TBGG- INTERACTIVE ALGEBRAIC GRID GENERATION
NASA Technical Reports Server (NTRS)
Smith, R. E.
1994-01-01
TBGG, Two-Boundary Grid Generation, applies an interactive algebraic grid generation technique in two dimensions. The program incorporates mathematical equations that relate the computational domain to the physical domain. TBGG has application to a variety of problems using finite difference techniques, such as computational fluid dynamics. Examples include the creation of a C-type grid about an airfoil and a nozzle configuration in which no left or right boundaries are specified. The underlying two-boundary technique of grid generation is based on Hermite cubic interpolation between two fixed, nonintersecting boundaries. The boundaries are defined by two ordered sets of points, referred to as the top and bottom. Left and right side boundaries may also be specified, and call upon linear blending functions to conform interior interpolation to the side boundaries. Spacing between physical grid coordinates is determined as a function of boundary data and uniformly spaced computational coordinates. Control functions relating computational coordinates to parametric intermediate variables that affect the distance between grid points are embedded in the interpolation formulas. A versatile control function technique with smooth cubic spline functions is also presented. The TBGG program is written in FORTRAN 77. It works best in an interactive graphics environment where computational displays and user responses are quickly exchanged. The program has been implemented on a CDC Cyber 170 series computer using NOS 2.4 operating system, with a central memory requirement of 151,700 (octal) 60 bit words. TBGG requires a Tektronix 4015 terminal and the DI-3000 Graphics Library of Precision Visuals, Inc. TBGG was developed in 1986.
A grid spacing control technique for algebraic grid generation methods
NASA Technical Reports Server (NTRS)
Smith, R. E.; Kudlinski, R. A.; Everton, E. L.
1982-01-01
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.
Structured adaptive grid generation using algebraic methods
NASA Technical Reports Server (NTRS)
Yang, Jiann-Cherng; Soni, Bharat K.; Roger, R. P.; Chan, Stephen C.
1993-01-01
The accuracy of the numerical algorithm depends not only on the formal order of approximation but also on the distribution of grid points in the computational domain. Grid adaptation is a procedure which allows optimal grid redistribution as the solution progresses. It offers the prospect of accurate flow field simulations without the use of an excessively timely, computationally expensive, grid. Grid adaptive schemes are divided into two basic categories: differential and algebraic. The differential method is based on a variational approach where a function which contains a measure of grid smoothness, orthogonality and volume variation is minimized by using a variational principle. This approach provided a solid mathematical basis for the adaptive method, but the Euler-Lagrange equations must be solved in addition to the original governing equations. On the other hand, the algebraic method requires much less computational effort, but the grid may not be smooth. The algebraic techniques are based on devising an algorithm where the grid movement is governed by estimates of the local error in the numerical solution. This is achieved by requiring the points in the large error regions to attract other points and points in the low error region to repel other points. The development of a fast, efficient, and robust algebraic adaptive algorithm for structured flow simulation applications is presented. This development is accomplished in a three step process. The first step is to define an adaptive weighting mesh (distribution mesh) on the basis of the equidistribution law applied to the flow field solution. The second, and probably the most crucial step, is to redistribute grid points in the computational domain according to the aforementioned weighting mesh. The third and the last step is to reevaluate the flow property by an appropriate search/interpolate scheme at the new grid locations. The adaptive weighting mesh provides the information on the desired concentration
Algebraic grid generation with corner singularities
NASA Technical Reports Server (NTRS)
Vinokur, M.; Lombard, C. K.
1983-01-01
A simple noniterative algebraic procedure is presented for generating smooth computational meshes on a quadrilateral topology. Coordinate distribution and normal derivative are provided on all boundaries, one of which may include a slope discontinuity. The boundary conditions are sufficient to guarantee continuity of global meshes formed of joined patches generated by the procedure. The method extends to 3-D. The procedure involves a synthesis of prior techniques stretching functions, cubic blending functions, and transfinite interpolation - to which is added the functional form of the corner solution. The procedure introduces the concept of generalized blending, which is implemented as an automatic scaling of the boundary derivatives for effective interpolation. Some implications of the treatment at boundaries for techniques solving elliptic PDE's are discussed in an Appendix.
Algebraic grid generation for wing-fuselage bodies
NASA Technical Reports Server (NTRS)
Smith, R. E.; Everton, E. L.; Kudlinski, R. A.
1984-01-01
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.
Algebraic grid generation about wing-fuselage bodies
NASA Technical Reports Server (NTRS)
Smith, R.E.; Kudlinski, R. A.; Everton, E. L.; Wiese, M. R.
1987-01-01
An algebraic procedure for generating boundary-fitted grids about wing-fuselage configurations is presented. A wing-fuselage configuration consists of two aircraft components specified by cross sections and mathematically represented by Coons' patches. Several grid blocks are constructed to cover the entire region surrounding the configuration, and each grid block maps into a computational cube. Grid points are first determined on the six boundary surfaces of a block and then in the interior. Grid points on the surface of the configuration are derived from the intersection of planes with the Coons' patch definition. Approximate arc length distributions along the resulting grid curves concentrate and disperse grid points. The two-boundary technique and transfinite interpolation are used to determine grid points on the remaining boundary surfaces and block interiors.
Algebraic grid generation with control points
NASA Technical Reports Server (NTRS)
Eiseman, Peter R.; Choo, Yung K.; Smith, Robert E.
1992-01-01
The control-point form (CPF) formulation is an algebraically defined class of coordinate transformations by means of which the interior form of the coordinates can be manipulated in the local fashion, and any boundary can be either specified or manipulated in a similar manner. Currently, the most intense activity involving CPF is with such graphic interactive codes as TurboI and TurboT, for which detailed illustrative examples are given; these have furnished experience on whose basis future interactive strategies can be developed.
Algebraic grid generation about wing-fuselage bodies
NASA Technical Reports Server (NTRS)
Smith, R. E.
1986-01-01
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. Each grid has six exterior 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 from the intersection of planes with the Coons' patch definition. Single-valued functions relating approximate arc lengths along the grid curves to a computational coordinate 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 grid.
Algebraic surface grid generation in three-dimensional space
NASA Technical Reports Server (NTRS)
Warsi, Saif
1992-01-01
An interactive program for algebraic generation of structured surface grids in three dimensional space was developed on the IRIS4D series workstations. Interactive tools are available to ease construction of edge curves and surfaces in 3-D space. Addition, removal, or redistribution of points at arbitrary locations on a general 3-D surface or curve is possible. Also, redistribution of surface grid points may be accomplished through use of conventional surface splines or a method called 'surface constrained transfinite interpolation'. This method allows the user to redistribute the grid points on the edges of a surface patch; the effect of the redistribution is then propagated to the remainder of the surface through a transfinite interpolation procedure where the grid points will be constrained to lie on the surface. The program was written to be highly functional and easy to use. A host of utilities are available to ease the grid generation process. Generality of the program allows the creation of single and multizonal surface grids according to the user requirements. The program communicates with the user through popup menus, windows, and the mouse.
On the applications of algebraic grid generation methods based on transfinite interpolation
NASA Technical Reports Server (NTRS)
Nguyen, Hung Lee
1989-01-01
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.
NASA Technical Reports Server (NTRS)
Shih, T. I.-P.; Roelke, R. J.; Steinthorsson, E.
1991-01-01
In order to study numerically details of the flow and heat transfer within coolant passages of turbine blades, a method must first be developed to generate grid systems within the very complicated geometries involved. In this study, a grid generation package was developed that is capable of generating the required grid systems. The package developed is based on an algebraic grid generation technique that permits the user considerable control over how grid points are to be distributed in a very explicit way. These controls include orthogonality of grid lines next to boundary surfaces and ability to cluster about arbitrary points, lines, and surfaces. This paper describes that grid generation package and shows how it can be used to generate grid systems within complicated-shaped coolant passages via an example.
An algebraic grid generation technique for multi body launch vehicle configurations
Balu, R.; Unnikrishnan, C.
1996-12-31
A simple algebraic grid generation method is used to generate three dimensional computational grids over multi body launch vehicle configurations. Sample grids for various configurations like, axisymmetric bodies with fins and multi body launch vehicles having a number of strap-on boosters, are presented. These grids appear to be of comparative quality to those generated by sophisticated techniques like Poisson`s equation solutions, which take enormous computing times. Viscous flow simulations using the present grids are found to be quite satisfactory for practical purposes.
Two and three dimensional grid generation by an algebraic homotopy procedure
NASA Technical Reports Server (NTRS)
Moitra, Anutosh
1990-01-01
An algebraic method for generating two- and three-dimensional grid systems for aerospace vehicles is presented. The method is based on algebraic procedures derived from homotopic relations for blending between inner and outer boundaries of any given configuration. Stable properties of homotopic maps have been exploited to provide near-orthogonality and specified constant spacing at the inner boundary. The method has been successfully applied to analytically generated blended wing-body configurations as well as discretely defined geometries such as the High-Speed Civil Transport Aircraft. Grid examples representative of the capabilities of the method are presented.
NASA Technical Reports Server (NTRS)
Moitra, Anutosh
1989-01-01
A fast and versatile procedure for algebraically generating boundary conforming computational grids for use with finite-volume Euler flow solvers is presented. A semi-analytic homotopic procedure is used to generate the grids. Grids generated in two-dimensional planes are stacked to produce quasi-three-dimensional grid systems. The body surface and outer boundary are described in terms of surface parameters. An interpolation scheme is used to blend between the body surface and the outer boundary in order to determine the field points. The method, albeit developed for analytically generated body geometries is equally applicable to other classes of geometries. The method can be used for both internal and external flow configurations, the only constraint being that the body geometries be specified in two-dimensional cross-sections stationed along the longitudinal axis of the configuration. Techniques for controlling various grid parameters, e.g., clustering and orthogonality are described. Techniques for treating problems arising in algebraic grid generation for geometries with sharp corners are addressed. A set of representative grid systems generated by this method is included. Results of flow computations using these grids are presented for validation of the effectiveness of the method.
