transition edge lines. The results suggest that the choice of matching depends strongly on the element formulations, (viz. displacement or assumed strain, etc.) and mesh refinement criteria employed, and to a lesser extent the choice of computer architecture (serial vs. parallel) and the equation solution procedures. A recommended pairing of some of the elements with the choice factors is suggested.
The first results of an axisymmetric magnetohydrodynamic (MHD) model of the interaction of an expanding cometary atmosphere with the solar wind are presented. The model assumes that far upstream the plasma flow lines are parallel to the magnetic field vector. The effects of mass loading and ion-neutral friction are taken into account by the governing equations, whcih are solved on an adaptively refined unstructured grid using a Monotone Upstream Centered Schemes for Conservative Laws (MUSCL)-type numerical technique. The combination of the adaptive refinement with the MUSCL-scheme allows the entire cometary atmosphere to be modeled, while still resolving both the shock and the near nucleus of the comet. The main findingsare the following: (1) A shock is formed approximately = 0.45 Mkm upstream of the comet (its location is controlled by the sonic and Alfvenic Mach numbers of the ambient solar wind flow and by the cometary mass addition rate). (2) A contact surface is formed approximately = 5,600 km upstream of the nucleus separating an outward expanding cometary ionosphere from the nearly stagnating solar wind flow. The location of the contact surface is controlled by the upstream flow conditions, the mass loading rate and the ion-neutral drag. The contact surface is also the boundary of the diamagnetic cavity. (3) A closed inner shock terminates the supersonic expansion of the cometary ionosphere. This inner shock is closer to the nucleus on dayside than on the nightside.
This workshop's double-wedge test problem is taken from one of a sequence of experiments which were performed in order to classify the various canonical interactions between a planar shock wave and a double wedge. Therefore to build up a reasonably broad picture of the performance of our mesh refinement algorithm we have simulated three of these experiments and not just the workshop case. Here, using the results from these simulations together with their experimental counterparts, we make some general observations concerning the development of mesh refinement schemes for shock wave phenomena.
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.
The COMET-AR User's Manual provides a reference manual for the Computational Structural Mechanics Testbed with Adaptive Refinement (COMET-AR), a software system developed jointly by Lockheed Palo Alto Research Laboratory and NASA Langley Research Center under contract NAS1-18444. The COMET-AR system is an extended version of an earlier finite element based structural analysis system called COMET, also developed by Lockheed and NASA. The primary extensions are the adaptive mesh refinement capabilities and a new "object-like" database interface that makes COMET-AR easier to extend further. This User's Manual provides a detailed description of the user interface to COMET-AR from the viewpoint of a structural analyst.
TURBO-GRD is a software system for interactive two-dimensional boundary/field grid generation. modification, and refinement. Its features allow users to explicitly control grid quality locally and globally. The grid control can be achieved interactively by using control points that the user picks and moves on the workstation monitor or by direct stretching and refining. The techniques used in the code are the control point form of algebraic grid generation, a damped cubic spline for edge meshing and parametric mapping between physical and computational domains. It also performs elliptic grid smoothing and free-form boundary control for boundary geometry manipulation. Internal block boundaries are constructed and shaped by using Bezier curve. Because TURBO-GRD is a highly interactive code, users can read in an initial solution, display its solution contour in the background of the grid and control net, and exercise grid modification using the solution contour as a guide. This process can be called an interactive solution-adaptive grid generation.
In this paper, we describe a community toolkit which is designed to provide parallel support with adaptive mesh capability for a large and important class of computational models, those using structured, logically cartesian meshes. The package of Fortran 90 subroutines, called PARAMESH, is designed to provide an application developer with an easy route to extend an existing serial code which uses a logically cartesian structured mesh into a parallel code with adaptive mesh refinement. Alternatively, in its simplest use, and with minimal effort, it can operate as a domain decomposition tool for users who want to parallelize their serial codes, but who do not wish to use adaptivity. The package can provide them with an incremental evolutionary path for their code, converting it first to uniformly refined parallel code, and then later if they so desire, adding adaptivity.
A local mesh refinement procedure for the CE/SE method which does not use an iterative procedure in the treatments of grid-to-grid communications is described. It is shown that a refinement ratio higher than ten can be applied successfully across a single coarse grid/fine grid interface.
This paper describes an active (real time) recognition strategy whereby information is inferred iteratively across several viewpoints in descent imagery. We will show how we use inverse theory within the context of parametric model generation, namely height and spectral reflection functions, to generate model assertions. Using this strategy in an active context implies that, from every viewpoint, the proposed system must refine its hypotheses taking into account the image and the effect of uncertainties as well. The proposed system employs probabilistic solutions to the problem of iteratively merging information (images) from several viewpoints. This involves feeding the posterior distribution from all previous images as a prior for the next view. Novel approaches will be developed to accelerate the inversion search using novel statistic implementations and reducing the model complexity using foveated vision. Foveated vision refers to imagery where the resolution varies across the image. In this paper, we allow the model to be foveated where the highest resolution region is called the foveation region. Typically, the images will have dynamic control of the location of the foveation region. For descent imagery in the Entry, Descent, and Landing (EDL) process, it is possible to have more than one foveation region. This research initiative is directed towards descent imagery in connection with NASA's EDL applications. Three-Dimensional Model Recognition, Generation, Fusion, Update, and Refinement (RGFUR or RG4) for height and the spectral reflection characteristics are in focus for various reasons, one of which is the prospect that their interpretation will provide for real time active vision for automated EDL.
