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A directional-split modular user-friendly grid-point distribution code is applied to several test problems. Grid-point spacing is determined by user-specified constants denoting maximum and minimum grid spacings and relating the relative influence of smoothness and orthogonality. Estimates of truncation error, in terms of flowfield gradients and/or geometric features, are used to determine the point distribution.
Significant enhancements are being implemented into the GRIDGEN3D, multiple block, structured grid generation software. Automatic, point-to-point, interblock connectivity will be possible through the addition of the domain entity to GRIDBLOCK's block construction process. Also, the unification of GRIDGEN2D and GRIDBLOCK has begun with the addition of edge grid point distribution capability to GRIDBLOCK. The geometric accuracy of surface grids and the ease with which databases may be obtained is being improved by adding support for standard computer-aided design formats (e.g., PATRAN Neutral and IGES files). Finally, volume grid quality was improved through addition of new SOR algorithm features and the new hybrid control function type to GRIDGEN3D.
An efficient computer program, called GRID2D/3D, was developed to generate single and composite grid systems within geometrically complex two- and three-dimensional (2- and 3-D) spatial domains that can deform with time. GRID2D/3D generates single grid systems by using algebraic grid generation methods based on transfinite interpolation in which the distribution of grid points within the spatial domain is controlled by stretching functions. All single grid systems generated by GRID2D/3D can have grid lines that are continuous and differentiable everywhere up to the second-order. Also, 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 continuous composite grid systems, the grid lines are continuous and differentiable everywhere up to the second-order except at interfaces where different single grid systems meet. At interfaces where different single grid systems meet, the grid lines are only differentiable up to the first-order. For 2-D spatial domains, the boundary curves are described by using either cubic or tension spline interpolation. For 3-D spatial domains, the boundary surfaces are described by using either linear Coon's interpolation, bi-hyperbolic spline interpolation, or a new technique referred to as 3-D bi-directional Hermite interpolation. Since grid systems generated by algebraic methods can have grid lines that overlap one another, GRID2D/3D contains a graphics package for evaluating the grid systems generated. With the graphics package, the user can generate grid systems in an interactive manner with the grid generation part of GRID2D/3D. GRID2D/3D is written in FORTRAN 77 and can be run on any IBM PC, XT, or AT compatible computer. In order to use GRID2D/3D on workstations or mainframe computers, some minor modifications must be made in the graphics part of the program; no modifications are needed in the grid generation part of the program. The theory and method used in GRID2D/3D is described.
An efficient computer program, called GRID2D/3D was developed to generate single and composite grid systems within geometrically complex two- and three-dimensional (2- and 3-D) spatial domains that can deform with time. GRID2D/3D generates single grid systems by using algebraic grid generation methods based on transfinite interpolation in which the distribution of grid points within the spatial domain is controlled by stretching functions. All single grid systems generated by GRID2D/3D can have grid lines that are continuous and differentiable everywhere up to the second-order. Also, 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 continuous composite grid systems, the grid lines are continuous and differentiable everywhere up to the second-order except at interfaces where different single grid systems meet. At interfaces where different single grid systems meet, the grid lines are only differentiable up to the first-order. For 2-D spatial domains, the boundary curves are described by using either cubic or tension spline interpolation. For 3-D spatial domains, the boundary surfaces are described by using either linear Coon's interpolation, bi-hyperbolic spline interpolation, or a new technique referred to as 3-D bi-directional Hermite interpolation. Since grid systems generated by algebraic methods can have grid lines that overlap one another, GRID2D/3D contains a graphics package for evaluating the grid systems generated. With the graphics package, the user can generate grid systems in an interactive manner with the grid generation part of GRID2D/3D. GRID2D/3D is written in FORTRAN 77 and can be run on any IBM PC, XT, or AT compatible computer. In order to use GRID2D/3D on workstations or mainframe computers, some minor modifications must be made in the graphics part of the program; no modifications are needed in the grid generation part of the program. This technical memorandum describes the theory and method used in GRID2D/3D.