Implementation of control point form of algebraic grid-generation technique
NASA Technical Reports Server (NTRS)
Choo, Yung K.; Miller, David P.; Reno, Charles J.
1991-01-01
The control point form (CPF) provides explicit control of physical grid shape and grid spacing through the movement of the control points. The control point array, called a control net, is a space grid type arrangement of locations in physical space with an index for each direction. As an algebraic method CPF is efficient and works well with interactive computer graphics. A family of menu-driven, interactive grid-generation computer codes (TURBO) is being developed by using CPF. Key features of TurboI (a TURBO member) are discussed and typical results are presented. TurboI runs on any IRIS 4D series workstation.
A three-dimensional algebraic grid generation scheme for gas turbine combustors with inclined slots
NASA Technical Reports Server (NTRS)
Yang, S. L.; Cline, M. C.; Chen, R.; Chang, Y. L.
1993-01-01
A 3D algebraic grid generation scheme is presented for generating the grid points inside gas turbine combustors with inclined slots. The scheme is based on the 2D transfinite interpolation method. Since the scheme is a 2D approach, it is very efficient and can easily be extended to gas turbine combustors with either dilution hole or slot configurations. To demonstrate the feasibility and the usefulness of the technique, a numerical study of the quick-quench/lean-combustion (QQ/LC) zones of a staged turbine combustor is given. Preliminary results illustrate some of the major features of the flow and temperature fields in the QQ/LC zones. Formation of co- and counter-rotating bulk flow and shape temperature fields can be observed clearly, and the resulting patterns are consistent with experimental observations typical of the confined slanted jet-in-cross flow. Numerical solutions show the method to be an efficient and reliable tool for generating computational grids for analyzing gas turbine combustors with slanted slots.
Algebraic grid generation using tensor product B-splines. Ph.D. Thesis
NASA Technical Reports Server (NTRS)
Saunders, B. V.
1985-01-01
Finite difference methods are more successful if the accompanying grid has lines which are smooth and nearly orthogonal. The development of an algorithm which produces such a grid when given the boundary description. Topological considerations in structuring the grid generation mapping are discussed. The concept of the degree of a mapping and how it can be used to determine what requirements are necessary if a mapping is to produce a suitable grid is examined. The grid generation algorithm uses a mapping composed of bicubic B-splines. Boundary coefficients are chosen so that the splines produce Schoenberg's variation diminishing spline approximation to the boundary. Interior coefficients are initially chosen to give a variation diminishing approximation to the transfinite bilinear interpolant of the function mapping the boundary of the unit square onto the boundary grid. The practicality of optimizing the grid by minimizing a functional involving the Jacobian of the grid generation mapping at each interior grid point and the dot product of vectors tangent to the grid lines is investigated. Grids generated by using the algorithm are presented.
Structured and unstructured grid generation.
Thompson, J F; Weatherill, N P
1992-01-01
Current techniques in composite-block-structured grid generation and unstructured grid generation for general 3D geometries are summarized, including both algebraic and elliptic generation procedures for the former and Delaunay tessellations for the latter. Citations of relevant theory are given. Examples of applications for several geometries are included. PMID:1424687
Barnhill, R.E.; Farin, G.; Hamann, B.
1995-12-31
This paper provides a basic overview of NURBS and their application to numerical grid generation. Curve/surface smoothing, accelerated grid generation, and the use of NURBS in a practical grid generation system are discussed.
Interactive solution-adaptive grid generation
NASA Technical Reports Server (NTRS)
Choo, Yung K.; Henderson, Todd L.
1992-01-01
TURBO-AD is an interactive solution-adaptive grid generation program under development. The program combines an interactive algebraic grid generation technique and a solution-adaptive grid generation technique into a single interactive solution-adaptive grid generation package. The control point form uses a sparse collection of control points to algebraically generate a field grid. This technique provides local grid control capability and is well suited to interactive work due to its speed and efficiency. A mapping from the physical domain to a parametric domain was used to improve difficulties that had been encountered near outwardly concave boundaries in the control point technique. Therefore, all grid modifications are performed on a unit square in the parametric domain, and the new adapted grid in the parametric domain is then mapped back to the physical domain. The grid adaptation is achieved by first adapting the control points to a numerical solution in the parametric domain using control sources obtained from flow properties. Then a new modified grid is generated from the adapted control net. This solution-adaptive grid generation process is efficient because the number of control points is much less than the number of grid points and the generation of a new grid from the adapted control net is an efficient algebraic process. TURBO-AD provides the user with both local and global grid controls.
Interactive solution-adaptive grid generation procedure
NASA Technical Reports Server (NTRS)
Henderson, Todd L.; Choo, Yung K.; Lee, Ki D.
1992-01-01
TURBO-AD is an interactive solution adaptive grid generation program under development. The program combines an interactive algebraic grid generation technique and a solution adaptive grid generation technique into a single interactive package. The control point form uses a sparse collection of control points to algebraically generate a field grid. This technique provides local grid control capability and is well suited to interactive work due to its speed and efficiency. A mapping from the physical domain to a parametric domain was used to improve difficulties encountered near outwardly concave boundaries in the control point technique. Therefore, all grid modifications are performed on the unit square in the parametric domain, and the new adapted grid is then mapped back to the physical domain. The grid adaption is achieved by adapting the control points to a numerical solution in the parametric domain using control sources obtained from the flow properties. Then a new modified grid is generated from the adapted control net. This process is efficient because the number of control points is much less than the number of grid points and the generation of the grid is an efficient algebraic process. TURBO-AD provides the user with both local and global controls.
Barnette, Daniel W.
2002-01-01
The present invention provides a method of grid generation that uses the geometry of the problem space and the governing relations to generate a grid. The method can generate a grid with minimized discretization errors, and with minimal user interaction. The method of the present invention comprises assigning grid cell locations so that, when the governing relations are discretized using the grid, at least some of the discretization errors are substantially zero. Conventional grid generation is driven by the problem space geometry; grid generation according to the present invention is driven by problem space geometry and by governing relations. The present invention accordingly can provide two significant benefits: more efficient and accurate modeling since discretization errors are minimized, and reduced cost grid generation since less human interaction is required.
An interactive grid generation technique for turbomachinery
NASA Technical Reports Server (NTRS)
Beach, Tim
1992-01-01
A combination algebraic/elliptic technique is presented for the generation of 3-D grids about turbomachinery blade rows for both axial and radial flow machinery. The technique is build around use of an advanced engineering workstation to construct several 2-D grids interactively on predetermined blade-to-blade surfaces. A 3-D grid is generated by interpolating these surface grids onto an axisymmetric grid. On each blade to blade surface, a grid is created using algebraic techniques near the blade to control orthogonality within the boundary layer region and elliptic techniques in the mid-passage to achieve smoothness. The interactive definition of bezier curves as internal boundaries is the key to simple construction. The approach is adapted for use with the average passage solution technique, although this is not a limitation for most other uses. A variety of examples are presented.
IGB grid: User's manual (A turbomachinery grid generation code)
NASA Technical Reports Server (NTRS)
Beach, T. A.; Hoffman, G.
1992-01-01
A grid generation code called IGB is presented for use in computational investigations of turbomachinery flowfields. It contains a combination of algebraic and elliptic techniques coded for use on an interactive graphics workstation. The instructions for use and a test case are included.
NASA Technical Reports Server (NTRS)
Ives, David
1995-01-01
This paper presents a highly automated hexahedral grid generator based on extensive geometrical and solid modeling operations developed in response to a vision of a designer-driven one day turnaround CFD process which implies a designer-driven one hour grid generation process.
Compactly Generated de Morgan Lattices, Basic Algebras and Effect Algebras
NASA Astrophysics Data System (ADS)
Paseka, Jan; Riečanová, Zdenka
2010-12-01
We prove that a de Morgan lattice is compactly generated if and only if its order topology is compatible with a uniformity on L generated by some separating function family on L. Moreover, if L is complete then L is (o)-topological. Further, if a basic algebra L (hence lattice with sectional antitone involutions) is compactly generated then L is atomic. Thus all non-atomic Boolean algebras as well as non-atomic lattice effect algebras (including non-atomic MV-algebras and orthomodular lattices) are not compactly generated.
Enhanced Elliptic Grid Generation
NASA Technical Reports Server (NTRS)
Kaul, Upender K.
2007-01-01
An enhanced method of elliptic grid generation has been invented. Whereas prior methods require user input of certain grid parameters, this method provides for these parameters to be determined automatically. "Elliptic grid generation" signifies generation of generalized curvilinear coordinate grids through solution of elliptic partial differential equations (PDEs). Usually, such grids are fitted to bounding bodies and used in numerical solution of other PDEs like those of fluid flow, heat flow, and electromagnetics. Such a grid is smooth and has continuous first and second derivatives (and possibly also continuous higher-order derivatives), grid lines are appropriately stretched or clustered, and grid lines are orthogonal or nearly so over most of the grid domain. The source terms in the grid-generating PDEs (hereafter called "defining" PDEs) make it possible for the grid to satisfy requirements for clustering and orthogonality properties in the vicinity of specific surfaces in three dimensions or in the vicinity of specific lines in two dimensions. The grid parameters in question are decay parameters that appear in the source terms of the inhomogeneous defining PDEs. The decay parameters are characteristic lengths in exponential- decay factors that express how the influences of the boundaries decrease with distance from the boundaries. These terms govern the rates at which distance between adjacent grid lines change with distance from nearby boundaries. Heretofore, users have arbitrarily specified decay parameters. However, the characteristic lengths are coupled with the strengths of the source terms, such that arbitrary specification could lead to conflicts among parameter values. Moreover, the manual insertion of decay parameters is cumbersome for static grids and infeasible for dynamically changing grids. In the present method, manual insertion and user specification of decay parameters are neither required nor allowed. Instead, the decay parameters are
Geometric and algebraic multigrid techniques for fluid dynamics problems on unstructured grids
NASA Astrophysics Data System (ADS)
Volkov, K. N.; Emel'yanov, V. N.; Teterina, I. V.