We study the propagation of waves across fixed mesh refinement boundaries in linear and nonlinear model equations in 1-D and 2-D, and in the 3-D Einstein equations of general relativity. We demonstrate that using linear interpolation to set the data in guard cells leads to the production of reflected waves at the refinement boundaries. Implementing quadratic interpolation to fill the guard cells eliminates these spurious signals.
Postprocessing of point-wise data is a fundamental process in many fields of research. Numerical differentiation is a key operation in computational electromagnetics. In the case of data obtained from a finite element method with automatic mesh refinement much work needs still to be done. This paper addresses some issues in differentiating data obtained from a finite element electromagnetic code with adaptive mesh refinement, and it proposes a methodology for deriving the electric field given the magnetic field on a mesh of linear triangular elements. The procedure itself is nevertheless more general and might be extended for numerically differentiating any point-wise solution based on triangular meshes.
We evolve a linearized (Teukolsky) solution of the Einstein equations with a non-linear Einstein solver. Using this testbed, we are able to show that such gravitational waves, defined by the Weyl scalars in the Newman-Penrose formalism, propagate faithfully across mesh refinement boundaries, and use, for the first time to our knowledge, a novel algorithm due to Misner to compute spherical harmonic components of our waveforms. We show that the algorithm performs extremely well, even when the extraction sphere intersects refinement boundaries.
Structural optimization is a field of research that has experienced noteworthy growth for many years. Researchers in this area have developed optimization tools to successfully design and model structures, typically minimizing mass while maintaining certain deflection and stress constraints. Numerous optimization studies have been performed to minimize mass, deflection and stress on a benchmark cantilever truss problem. Predominantly traditional optimization theory is applied to this problem. The cross-sectional area of each member is optimized to minimize the aforementioned objectives. This paper will present a structural optimization technique that has been previously applied to compliant mechanism design. This technique demonstrates a method that combines topology optimization, geometric refinement, finite element analysis, and two forms of evolutionary computation: Genetic Algorithms and Differential Evolution to successfully optimize a benchmark structural optimization problem. An non-traditional solution to the benchmark problem is presented in this paper, specifically a geometrically refined topological solution. The design process begins with an alternate control mesh formulation, multilevel geometric smoothing operation, and an elastostatic structural analysis. The design process is wrapped in an evolutionary computing optimization toolset.
We propose an abstraction-based model checking method which relies on refinement of an under-approximation of the feasible behaviors of the system under analysis. The method preserves errors to safety properties, since all analyzed behaviors are feasible by definition. The method does not require an abstract transition relation to he generated, but instead executes the concrete transitions while storing abstract versions of the concrete states, as specified by a set of abstraction predicates. For each explored transition. the method checks, with the help of a theorem prover, whether there is any loss of precision introduced by abstraction. The results of these checks are used to decide termination or to refine the abstraction, by generating new abstraction predicates. If the (possibly infinite) concrete system under analysis has a finite bisimulation quotient, then the method is guaranteed to eventually explore an equivalent finite bisimilar structure. We illustrate the application of the approach for checking concurrent programs. We also show how a lightweight variant can be used for efficient software testing.
Structural optimization is a field of research that has experienced noteworthy growth for many years. Researchers in this area have developed optimization tools to successfully design and model structures, typically minimizing mass while maintaining certain deflection and stress constraints. Numerous optimization studies have been performed to minimize mass, deflection, and stress on a benchmark cantilever truss problem. Predominantly traditional optimization theory is applied to this problem. The cross-sectional area of each member is optimized to minimize the aforementioned objectives. This Technical Publication (TP) presents a structural optimization technique that has been previously applied to compliant mechanism design. This technique demonstrates a method that combines topology optimization, geometric refinement, finite element analysis, and two forms of evolutionary computation: genetic algorithms and differential evolution to successfully optimize a benchmark structural optimization problem. A nontraditional solution to the benchmark problem is presented in this TP, specifically a geometrically refined topological solution. The design process begins with an alternate control mesh formulation, multilevel geometric smoothing operation, and an elastostatic structural analysis. The design process is wrapped in an evolutionary computing optimization toolset.
A method of zone refining a crystal wafer (116 FIG. 1) comprising the steps of focusing a laser beam to a small spot (120) of selectable size on the surface of the crystal wafer (116) to melt a spot on the crystal wafer, scanning the small laser beam spot back and forth across the surface of the crystal wafer (116) at a constant velocity, and moving the scanning laser beam across a predetermined zone of the surface of the crystal wafer (116) in a direction normal to the laser beam scanning direction and at a selectible velocity to melt and refine the entire crystal wafer (116).