A new method of background grid construction is introduced for generation of unstructured tetrahedral grids using the advancing-front technique. Unlike the conventional triangular/tetrahedral background grids which are difficult to construct and usually inadequate in performance, the new method exploits the simplicity of uniform Cartesian meshes and provides grids of better quality. The approach is analogous to solving a steady-state heat conduction problem with discrete heat sources. The spacing parameters of grid points are distributed over the nodes of a Cartesian background grid by interpolating from a few prescribed sources and solving a Poisson equation. To increase the control over the grid point distribution, a directional clustering approach is used. The new method is convenient to use and provides better grid quality and flexibility. Sample results are presented to demonstrate the power of the method.
Development of HPF versions of NPB and ARC3D has shown that HPF provides an efficient, concise way to express parallelism and to organize data traffic. The use of HPF, as noted in the papers, requires an intimate knowledge of the applications and a detailed analysis of data affinity, data movement, and data granularity. To simplify and accelerate the task of developing HPF versions of existing CFD applications we have designed and implemented ADAPT (Automatic Data Alignment and Placement Tool). ADAPT analyzes a CFD application working on a single structured grid and generates HPF TEMPLATE, (RE)DISTRIBUTION, ALIGNMENT, and INDEPENDENT directives. The directives can be generated on the nest level, subroutine level, application level, or on the application interface level. ADAPT annotates an existing CFD FORTRAN application, performing computations on single or multiple grids. On each grid the application is considered as a sequence of operators, each applied to a set of variables defined in a particular grid domain. ADAPT automatically detects implicit operators (i.e., having data dependences) and explicit operators (without data dependences). For parallelization of an explicit operator ADAPT creates a template for the operator domain, aligns arrays used in the operator with the template, distributes the template, and declares the loops over the distributed dimensions as INDEPENDENT. For parallelization of an implicit operator, the distribution of the operator's domain should be consistent with the operator's dependences. Any dependence between sections distributed on different processors would preclude parallelization if the compiler does not have an ability to pipeline computations. If a data distribution is "orthogonal" to the dependences of an implicit operator, then the loop which implements the operator can be declared as INDEPENDENT. ADAPT starts with an analysis of array index expressions of the loop nests. For each pair of arrays referenced in an assignment statement, it generates an arc in the alignment graph and annotates it with an affinity relation. The template, alignment, and distribution directives for a particular loop nest are then derived from a transitive closure of the affinity relation. A compromise of data distributions in different nests and subroutines is achieved by merging annotated alignment graphs for adjacent nests/stibroutine calls in the nest/call graph of the application in the process called distribution lifting. ADAPT has been implemented as a C++ program running in conjunction with a parallelization tool called CAPTools. ADAPT uses the parse tree, interprocedural analysis and application database generated by CAPTools. It also uses the Directed Graph class, initially implemented in p2d2 (parallel debugger oi distributed programs), and some other classes supporting symbolic computations. ADAPT uses data distribution techniques described. ADAPT was tested with ARC3D and the FT benchmark and has demonstrated a code performance within a factor of 1.5 of handwritten versions.
A scheme is presented for the automatic generation of structured overset meshes ongeometries that are defined by Boundary Representation (BRep) solids. The surface meshsystem consists of face, edge and node meshes corresponding to the three respective basicBRep entity types. A cut-cell method is introduced to improve robustness of the on-geometrydetermination test for a face mesh grid point. A geometric component tagging scheme is utilizedto enhance local grid point distribution on a configuration with a large range of geometricscales. A cap grid topology is automatically utilized around the trailing edge of wing and tailtips to enhance mesh quality and to enable more effective surface coverage. Robustness of thehyperbolic surface marching method is improved by replacing the point projection scheme witha walking scheme. Relaxation of surface grid spacing at concave corners enables automatedhigh quality hyperbolic volume mesh creation. Domain connectivity is automatically performedon the surface mesh system. A variety of test cases are presented including a re-entry capsule,two models of the Juncture Flow Experiment wing-body, five rotorcraft concept vehicles, andvarious components of the High-Lift Common Research Model from the High-Lift PredictionWorkshop 4.