2016-02-01
Issues concerning the implementation and practical application of geometric and algebraic multigrid techniques for solving systems of difference equations generated by the finite volume discretization of the Euler and Navier-Stokes equations on unstructured grids are studied. The construction of prolongation and interpolation operators, as well as grid levels of various resolutions, is discussed. The results of the application of geometric and algebraic multigrid techniques for the simulation of inviscid and viscous compressible fluid flows over an airfoil are compared. Numerical results show that geometric methods ensure faster convergence and weakly depend on the method parameters, while the efficiency of algebraic methods considerably depends on the input parameters.
TIGGERC: Turbomachinery Interactive Grid Generator for 2-D Grid Applications and Users Guide
NASA Technical Reports Server (NTRS)
Miller, David P.
1994-01-01
A two-dimensional multi-block grid generator has been developed for a new design and analysis system for studying multiple blade-row turbomachinery problems. TIGGERC is a mouse driven, interactive grid generation program which can be used to modify boundary coordinates and grid packing and generates surface grids using a hyperbolic tangent or algebraic distribution of grid points on the block boundaries. The interior points of each block grid are distributed using a transfinite interpolation approach. TIGGERC can generate a blocked axisymmetric H-grid, C-grid, I-grid or O-grid for studying turbomachinery flow problems. TIGGERC was developed for operation on Silicon Graphics workstations. Detailed discussion of the grid generation methodology, menu options, operational features and sample grid geometries are presented.
Elliptic surface grid generation on minimal and parametrized surfaces
NASA Technical Reports Server (NTRS)
Spekreijse, S. P.; Nijhuis, G. H.; Boerstoel, J. W.
1995-01-01
An elliptic grid generation method, which generates boundary conforming grids in a two dimensional physical space, is presented. The method is based on the composition of an algebraic and elliptic transformation. The composite mapping obeys the Poisson grid generation system with control functions specified by the algebraic transformation. It is shown that the grid generation on a minimal surface in a three dimensional space is equivalent to the grid generation in a two dimensional domain in physical space. A second elliptic grid generation method, which generates boundary conforming grids on smooth surfaces, is presented. Concerning surface modeling, it is shown that bicubic Hermit interpolation is an excellent method to generate a smooth surface crossing a discrete set of control points.
Interactive surface grid generation
NASA Technical Reports Server (NTRS)
Luh, Raymond Ching-Chung; Pierce, Lawrence E.; Yip, David
1991-01-01
This paper describes a surface grid generation tool called S3D. It is the result of integrating a robust and widely applicable interpolation technique with the latest in workstation technology. Employing the use of a highly efficient and user-friendly graphical interface, S3D permits real-time interactive analyses of surface geometry data and facilitates the construction of surface grids for a wide range of applications in Computational Fluid Dynamics (CFD). The design objectives are for S3D to be stand-alone and easy to use so that CFD analysts can take a hands-on approach toward most if not all of their surface grid generation needs. Representative examples of S3D applications are presented in describing the various elements involved in the process.
OVERGRID: A Unified Overset Grid Generation Graphical Interface
NASA Technical Reports Server (NTRS)
Chan, William M.; Akien, Edwin W. (Technical Monitor)
1999-01-01
This paper presents a unified graphical interface and gridding strategy for performing overset grid generation. The interface called OVERGRID has been specifically designed to follow an efficient overset gridding strategy, and contains general grid manipulation capabilities as well as modules that are specifically suited for overset grids. General grid utilities include functions for grid redistribution, smoothing, concatenation, extraction, extrapolation, projection, and many others. Modules specially tailored for overset grids include a seam curve extractor, hyperbolic and algebraic surface grid generators, a hyperbolic volume grid generator, and a Cartesian box grid generator, Grid visualization is achieved using OpenGL while widgets are constructed with Tcl/Tk. The software is portable between various platforms from UNIX workstations to personal computers.
Hybrid Grid Generation Using NW Grid
Jones-Oliveira, Janet B.; Oliveira, Joseph S.; Trease, Lynn L.; Trease, Harold E.; B.K. Soni, J. Hauser, J.F. Thompson, P.R. Eiseman
2000-09-01
We describe the development and use of a hybrid n-dimensional grid generation system called NWGRID. The Applied Mathematics Group at Pacific Northwest National Laboratory (PNNL) is developing this tool to support the Laboratory's computational science efforts in chemistry, biology, engineering and environmental (subsurface and atmospheric) modeling. NWGRID is the grid generation system, which is designed for multi-scale, multi-material, multi-physics, time-dependent, 3-D, hybrid grids that are either statically adapted or evolved in time. NWGRID'S capabilities include static and dynamic grids, hybrid grids, managing colliding surfaces, and grid optimization[using reconnections, smoothing, and adaptive mesh refinement (AMR) algorithms]. NWGRID'S data structure can manage an arbitrary number of grid objects, each with an arbitrary number of grid attributes. NWGRID uses surface geometry to build volumes by using combinations of Boolean operators and order relations. Point distributions can be input, generated using either ray shooting techniques or defined point-by-point. Connectivity matrices are then generated automatically for all variations of hybrid grids.
NASA Technical Reports Server (NTRS)
Seki, Rycichi
1989-01-01
Because the governing equations in fluid dynamics contain partial differentials and are too difficult in most cases to solve analytically, these differentials are generally replaced by finite difference terms. These terms contain terms in the solution at nearby states. This procedure discretizes the field into a finite number of states. These states, when plotted, form a grid, or mesh, of points. It is at these states, or field points, that the solution is found. The optimum choice of states, the x, y, z coordinate values, minimizes error and computational time. But the process of finding these states is made more difficult by complex boundaries, and by the need to control step size differences between the states, that is, the need to control the spacing of field points. One solution technique uses a different set of state variables, which define a different coordinate system, to generate the grid more easily. A new method, developed by Dr. Joseph Steger, combines elliptic and hyperbolic partial differential equations into a mapping function between the physical and computational coordinate systems. This system of equations offers more control than either equation provides alone. The Steger algorithm was modified in order to allow bodies with stronger concavities to be used, offering the possibility of generating a single grid about multiple bodies. Work was also done on identifying areas where grid breakdown occurs.
Grid generation research at OSU
NASA Technical Reports Server (NTRS)
Nakamura, S.
1992-01-01
In the last two years, effort was concentrated on: (1) surface modeling; (2) surface grid generation; and (3) 3-D flow space grid generation. The surface modeling shares the same objectives as the surface modeling in computer aided design (CAD), so software available in CAD can in principle be used for solid modeling. Unfortunately, however, the CAD software cannot be easily used in practice for grid generation purposes, because they are not designed to provide appropriate data base for grid generation. Therefore, we started developing a generalized surface modeling software from scratch, that provides the data base for the surface grid generation. Generating surface grid is an important step in generating a 3-D space for flow space. To generate a surface grid on a given surface representation, we developed a unique algorithm that works on any non-smooth surfaces. Once the surface grid is generated, a 3-D space can be generated. For this purpose, we also developed a new algorithm, which is a hybrid of the hyperbolic and the elliptic grid generation methods. With this hybrid method, orthogonality of the grid near the solid boundary can be easily achieved without introducing empirical fudge factors. Work to develop 2-D and 3-D grids for turbomachinery blade geometries was performed, and as an extension of this research we are planning to develop an adaptive grid procedure with an interactive grid environment.
TIGGERC: Turbomachinery interactive grid generator energy distributor and restart code
NASA Technical Reports Server (NTRS)
Miller, David P.
1992-01-01
A two dimensional multi-block grid generator was developed for a new design and analysis system for studying multi-blade row turbomachinery problems with an axisymmetric viscous/inviscid 'average passage' through flow code. TIGGERC is a mouse driven, fully interactive grid generation program which can be used to modify boundary coordinates and grid packing. TIGGERC generates grids using a hyperbolic tangent or algebraic distribution of grid points on the block boundaries and the interior points of each block grid are distributed using a transfinite interpolation approach. TIGGERC generates a blocked axisymmetric H grid, C grid, I grid, or O grid for studying turbomachinery flow problems. TIGGERC was developed for operation on small high speed graphic workstations.
Elliptic surface grid generation on minimal and parmetrized surfaces
NASA Technical Reports Server (NTRS)
Spekreijse, S. P.; Nijhuis, G. H.; Boerstoel, J. W.
1995-01-01
An elliptic grid generation method is presented which generates excellent boundary conforming grids in domains in 2D physical space. The method is based on the composition of an algebraic and elliptic transformation. The composite mapping obeys the familiar Poisson grid generation system with control functions specified by the algebraic transformation. New expressions are given for the control functions. Grid orthogonality at the boundary is achieved by modification of the algebraic transformation. It is shown that grid generation on a minimal surface in 3D physical space is in fact equivalent to grid generation in a domain in 2D physical space. A second elliptic grid generation method is presented which generates excellent boundary conforming grids on smooth surfaces. It is assumed that the surfaces are parametrized and that the grid only depends on the shape of the surface and is independent of the parametrization. Concerning surface modeling, it is shown that bicubic Hermite interpolation is an excellent method to generate a smooth surface which is passing through a given discrete set of control points. In contrast to bicubic spline interpolation, there is extra freedom to model the tangent and twist vectors such that spurious oscillations are prevented.
Coarse-grid selection for parallel algebraic multigrid
Cleary, A. J., LLNL
1998-06-01
The need to solve linear systems arising from problems posed on extremely large, unstructured grids has sparked great interest in parallelizing algebraic multigrid (AMG) To date, however, no parallel AMG algorithms exist We introduce a parallel algorithm for the selection of coarse-grid points, a crucial component of AMG, based on modifications of certain paallel independent set algorithms and the application of heuristics designed to insure the quality of the coarse grids A prototype serial version of the algorithm is implemented, and tests are conducted to determine its effect on multigrid convergence, and AMG complexity
Interactive grid generation for turbomachinery flow field simulations
NASA Technical Reports Server (NTRS)
Choo, Yung K.; Reno, Charles; Eiseman, Peter R.
1988-01-01
The control point form of algebraic grid generation presented provides the means that are needed to generate well structured grids of turbomachinery flow simulations. It uses a sparse collection of control points distributed over the flow domain. The shape and position of coordinate curves can be adjusted from these control points while the grid conforms precisely to all boundaries. An interactive program called TURBO, which uses the control point form, is being developed. Basic features of the code are discussed and sample grids are presented. A finite volume LU implicit scheme is used to simulate flow in a turbine cascade on the grid generated by the program.
Interactive grid generation for turbomachinery flow field simulations
NASA Technical Reports Server (NTRS)
Choo, Yung K.; Eiseman, Peter R.; Reno, Charles
1988-01-01
The control point form of algebraic grid generation presented provides the means that are needed to generate well structured grids for turbomachinery flow simulations. It uses a sparse collection of control points distributed over the flow domain. The shape and position of coordinate curves can be adjusted from these control points while the grid conforms precisely to all boundaries. An interactive program called TURBO, which uses the control point form, is being developed. Basic features of the code are discussed and sample grids are presented. A finite volume LU implicit scheme is used to simulate flow in a turbine cascade on the grid generated by the program.
Grid generation for turbomachinery problems
NASA Technical Reports Server (NTRS)
Steinhoff, J.; Reddy, K. C.
1986-01-01
The development of a computer code to generate numerical grids for complex internal flow systems such as the fluid flow inside the space shuttle main engine is outlined. The blending technique for generating a grid for stator-rotor combination at a particular radial section is examined. The computer programs which generate these grids are listed in the Appendices. These codes are capable of generating grids at different cross sections and thus providng three dimensional stator-rotor grids for the turbomachinery of the space shuttle main engine.
Non-Galerkin Coarse Grids for Algebraic Multigrid
Falgout, Robert D.; Schroder, Jacob B.
2014-06-26
Algebraic multigrid (AMG) is a popular and effective solver for systems of linear equations that arise from discretized partial differential equations. And while AMG has been effectively implemented on large scale parallel machines, challenges remain, especially when moving to exascale. Particularly, stencil sizes (the number of nonzeros in a row) tend to increase further down in the coarse grid hierarchy, and this growth leads to more communication. Therefore, as problem size increases and the number of levels in the hierarchy grows, the overall efficiency of the parallel AMG method decreases, sometimes dramatically. This growth in stencil size is due to the standard Galerkin coarse grid operator, $P^T A P$, where $P$ is the prolongation (i.e., interpolation) operator. For example, the coarse grid stencil size for a simple three-dimensional (3D) seven-point finite differencing approximation to diffusion can increase into the thousands on present day machines, causing an associated increase in communication costs. We therefore consider algebraically truncating coarse grid stencils to obtain a non-Galerkin coarse grid. First, the sparsity pattern of the non-Galerkin coarse grid is determined by employing a heuristic minimal “safe” pattern together with strength-of-connection ideas. Second, the nonzero entries are determined by collapsing the stencils in the Galerkin operator using traditional AMG techniques. The result is a reduction in coarse grid stencil size, overall operator complexity, and parallel AMG solve phase times.
TDIGG - TWO-DIMENSIONAL, INTERACTIVE GRID GENERATION CODE
NASA Technical Reports Server (NTRS)
Vu, B. T.
1994-01-01
TDIGG is a fast and versatile program for generating two-dimensional computational grids for use with finite-difference flow-solvers. Both algebraic and elliptic grid generation systems are included. The method for grid generation by algebraic transformation is based on an interpolation algorithm and the elliptic grid generation is established by solving the partial differential equation (PDE). Non-uniform grid distributions are carried out using a hyperbolic tangent stretching function. For algebraic grid systems, interpolations in one direction (univariate) and two directions (bivariate) are considered. These interpolations are associated with linear or cubic Lagrangian/Hermite/Bezier polynomial functions. The algebraic grids can subsequently be smoothed using an elliptic solver. For elliptic grid systems, the PDE can be in the form of Laplace (zero forcing function) or Poisson. The forcing functions in the Poisson equation come from the boundary or the entire domain of the initial algebraic grids. A graphics interface procedure using the Silicon Graphics (GL) Library is included to allow users to visualize the grid variations at each iteration. This will allow users to interactively modify the grid to match their applications. TDIGG is written in FORTRAN 77 for Silicon Graphics IRIS series computers running IRIX. This package requires either MIT's X Window System, Version 11 Revision 4 or SGI (Motif) Window System. A sample executable is provided on the distribution medium. It requires 148K of RAM for execution. The standard distribution medium is a .25 inch streaming magnetic IRIX tape cartridge in UNIX tar format. This program was developed in 1992.
Grid generation strategies for turbomachinery configurations
NASA Astrophysics Data System (ADS)
Lee, K. D.; Henderson, T. L.
1991-01-01
Turbomachinery flow fields involve unique grid generation issues due to their geometrical and physical characteristics. Several strategic approaches are discussed to generate quality grids. The grid quality is further enhanced through blending and adapting. Grid blending smooths the grids locally through averaging and diffusion operators. Grid adaptation redistributes the grid points based on a grid quality assessment. These methods are demonstrated with several examples.
TIGER: Turbomachinery interactive grid generation
NASA Technical Reports Server (NTRS)
Soni, Bharat K.; Shih, Ming-Hsin; Janus, J. Mark
1992-01-01
A three dimensional, interactive grid generation code, TIGER, is being developed for analysis of flows around ducted or unducted propellers. TIGER is a customized grid generator that combines new technology with methods from general grid generation codes. The code generates multiple block, structured grids around multiple blade rows with a hub and shroud for either C grid or H grid topologies. The code is intended for use with a Euler/Navier-Stokes solver also being developed, but is general enough for use with other flow solvers. TIGER features a silicon graphics interactive graphics environment that displays a pop-up window, graphics window, and text window. The geometry is read as a discrete set of points with options for several industrial standard formats and NASA standard formats. Various splines are available for defining the surface geometries. Grid generation is done either interactively or through a batch mode operation using history files from a previously generated grid. The batch mode operation can be done either with a graphical display of the interactive session or with no graphics so that the code can be run on another computer system. Run time can be significantly reduced by running on a Cray-YMP.
Grid generation using classical techniques
NASA Technical Reports Server (NTRS)
Moretti, G.
1980-01-01
A brief historical review of conformal mapping and its applications to problems in fluid mechanics and electromagnetism is presented. The use of conformal mapping as a grid generator is described. The philosophy of the 'closed form' approach and its application to a Neumann problem is discussed. Karman-Trefftz mappings and grids for ablated, three dimensional bodies are also discussed.
Intelligent automated surface grid generation
NASA Technical Reports Server (NTRS)
Yao, Ke-Thia; Gelsey, Andrew
1995-01-01
The goal of our research is to produce a flexible, general grid generator for automated use by other programs, such as numerical optimizers. The current trend in the gridding field is toward interactive gridding. Interactive gridding more readily taps into the spatial reasoning abilities of the human user through the use of a graphical interface with a mouse. However, a sometimes fruitful approach to generating new designs is to apply an optimizer with shape modification operators to improve an initial design. In order for this approach to be useful, the optimizer must be able to automatically grid and evaluate the candidate designs. This paper describes and intelligent gridder that is capable of analyzing the topology of the spatial domain and predicting approximate physical behaviors based on the geometry of the spatial domain to automatically generate grids for computational fluid dynamics simulators. Typically gridding programs are given a partitioning of the spatial domain to assist the gridder. Our gridder is capable of performing this partitioning. This enables the gridder to automatically grid spatial domains of wide range of configurations.
LAPS Grid generation and adaptation
NASA Astrophysics Data System (ADS)
Pagliantini, Cecilia; Delzanno, Gia Luca; Guo, Zehua; Srinivasan, Bhuvana; Tang, Xianzhu; Chacon, Luis
2011-10-01
LAPS uses a common-data framework in which a general purpose grid generation and adaptation package in toroidal and simply connected domains is implemented. The initial focus is on implementing the Winslow/Laplace-Beltrami method for generating non-overlapping block structured grids. This is to be followed by a grid adaptation scheme based on Monge-Kantorovich optimal transport method [Delzanno et al., J. Comput. Phys,227 (2008), 9841-9864], that equidistributes application-specified error. As an initial set of applications, we will lay out grids for an axisymmetric mirror, a field reversed configuration, and an entire poloidal cross section of a tokamak plasma reconstructed from a CMOD experimental shot. These grids will then be used for computing the plasma equilibrium and transport in accompanying presentations. A key issue for Monge-Kantorovich grid optimization is the choice of error or monitor function for equi-distribution. We will compare the Operator Recovery Error Source Detector (ORESD) [Lapenta, Int. J. Num. Meth. Eng,59 (2004) 2065-2087], the Tau method and a strategy based on the grid coarsening [Zhang et al., AIAA J,39 (2001) 1706-1715] to find an ``optimal'' grid. Work supported by DOE OFES.