The LGP successfully demonstrated that grid technology could be used to create a collaboration among research scientists, their science development machines, and distributed data to create a science production system in a nationally distributed environment. Grid technology provides a low cost and effective method of enabling production of science products by the science community. To demonstrate this, the LGP partnered with NASA GSFC scientists and used their existing science algorithms to generate virtual Landsat-like data products using distributed data resources. LGP created 48 output composite scenes with 4 input scenes each for a total of 192 scienes processed in parallel. The demonstration took 12 hours, which beat the requirement by almost 50 percent, well within the LDCM requirement to process 250 scenes per day. The LGP project also showed the successful use of workflow tools to automate the processing. Investing in this technology has led to funding for a ROSES ACCESS proposal. The proposal intends to enable an expert science user to produce products from a number of similar distributed instrument data sets using the Land Cover Change Community-based Processing and Analysis System (LC-ComPS) Toolbox. The LC-ComPS Toolbox is a collection of science algorithms that enable the generation of data with ground resolution on the order of Landsat-class instruments.
A primary scientific objective for solar flare research during the rapidly approaching maximum in solar activity is the imaging of gamma-ray and hard x ray sources of solar flare emissions. These goals will be pursued by the Gamma Ray Imaging Device (GRID) instrument, one of three instruments recently selected for NASA's Max '91 Solar Balloon Program. The GRID instrument is based on the technique of Fourier transform imaging and utilizes scanning modulation grid collimator optics to provide full-Sun imaging with 1.9-arcsecond resolution over the energy range from 20 to 700 keV at time resolutions from 0.1 to 2 s. The GRID telescope will employ 32 subcollimators, each composed of a matched pair of high-Z collimator grids separated by 5.2 meters and a phoswich scintillation spectrometer detector having no spatial resolution. The subcollimators and integrally-mounted fine aspect system are contained within a telescope canister which will be pointed to 0.1 degree accuracy and cyclically scanned to produce source modulation. The 32 subcollimators provide a uniform distribution of grid slit orientations and a logarithmic distribution of slit spacings corresponding to angular dimensions of 1.9 arcseconds to several arcminutes. The instrument is several orders of magnitude more sensitive than the HXIS instrument on the Solar Maximum Mission (SMM) and nearly 10 times more sensitive than any similar instrument scheduled to fly during the next solar maximum. The payload, designed for long-duration high-altitude balloon capability, is scheduled for its first science flight (8 to 14 days duration) from the Antarctic in January of 1992.
The Earth System Grid Federation (ESGF) is a multi-agency, international collaboration that aims at developing the software infrastructure needed to facilitate and empower the study of climate change on a global scale. The ESGF's architecture employs a system of geographically distributed peer nodes, which are independently administered yet united by the adoption of common federation protocols and application programming interfaces (APIs). The cornerstones of its interoperability are the peer-to-peer messaging that is continuously exchanged among all nodes in the federation; a shared architecture and API for search and discovery; and a security infrastructure based on industry standards (OpenID, SSL, GSI and SAML). The ESGF software is developed collaboratively across institutional boundaries and made available to the community as open source. It has now been adopted by multiple Earth science projects and allows access to petabytes of geophysical data, including the entire model output used for the next international assessment report on climate change (IPCC-AR5) and a suite of satellite observations (obs4MIPs) and reanalysis data sets (ANA4MIPs).
The effects of truncation error on the numerical solution of transonic flows using the full potential equation are studied. The effects of adapting grid point distributions to various solution aspects including shock waves is also discussed. A conclusion is that a rapid change of grid spacing is damaging to the accuracy of the flow solution. Therefore, in a solution adaptive grid application an optimal grid is obtained as a tradeoff between the amount of grid refinement and the rate of grid stretching.
A technique which controls the spacing of grid points in algebraically defined coordinate transformations is described. The technique is based on the generation of control functions which map a uniformly distributed computational grid onto parametric variables defining the physical grid. The control functions are smoothed cubic splines. Sets of control points are input for each coordinate directions to outline the control functions. Smoothed cubic spline functions are then generated to approximate the input data. The technique works best in an interactive graphics environment where control inputs and grid displays are nearly instantaneous. The technique is illustrated with the two-boundary grid generation algorithm.
The grid point distribution used in solving a partial differential equation using a numerical method has a substantial influence on the quality of the solution. An adaptive grid which adjusts as the solution changes provides the best results when the number of grid points available for use during the calculation is fixed. Basic concepts used in generating and applying adaptive grids are reviewed in this paper, and examples illustrating applications of these concepts are presented.