Elliptic Volume Grid Generation for Viscous CFD Parametric Design Studies
NASA Technical Reports Server (NTRS)
Alter, Stephen J.; Cheatwood, F. McNeil
1996-01-01
This paper presents a robust method for the generation of zonal volume grids of design parametrics for aerodynamic configurations. The process utilizes simple algebraic techniques with parametric splines coupled with elliptic volume grid generation to generate isolated zonal grids for changes in body configuration needed to perform parametric design studies. Speed of the algorithm is maximized through the algebraic methods and reduced number of grid points to be regenerated for each design parametric without sacrificing grid quality and continuity within the volume domain. The method is directly applicable to grid reusability, because it modifies existing ow adapted volume grids and enables the user to restart the CFD solution process with an established flow field. Use of this zonal approach reduces computer usage time to create new volume grids for design parametric studies by an order of magnitude, as compared to current methods which require the regeneration of an entire volume grid. A sample configuration of a proposed Single Stage-to-Orbit Vehicle is used to illustrate an application of this method.
NASA Technical Reports Server (NTRS)
Jameson, Leland
1996-01-01
Wavelets can provide a basis set in which the basis functions are constructed by dilating and translating a fixed function known as the mother wavelet. The mother wavelet can be seen as a high pass filter in the frequency domain. The process of dilating and expanding this high-pass filter can be seen as altering the frequency range that is 'passed' or detected. The process of translation moves this high-pass filter throughout the domain, thereby providing a mechanism to detect the frequencies or scales of information at every location. This is exactly the type of information that is needed for effective grid generation. This paper provides motivation to use wavelets for grid generation in addition to providing the final product: source code for wavelet-based grid generation.
Kim, Joshua; Ionascu, Dan; Zhang, Tiezhi
2013-01-01
Purpose: To accelerate iterative algebraic reconstruction algorithms using a cylindrical image grid. Methods: Tetrahedron beam computed tomography (TBCT) is designed to overcome the scatter and detector problems of cone beam computed tomography (CBCT). Iterative algebraic reconstruction algorithms have been shown to mitigate approximate reconstruction artifacts that appear at large cone angles, but clinical implementation is limited by their high computational cost. In this study, a cylindrical voxelization method on a cylindrical grid is developed in order to take advantage of the symmetries of the cylindrical geometry. The cylindrical geometry is a natural fit for the circular scanning trajectory employed in volumetric CT methods such as CBCT and TBCT. This method was implemented in combination with the simultaneous algebraic reconstruction technique (SART). Both two- and three-dimensional numerical phantoms as well as a patient CT image were utilized to generate the projection sets used for reconstruction. The reconstructed images were compared to the original phantoms using a set of three figures of merit (FOM). Results: The cylindrical voxelization on a cylindrical reconstruction grid was successfully implemented in combination with the SART reconstruction algorithm. The FOM results showed that the cylindrical reconstructions were able to maintain the accuracy of the Cartesian reconstructions. In three dimensions, the cylindrical method provided better accuracy than the Cartesian methods. At the same time, the cylindrical method was able to provide a speedup factor of approximately 40 while also reducing the system matrix storage size by 2 orders of magnitude. Conclusions: TBCT image reconstruction using a cylindrical image grid was able to provide a significant improvement in the reconstruction time and a more compact system matrix for storage on the hard drive and in memory while maintaining the image quality provided by the Cartesian voxelization on a
A paradigm for parallel unstructured grid generation
Gaither, A.; Marcum, D.; Reese, D.
1996-12-31
In this paper, a sequential 2D unstructured grid generator based on iterative point insertion and local reconnection is coupled with a Delauney tessellation domain decomposition scheme to create a scalable parallel unstructured grid generator. The Message Passing Interface (MPI) is used for distributed communication in the parallel grid generator. This work attempts to provide a generic framework to enable the parallelization of fast sequential unstructured grid generators in order to compute grand-challenge scale grids for Computational Field Simulation (CFS). Motivation for moving from sequential to scalable parallel grid generation is presented. Delaunay tessellation and iterative point insertion and local reconnection (advancing front method only) unstructured grid generation techniques are discussed with emphasis on how these techniques can be utilized for parallel unstructured grid generation. Domain decomposition techniques are discussed for both Delauney and advancing front unstructured grid generation with emphasis placed on the differences needed for both grid quality and algorithmic efficiency.
A grid generation system for multi-disciplinary design optimization
NASA Technical Reports Server (NTRS)
Jones, William T.; Samareh-Abolhassani, Jamshid
1995-01-01
A general multi-block three-dimensional volume grid generator is presented which is suitable for Multi-Disciplinary Design Optimization. The code is timely, robust, highly automated, and written in ANSI 'C' for platform independence. Algebraic techniques are used to generate and/or modify block face and volume grids to reflect geometric changes resulting from design optimization. Volume grids are generated/modified in a batch environment and controlled via an ASCII user input deck. This allows the code to be incorporated directly into the design loop. Generated volume grids are presented for a High Speed Civil Transport (HSCT) Wing/Body geometry as well a complex HSCT configuration including horizontal and vertical tails, engine nacelles and pylons, and canard surfaces.
Automatic Overset Grid Generation with Heuristic Feedback Control
NASA Technical Reports Server (NTRS)
Robinson, Peter I.
2001-01-01
An advancing front grid generation system for structured Overset grids is presented which automatically modifies Overset structured surface grids and control lines until user-specified grid qualities are achieved. The system is demonstrated on two examples: the first refines a space shuttle fuselage control line until global truncation error is achieved; the second advances, from control lines, the space shuttle orbiter fuselage top and fuselage side surface grids until proper overlap is achieved. Surface grids are generated in minutes for complex geometries. The system is implemented as a heuristic feedback control (HFC) expert system which iteratively modifies the input specifications for Overset control line and surface grids. It is developed as an extension of modern control theory, production rules systems and subsumption architectures. The methodology provides benefits over the full knowledge lifecycle of an expert system for knowledge acquisition, knowledge representation, and knowledge execution. The vector/matrix framework of modern control theory systematically acquires and represents expert system knowledge. Missing matrix elements imply missing expert knowledge. The execution of the expert system knowledge is performed through symbolic execution of the matrix algebra equations of modern control theory. The dot product operation of matrix algebra is generalized for heuristic symbolic terms. Constant time execution is guaranteed.
Complex Volume Grid Generation Through the Use of Grid Reusability
NASA Technical Reports Server (NTRS)
Alter, Stephen J.
1997-01-01
This paper presents a set of surface and volume grid generation techniques which reuse existing surface and volume grids. These methods use combinations of data manipulations to reduce grid generation time, improve grid characteristics, and increase the capabilities of existing domain discretization software. The manipulation techniques utilize physical and computational domains to produce basis function on which to operate and modify grid character and smooth grids using Trans-Finite Interpolation, a vector interpolation method and parametric re-mapping technique. With these new techniques, inviscid grids can be converted to viscous grids, multiple zone grid adaption can be performed to improve CFD solver efficiency, and topological changes to improve modeling of flow fields can be done simply and quickly. Examples of these capabilities are illustrated as applied to various configurations.
Tuned grid generation with ICEM CFD
NASA Technical Reports Server (NTRS)
Wulf, Armin; Akdag, Vedat
1995-01-01
ICEM CFD is a CAD based grid generation package that supports multiblock structured, unstructured tetrahedral and unstructured hexahedral grids. Major development efforts have been spent to extend ICEM CFD's multiblock structured and hexahedral unstructured grid generation capabilities. The modules added are: a parametric grid generation module and a semi-automatic hexahedral grid generation module. A fully automatic version of the hexahedral grid generation module for around a set of predefined objects in rectilinear enclosures has been developed. These modules will be presented and the procedures used will be described, and examples will be discussed.
Grid-coordinate generation program
Cosner, Oliver J.; Horwich, Esther
1974-01-01
This program description of the grid-coordinate generation program is written for computer users who are familiar with digital aquifer models. The program computes the coordinates for a variable grid -used in the 'Pinder Model' (a finite-difference aquifer simulator), for input to the CalComp GPCP (general purpose contouring program). The program adjusts the y-value by a user-supplied constant in order to transpose the origin of the model grid from the upper left-hand corner to the lower left-hand corner of the grid. The user has the options of, (1.) choosing the boundaries of the plot; (2.) adjusting the z-values (altitudes) by a constant; (3.) deleting superfluous z-values and (4.) subtracting the simulated surfaces from each other to obtain the decline. Output of this program includes the fixed format CNTL data cards and the other data cards required for input to GPCP. The output from GPCP then is used to produce a potentiometric map or a decline map by means of the CalComp plotter.
Survey of Volumetric Grid Generators
NASA Technical Reports Server (NTRS)
Woo, Alex; Volakis, John; Hulbert, Greg; Case, Jeff; Presley, Leroy L. (Technical Monitor)
1994-01-01
This document is the result of an Internet Survey of Volumetric grid generators. As such we have included information from only the responses which were sent to us. After the initial publication and posting of this survey, we would encourage authors and users of grid generators to send further information. Here is the initial query posted to SIGGRID@nas and the USENET group sci.physics.computational.fluid-dynamics. Date: Sun, 30 Jan 94 11:37:52 -0800 From: woo (Alex Woo x6010 227-6 rm 315) Subject: Info Sought for Survey of Grid Generators I am collecting information and reviews of both government sponsored and commercial mesh generators for large scientific calculations, both block structured and unstructured. If you send me a review of a mesh generator, please indicate its availability and cost. If you are a commercial concern with information on a product, please also include references for possible reviewers. Please email to woo@ra-next.arc.nasa.gov. I will post a summary and probably write a short note for the IEEE Antennas and Propagation Magazine. Alex Woo, MS 227-6 woo@ames.arc.nasa.gov NASA Ames Research Center NASAMAIL ACWOO Moffett Field, CA 94035-1000 SPANET 24582::W00 (415) 604-6010 (FAX) 604-4357 fhplabs,decwrl,uunet)!ames!woo Disclaimer: These are not official statements of NASA or EMCC. We did not include all the submitted text here. Instead we have created a database entry in the freely available and widely used BIBTeX format which has an Uniform Resource Locator (URL) field pointing to more details. The BIBTeX database is modeled after those available from the BIBNET project at University of Utah.
Multiblock grid generation for jet engine configurations
NASA Technical Reports Server (NTRS)
Stewart, Mark E. M.
1992-01-01
The goal was to create methods for generating grids with minimal human intervention that are applicable to a wide range of problems and compatible with existing numerical methods and with existing and proposed computers. The following topics that are related to multiblock grid generation are briefly covered in viewgraph form: finding a domain decomposition, dimensioning grids, grid smoothing, manipulating grids and decompositions, and some specializations for jet engine configurations.
Grid generation for the solution of partial differential equations
NASA Technical Reports Server (NTRS)
Eiseman, Peter R.; Erlebacher, Gordon
1987-01-01
A general survey of grid generators is presented with a concern for understanding why grids are necessary, how they are applied, and how they are generated. After an examination of the need for meshes, the overall applications setting is established with a categorization of the various connectivity patterns. This is split between structured grids and unstructured meshes. Altogether, the categorization establishes the foundation upon which grid generation techniques are developed. The two primary categories are algebraic techniques and partial differential equation techniques. These are each split into basic parts, and accordingly are individually examined in some detail. In the process, the interrelations between the various parts are accented. From the established background in the primary techniques, consideration is shifted to the topic of interactive grid generation and then to adaptive meshes. The setting for adaptivity is established with a suitable means to monitor severe solution behavior. Adaptive grids are considered first and are followed by adaptive triangular meshes. Then the consideration shifts to the temporal coupling between grid generators and PDE-solvers. To conclude, a reflection upon the discussion, herein, is given.
Grid generation for the solution of partial differential equations
NASA Technical Reports Server (NTRS)
Eiseman, Peter R.; Erlebacher, Gordon
1989-01-01
A general survey of grid generators is presented with a concern for understanding why grids are necessary, how they are applied, and how they are generated. After an examination of the need for meshes, the overall applications setting is established with a categorization of the various connectivity patterns. This is split between structured grids and unstructured meshes. Altogether, the categorization establishes the foundation upon which grid generation techniques are developed. The two primary categories are algebraic techniques and partial differential equation techniques. These are each split into basic parts, and accordingly are individually examined in some detail. In the process, the interrelations between the various parts are accented. From the established background in the primary techniques, consideration is shifted to the topic of interactive grid generation and then to adaptive meshes. The setting for adaptivity is established with a suitable means to monitor severe solution behavior. Adaptive grids are considered first and are followed by adaptive triangular meshes. Then the consideration shifts to the temporal coupling between grid generators and PDE-solvers. To conclude, a reflection upon the discussion, herein, is given.
Best Practices In Overset Grid Generation
NASA Technical Reports Server (NTRS)
Chan, William M.; Gomez, Reynaldo J., III; Rogers, Stuart E.; Buning, Pieter G.; Kwak, Dochan (Technical Monitor)
2002-01-01
Grid generation for overset grids on complex geometry can be divided into four main steps: geometry processing, surface grid generation, volume grid generation and domain connectivity. For each of these steps, the procedures currently practiced by experienced users are described. Typical problems encountered are also highlighted and discussed. Most of the guidelines are derived from experience on a variety of problems including space launch and return vehicles, subsonic transports with propulsion and high lift devices, supersonic vehicles, rotorcraft vehicles, and turbomachinery.
GridTool: A surface modeling and grid generation tool
NASA Technical Reports Server (NTRS)
Samareh-Abolhassani, Jamshid
1995-01-01
GridTool is designed around the concept that the surface grids are generated on a set of bi-linear patches. This type of grid generation is quite easy to implement, and it avoids the problems associated with complex CAD surface representations and associated surface parameterizations. However, the resulting surface grids are close to but not on the original CAD surfaces. This problem can be alleviated by projecting the resulting surface grids onto the original CAD surfaces. GridTool is designed primary for unstructured grid generation systems. Currently, GridTool supports VGRID and FELISA systems, and it can be easily extended to support other unstructured grid generation systems. The data in GridTool is stored parametrically so that once the problem is set up, one can modify the surfaces and the entire set of points, curves and patches will be updated automatically. This is very useful in a multidisciplinary design and optimization process. GridTool is written entirely in ANSI 'C', the interface is based on the FORMS library, and the graphics is based on the GL library. The code has been tested successfully on IRIS workstations running IRIX4.0 and above. The memory is allocated dynamically, therefore, memory size will depend on the complexity of geometry/grid. GridTool data structure is based on a link-list structure which allows the required memory to expand and contract dynamically according to the user's data size and action. Data structure contains several types of objects such as points, curves, patches, sources and surfaces. At any given time, there is always an active object which is drawn in magenta, or in their highlighted colors as defined by the resource file which will be discussed later.
Parallel grid generation algorithm for distributed memory computers
NASA Technical Reports Server (NTRS)
Moitra, Stuti; Moitra, Anutosh
1994-01-01
A parallel grid-generation algorithm and its implementation on the Intel iPSC/860 computer are described. The grid-generation scheme is based on an algebraic formulation of homotopic relations. Methods for utilizing the inherent parallelism of the grid-generation scheme are described, and implementation of multiple levELs of parallelism on multiple instruction multiple data machines are indicated. The algorithm is capable of providing near orthogonality and spacing control at solid boundaries while requiring minimal interprocessor communications. Results obtained on the Intel hypercube for a blended wing-body configuration are used to demonstrate the effectiveness of the algorithm. Fortran implementations bAsed on the native programming model of the iPSC/860 computer and the Express system of software tools are reported. Computational gains in execution time speed-up ratios are given.
Progress in Grid Generation: From Chimera to DRAGON Grids
NASA Technical Reports Server (NTRS)
Liou, Meng-Sing; Kao, Kai-Hsiung
1994-01-01
Hybrid grids, composed of structured and unstructured grids, combines the best features of both. The chimera method is a major stepstone toward a hybrid grid from which the present approach is evolved. The chimera grid composes a set of overlapped structured grids which are independently generated and body-fitted, yielding a high quality grid readily accessible for efficient solution schemes. The chimera method has been shown to be efficient to generate a grid about complex geometries and has been demonstrated to deliver accurate aerodynamic prediction of complex flows. While its geometrical flexibility is attractive, interpolation of data in the overlapped regions - which in today's practice in 3D is done in a nonconservative fashion, is not. In the present paper we propose a hybrid grid scheme that maximizes the advantages of the chimera scheme and adapts the strengths of the unstructured grid while at the same time keeps its weaknesses minimal. Like the chimera method, we first divide up the physical domain by a set of structured body-fitted grids which are separately generated and overlaid throughout a complex configuration. To eliminate any pure data manipulation which does not necessarily follow governing equations, we use non-structured grids only to directly replace the region of the arbitrarily overlapped grids. This new adaptation to the chimera thinking is coined the DRAGON grid. The nonstructured grid region sandwiched between the structured grids is limited in size, resulting in only a small increase in memory and computational effort. The DRAGON method has three important advantages: (1) preserving strengths of the chimera grid; (2) eliminating difficulties sometimes encountered in the chimera scheme, such as the orphan points and bad quality of interpolation stencils; and (3) making grid communication in a fully conservative and consistent manner insofar as the governing equations are concerned. To demonstrate its use, the governing equations are
Generating Three-Dimensional Grids About Anything
NASA Technical Reports Server (NTRS)
Sorenson, Reese L.
1991-01-01
Three-Dimensional Grids About Anything by Poisson's Equation (3DGRAPE) computer program designed to make computational grids in or about almost any shape. Generated by solution of Poisson's differential equations in three dimensions. Program automatically finds its own values for inhomogeneous terms giving near-orthogonality and controlled grid-cell height at boundaries. Grids generated applied to both viscous and inviscid aerodynamic problems, and to problems in other areas of fluid dynamics. Written in 100 percent FORTRAN 77.
Generating Composite Overlapping Grids on CAD Geometries
Henshaw, W.D.
2002-02-07
We describe some algorithms and tools that have been developed to generate composite overlapping grids on geometries that have been defined with computer aided design (CAD) programs. This process consists of five main steps. Starting from a description of the surfaces defining the computational domain we (1) correct errors in the CAD representation, (2) determine topology of the patched-surface, (3) build a global triangulation of the surface, (4) construct structured surface and volume grids using hyperbolic grid generation, and (5) generate the overlapping grid by determining the holes and the interpolation points. The overlapping grid generator which is used for the final step also supports the rapid generation of grids for block-structured adaptive mesh refinement and for moving grids. These algorithms have been implemented as part of the Overture object-oriented framework.
Geometry modeling and multi-block grid generation for turbomachinery configurations
NASA Technical Reports Server (NTRS)
Shih, Ming H.; Soni, Bharat K.