Algebraic grid generation methods based on transfinite interpolation called the two-boundary and four-boundary methods are applied for generating grids with highly complex boundaries. These methods yield grid point distributions that allow for accurate application to regions of sharp gradients in the physical domain or time-dependent problems with small length scale phenomena. Algebraic grids are derived using the two-boundary and four-boundary methods for applications in both two- and three-dimensional domains. Grids are developed for distinctly different geometrical problems and the two-boundary and four-boundary methods are demonstrated to be applicable to a wide class of geometries.
Automation of overset structured surface mesh generation has recently been accomplished by the creation of face, edge, and node meshes based on Boundary Representation solids as the geometry input. The current work continues the automation effort in overset volume mesh generation and domain connectivity based on the auto-generated surface meshes. All near-body curvilinear volume meshes are automatically generated using hyperbolic methods. Automation of this step is enabled by appropriate surface grid point distribution, and selection of boundary-splay and smoothing parameters based on concave and convex surface features. The off-body domain is covered by two automatically generated grid systems. The first contains a single Cartesian mesh with a uniform core enclosing all near-body volume meshes and stretched layers that extend to the far field, while the second consists of a set of small stretched Cartesian grids covering pockets of off-body orphan points. With high quality mesh overlap mostly guaranteed by the surface meshing scheme, orphan points that need to be covered by the second Cartesian mesh system are located away from the fine grid spacing region near the wall. Using line-segment and ray-pierce tests against the surface grids, hole-cutting is accomplished on both near and off-body volume grids resulting in appropriate clearances from the wall. The complete mesh generation automation process is demonstrated on five test cases where flow solutions are also computed and compared with solutions obtained using other methods.
An algebraic procedure for the generation of boundary-fitted grids about wing-fuselage configurations is presented. A wing-fuselage configuration is specified by cross sections and mathematically represented by Coons' patches. A configuration is divided into sections so that several grid blocks that either adjoin each other or partially overlap each other can be generated, and each grid has six surfaces that map into a computational cube. Grids are first determined on the six boundary surfaces and then in the interior. Grid curves that are on the surface of the configuration are derived using plane-patch intersections, and single-valued functions relating approximate arc lengths along the curves to computational coordinates define the distribution of grid points. The two-boundary technique and transfinite interpolation are used to determine the boundary surface grids that are not on the configuration, and transfinite interpolation with linear blending functions is used to determine the interior grids.
NASA Glenn Research Center, in collaboration with the aerospace industry and academia, has begun the development of technology for a future hybrid-wing body electric airplane with a turboelectric distributed propulsion (TeDP) system. It is essential to design a subscale system to emulate the TeDP power grid, which would enable rapid analysis and demonstration of the proof-of-concept of the TeDP electrical system. This paper describes how small electrical machines with their controllers can emulate all the components in a TeDP power train. The whole system model in Matlab/Simulink was first developed and tested in simulation, and the simulation results showed that system dynamic characteristics could be implemented by using the closed-loop control of the electric motor drive systems. Then we designed a subscale experimental system to emulate the entire power system from the turbine engine to the propulsive fans. Firstly, we built a system to emulate a gas turbine engine driving a generator, consisting of two permanent magnet (PM) motors with brushless motor drives, coupled by a shaft. We programmed the first motor and its drive to mimic the speed-torque characteristic of the gas turbine engine, while the second motor and drive act as a generator and produce a torque load on the first motor. Secondly, we built another system of two PM motors and drives to emulate a motor driving a propulsive fan. We programmed the first motor and drive to emulate a wound-rotor synchronous motor. The propulsive fan was emulated by implementing fan maps and flight conditions into the fourth motor and drive, which produce a torque load on the driving motor. The stator of each PM motor is designed to travel axially to change the coupling between rotor and stator. This feature allows the PM motor to more closely emulate a wound-rotor synchronous machine. These techniques can convert the plain motor system into a unique TeDP power grid emulator that enables real-time simulation performance using hardware-in-the-loop (HIL).
In this paper, we propose a distributed approach for mapping a single large application to a heterogeneous grid environment. To minimize the execution time of the parallel application, we distribute the mapping overhead to the available nodes of the grid. This approach not only provides a fast mapping of tasks to resources but is also scalable. We adopt a hierarchical grid model and accomplish the job of mapping tasks to this topology using a scheduler tree. Results show that our three-phase algorithm provides high quality mappings, and is fast and scalable.