1992-01-01
An interactive 3D grid generation code, Turbomachinery Interactive Grid genERation (TIGER), was developed for general turbomachinery configurations. TIGER features the automatic generation of multi-block structured grids around multiple blade rows for either internal, external, or internal-external turbomachinery flow fields. Utilization of the Bezier's curves achieves a smooth grid and better orthogonality. TIGER generates the algebraic grid automatically based on geometric information provided by its built-in pseudo-AI algorithm. However, due to the large variation of turbomachinery configurations, this initial grid may not always be as good as desired. TIGER therefore provides graphical user interactions during the process which allow the user to design, modify, as well as manipulate the grid, including the capability of elliptic surface grid generation.
Grid generation for 3D turbomachinery configurations
NASA Technical Reports Server (NTRS)
Shih, Ming-Hsin; Soni, Bharat K.
1992-01-01
A numerical grid generation algorithm associated with the flow field about turbomachinery geometries is presented. Graphical user interface is developed with the FORMS Library to create an interactive, user-friendly working environment. This customized algorithm reduces the man-hours required to generate a grid associated with turbomachinery geometry, as compared to those required by general-purpose grid generation softwares. Bezier curves are utilized both interactively and automatically to accomplish grid line smoothness and orthogonality. Graphical user interactions are provided in the algorithm and allow the user to design and manipulate the grid lines with a mouse.
Grid Generation Techniques Utilizing the Volume Grid Manipulator
NASA Technical Reports Server (NTRS)
Alter, Stephen J.
1998-01-01
This paper presents grid generation techniques available in the Volume Grid Manipulation (VGM) code. The VGM code is designed to manipulate existing line, surface and volume grids to improve the quality of the data. It embodies an easy to read rich language of commands that enables such alterations as topology changes, grid adaption and smoothing. Additionally, the VGM code can be used to construct simplified straight lines, splines, and conic sections which are common curves used in the generation and manipulation of points, lines, surfaces and volumes (i.e., grid data). These simple geometric curves are essential in the construction of domain discretizations for computational fluid dynamic simulations. By comparison to previously established methods of generating these curves interactively, the VGM code provides control of slope continuity and grid point-to-point stretchings as well as quick changes in the controlling parameters. The VGM code offers the capability to couple the generation of these geometries with an extensive manipulation methodology in a scripting language. The scripting language allows parametric studies of a vehicle geometry to be efficiently performed to evaluate favorable trends in the design process. As examples of the powerful capabilities of the VGM code, a wake flow field domain will be appended to an existing X33 Venturestar volume grid; negative volumes resulting from grid expansions to enable flow field capture on a simple geometry, will be corrected; and geometrical changes to a vehicle component of the X33 Venturestar will be shown.
Workshop on Grid Generation and Related Areas
NASA Technical Reports Server (NTRS)
1992-01-01
A collection of papers given at the Workshop on Grid Generation and Related Areas is presented. The purpose of this workshop was to assemble engineers and scientists who are currently working on grid generation for computational fluid dynamics (CFD), surface modeling, and related areas. The objectives were to provide an informal forum on grid generation and related topics, to assess user experience, to identify needs, and to help promote synergy among engineers and scientists working in this area. The workshop consisted of four sessions representative of grid generation and surface modeling research and application within NASA LeRC. Each session contained presentations and an open discussion period.
TURBOGRID - Turbomachinery applications of grid generation
NASA Astrophysics Data System (ADS)
Soni, Bharat K.; Shih, Ming-Hsin
1990-07-01
Numerical grid generation algorithm associated with the field region about turbomachinery systems is presented. The algorithm is incorporated as a module, TIGER (Turbomachinery Interactive Grid genERation) of the modular general purpose computer code GENIE. Interactive definitions of the mathematical description of blades, hub and shroud with minimal user interactions, adaption of the weighted transfinite interpolation technique for efficient generation of grid blocks/zones, automatic construction of the Bezier curves to accomplish slope continuity, and efficient utilization of IRIS-graphics capabilities are the salient features of this algorithm which results in a significant time savings for a given turbomachinery geometry-grid application.
NASA Technical Reports Server (NTRS)
Golik, W. L.
1996-01-01
A robust solver for the elliptic grid generation equations is sought via a numerical study. The system of PDEs is discretized with finite differences, and multigrid methods are applied to the resulting nonlinear algebraic equations. Multigrid iterations are compared with respect to the robustness and efficiency. Different smoothers are tried to improve the convergence of iterations. The methods are applied to four 2D grid generation problems over a wide range of grid distortions. The results of the study help to select smoothing schemes and the overall multigrid procedures for elliptic grid generation.
Getting a Grip on Grid Generation
NASA Technical Reports Server (NTRS)
2002-01-01
GridPro is an automatic, object-oriented, multi-block grid generator that provides ease of use, high quality, rapid production, and parametric design. When paired with a 3-D graphic user interface called az- Manager, GridPro presents users with an extremely efficient, interactive capability to build topology, edit surfaces, set computational fluid dynamics (CFD) boundary conditions, and view multi-block grids. The origins of the GridPro technology date back to a 1989 SBIR contract with NASA's Glenn Research Center, in which Glenn was seeking a multi-block grid generation program that would run automatically upon identifying a pattern of grid blocks supplied by a user. The technology is currently used in many engineering fields, including aerospace, turbo- machinery, automotive, and chemical industries.
Grid generation: A view from the trenches
NASA Technical Reports Server (NTRS)
Ives, David; Miller, Robert; Siddons, William; Vandyke, Kevin
1995-01-01
This paper presents 'A view from the trenches' on CFD grid generation from a Pratt & Whitney perspective. We anticipate that other organizations have similar views. We focus on customer expectations and the consequent requirements. We enunciate a vision for grid generation, discuss issues that developers must recognize.
VGRIDSG: An unstructured surface grid generation program
NASA Technical Reports Server (NTRS)
Bockelie, Michael J.
1993-01-01
This report contains an overview of the VGRIDSG unstructured surface grid generation program. The VGRIDSG program was created from the VGRID3D unstructured grid generation program developed by Vigyan, Inc. The purpose of this report is to document the changes from the original VGRID3D program and to describe the capabilities of the new program.
NASA Technical Reports Server (NTRS)
Shih, T. I.-P.; Bailey, R. T.; Nguyen, H. L.; Roelke, R. J.
1990-01-01
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
Unstructured grid generation using the distance function
NASA Technical Reports Server (NTRS)
Bihari, Barna L.; Chakravarthy, Sukumar R.
1991-01-01
A new class of methods for obtaining level sets to generate unstructured grids is presented. The consecutive grid levels are computed using the distance functions, which corresponds to solving the Hamilton-Jacobi equations representing the equations of motion of fronts propagating with curvature-dependent speed. The relationship between the distance function and the governing equations will be discussed as well as its application to generating grids. Multi-ply connected domains and complex geometries are handled naturally, with a straightforward generalization to several space dimensions. The grid points for the unstructured grid are obtained simultaneously with the grid levels. The search involved in checking for overlapping triangles is minimized by triangulating the entire domain one level at a time.
Modeling and Grid Generation of Iced Airfoils
NASA Technical Reports Server (NTRS)
Vickerman, Mary B.; Baez, Marivell; Braun, Donald C.; Hackenberg, Anthony W.; Pennline, James A.; Schilling, Herbert W.
2007-01-01
SmaggIce Version 2.0 is a software toolkit for geometric modeling and grid generation for two-dimensional, singleand multi-element, clean and iced airfoils. A previous version of SmaggIce was described in Preparing and Analyzing Iced Airfoils, NASA Tech Briefs, Vol. 28, No. 8 (August 2004), page 32. To recapitulate: Ice shapes make it difficult to generate quality grids around airfoils, yet these grids are essential for predicting ice-induced complex flow. This software efficiently creates high-quality structured grids with tools that are uniquely tailored for various ice shapes. SmaggIce Version 2.0 significantly enhances the previous version primarily by adding the capability to generate grids for multi-element airfoils. This version of the software is an important step in streamlining the aeronautical analysis of ice airfoils using computational fluid dynamics (CFD) tools. The user may prepare the ice shape, define the flow domain, decompose it into blocks, generate grids, modify/divide/merge blocks, and control grid density and smoothness. All these steps may be performed efficiently even for the difficult glaze and rime ice shapes. Providing the means to generate highly controlled grids near rough ice, the software includes the creation of a wrap-around block (called the "viscous sublayer block"), which is a thin, C-type block around the wake line and iced airfoil. For multi-element airfoils, the software makes use of grids that wrap around and fill in the areas between the viscous sub-layer blocks for all elements that make up the airfoil. A scripting feature records the history of interactive steps, which can be edited and replayed later to produce other grids. Using this version of SmaggIce, ice shape handling and grid generation can become a practical engineering process, rather than a laborious research effort.
NASA Technical Reports Server (NTRS)
Rostand, Philippe
1988-01-01
The incorporation of algebraic turbulence models in a solver for the 2-D compressible Navier-Stokes equations using triangular grids is described. A practical way to use the Cebeci Smith model, and to modify it in separated regions is proposed. The ability of the model to predict high speed, perfect gas boundary layers is investigated from a numerical point of view.
Algebraic grid adaptation method using non-uniform rational B-spline surface modeling
NASA Technical Reports Server (NTRS)
Yang, Jiann-Cherng; Soni, B. K.
1992-01-01
An algebraic adaptive grid system based on equidistribution law and utilized by the Non-Uniform Rational B-Spline (NURBS) surface for redistribution is presented. A weight function, utilizing a properly weighted boolean sum of various flow field characteristics is developed. Computational examples are presented to demonstrate the success of this technique.
Unstructured Grid Generation Techniques and Software
NASA Technical Reports Server (NTRS)
Posenau, Mary-Anne K. (Editor)
1993-01-01
The Workshop on Unstructured Grid Generation Techniques and Software was conducted for NASA to assess its unstructured grid activities, improve the coordination among NASA centers, and promote technology transfer to industry. The proceedings represent contributions from Ames, Langley, and Lewis Research Centers, and the Johnson and Marshall Space Flight Centers. This report is a compilation of the presentations made at the workshop.
Towards classical spectrum generating algebras for f-deformations
NASA Astrophysics Data System (ADS)
Kullock, Ricardo; Latini, Danilo
2016-01-01
In this paper we revise the classical analog of f-oscillators, a generalization of q-oscillators given in Man'ko et al. (1997) [8], in the framework of classical spectrum generating algebras (SGA) introduced in Kuru and Negro (2008) [9]. We write down the deformed Poisson algebra characterizing the entire family of non-linear oscillators and construct its general solution algebraically. The latter, covering the full range of f-deformations, shows an energy dependence both in the amplitude and the frequency of the motion.
A mathematical basis for automated structured grid generation with close coupling to the flow solver
Barnette, D.W.
1998-02-01
The first two truncation error terms resulting from finite differencing the convection terms in the two-dimensional Navier-Stokes equations are examined for the purpose of constructing two-dimensional grid generation schemes. These schemes are constructed such that the resulting grid distributions drive the error terms to zero. Two sets of equations result, one for each error term, that show promise in generating grids that provide more accurate flow solutions and possibly faster convergence. One set results in an algebraic scheme that drives the first truncation term to zero, and the other a hyperbolic scheme that drives the second term to zero. Also discussed is the possibility of using the schemes in sequentially constructing a grid in an iterative algorithm involving the flow solver. In essence, the process is envisioned to generate not only a flow field solution but the grid as well, rendering the approach a hands-off method for grid generation
NURBS evaluation and utilization for grid generation
Yu, Tzu-Yi; Soni, B.K.
1996-12-31
In the last few years, Non-Uniform Rational BSpline (NURBS) has evolved as an essential tool for a semi-analytical representation of geometrical entities encountered in Computational Field Simulation (CFS). The grid generation techniques based on NURBS have been developed and reported in the literature by various researchers. However, the evaluation of NURBS for surface/volume grid point generation is time consuming and the representation of widely utilized aerodynamic shapes into NURBS is not trivial. This paper addressed these issues. An enhanced algorithm for NURBS evaluation based on the proper utilization of the basis functions is presented. An accurate representation of the widely utilized transition duct designed by using superellipse equation is developed. An example of the NURBS surface definition to a 3D volume and its utilization in grid adaptation by combing NURBS with elliptic generation system is presented. The computational example involving a flow field around a generic missile configuration is presented for demonstrating grid adaptation.
Rigel: An interactive structured grid generation system
Hachfeld, W.D.; Khamayseh, A.K.; Hansen, G.A.
1998-02-01
An interactive structured grid generation application that facilitates the construction of complex, discretized, simulation models directly from the original CAD geometry specifications is presented. The application, named Rigel, reads physical model descriptions generated by modern CAD packages. Rigel includes a suite of interactive geometry editing functions to assist the user in the construction of a topologically correct geometry from the original CAD specification. Once a topologically correct geometry is created, an interactively steered grid generation capability is provided to facilitate the construction of an appropriate discretization for the simulation. Grid quality enhancement is supported with the application of user-directed elliptic smoothing, refinement, and coarsening operators. After a grid is completed, various output filters are supplied to write an input file for the target simulation code. This paper is intended to provide an overview of the mechanics of this process and to highlight some of the novel algorithms and techniques employed.
Elliptic generation of composite three-dimensional grids about realistic aircraft
NASA Technical Reports Server (NTRS)
Sorenson, Reese L.
1986-01-01
An elliptic method for generating composite grids about realistic aircraft is presented. A body-conforming grid is first generated about the entire aircraft by the solution of Poisson's differential equation. This grid has relatively coarse spacing, and it covers the entire physical domain. At boundary surfaces, cell size is controlled and cell skewness is nearly eliminated by inhomogeneous terms, which are found automatically by the program. Certain regions of the grid in which high gradients are expected, and which map into rectangular solids in the computational domain, are then designated for zonal refinement. Spacing in the zonal grids is reduced by adding points with a simple, algebraic scheme. Details of the grid-generation method are presented along with results of the present application, a wing/body configuration based on the F-16 fighter aircraft.
Elliptic generation of composite three-dimensional grids about realistic aircraft
NASA Technical Reports Server (NTRS)
Sorenson, R. L.
1986-01-01
An elliptic method for generating composite grids about realistic aircraft is presented. A body-conforming grid is first generated about the entire aircraft by the solution of Poisson's differential equation. This grid has relatively coarse spacing, and it covers the entire physical domain. At boundary surfaces, cell size is controlled and cell skewness is nearly eliminated by inhomogeneous terms, which are found automatically by the program. Certain regions of the grid in which high gradients are expected, and which map into rectangular solids in the computational domain, are then designated for zonal refinement. Spacing in the zonal grids is reduced by adding points with a simple, algebraic scheme. Details of the grid generation method are presented along with results of the present application, a wing-body configuration based on the F-16 fighter aircraft.
NASA Technical Reports Server (NTRS)
Steinthorsson, E.; Shih, T. I-P.; Roelke, R. J.
1991-01-01
In order to generate good quality systems for complicated three-dimensional spatial domains, the grid-generation method used must be able to exert rather precise controls over grid-point distributions. Several techniques are presented that enhance control of grid-point distribution for a class of algebraic grid-generation methods known as the two-, four-, and six-boundary methods. These techniques include variable stretching functions from bilinear interpolation, interpolating functions based on tension splines, and normalized K-factors. The techniques developed in this study were incorporated into a new version of GRID3D called GRID3D-v2. The usefulness of GRID3D-v2 was demonstrated by using it to generate a three-dimensional grid system in the coolent passage of a radial turbine blade with serpentine channels and pin fins.
Multiblock grid generation with automatic zoning
NASA Technical Reports Server (NTRS)
Eiseman, Peter R.
1995-01-01
An overview will be given for multiblock grid generation with automatic zoning. We shall explore the many advantages and benefits of this exciting technology and will also see how to apply it to a number of interesting cases. The technology is available in the form of a commercial code, GridPro(registered trademark)/az3000. This code takes surface geometry definitions and patterns of points as its primary input and produces high quality grids as its output. Before we embark upon our exploration, we shall first give a brief background of the environment in which this technology fits.
Introduction to grid generation systems in turbomachinery
NASA Astrophysics Data System (ADS)
Camarero, R.; Ozell, B.; Reggio, M.; Caron, A.
Body-fitted curvilinear grid generation for the numerical simulation of three dimensional flow in turbomachines is introduced. The grids yield coordinate curves aligned with the domain boundaries. The numerical scheme for the governing equations is carried out on a rectangular mesh, giving a simpler and more accurate algorithm since bondaries coincide with coordinate grids, and no interpolation is required. The geometric complexity, through the transformation, is imbedded into the coefficients of the governing equations, affording the possibility of writing generalized codes applicable to a variety of geometries. This results in a great saving in the code development effort.
Computer Program For Generation Of Surface Grids
NASA Technical Reports Server (NTRS)
Ching, Raymond; Pierce, Lawrence
1993-01-01
S3D is useful computer program for generation of grids on surfaces of bodies having complicated shapes. Product of integration of robust and widely applicable interpolation technique with latest in computer-workstation technology. Incorporates highly efficient and easy-to-use graphical-interface software, enables real-time and interactive analyses of surface-geometry data and facilitates construction of surface grids.
Spectral Topography Generation for Arbitrary Grids
NASA Astrophysics Data System (ADS)
Oh, T. J.
2015-12-01
A new topography generation tool utilizing spectral transformation technique for both structured and unstructured grids is presented. For the source global digital elevation data, the NASA Shuttle Radar Topography Mission (SRTM) 15 arc-second dataset (gap-filling by Jonathan de Ferranti) is used and for land/water mask source, the NASA Moderate Resolution Imaging Spectroradiometer (MODIS) 30 arc-second land water mask dataset v5 is used. The original source data is coarsened to a intermediate global 2 minute lat-lon mesh. Then, spectral transformation to the wave space and inverse transformation with wavenumber truncation is performed for isotropic topography smoothness control. Target grid topography mapping is done by bivariate cubic spline interpolation from the truncated 2 minute lat-lon topography. Gibbs phenomenon in the water region can be removed by overwriting ocean masked target coordinate grids with interpolated values from the intermediate 2 minute grid. Finally, a weak smoothing operator is applied on the target grid to minimize the land/water surface height discontinuity that might have been introduced by the Gibbs oscillation removal procedure. Overall, the new topography generation approach provides spectrally-derived, smooth topography with isotropic resolution and minimum damping, enabling realistic topography forcing in the numerical model. Topography is generated for the cubed-sphere grid and tested on the KIAPS Integrated Model (KIM).
The 3D Euler solutions using automated Cartesian grid generation
NASA Technical Reports Server (NTRS)
Melton, John E.; Enomoto, Francis Y.; Berger, Marsha J.
1993-01-01
Viewgraphs on 3-dimensional Euler solutions using automated Cartesian grid generation are presented. Topics covered include: computational fluid dynamics (CFD) and the design cycle; Cartesian grid strategy; structured body fit; grid generation; prolate spheroid; and ONERA M6 wing.
Three-dimensional surface grid generation for calculation of thermal radiation shape factors
NASA Technical Reports Server (NTRS)
Aly, Hany M.
1992-01-01
A technique is described to generate three dimensional surface grids suitable for calculating shape factors for thermal radiative heat transfer. The surface under consideration is approximated by finite triangular elements generated in a special manner. The grid is generated by dividing the surface into a two dimensional array of nodes. Each node is defined by its coordinates. Each set of four adjacent nodes is used to construct two triangular elements. Each triangular element is characterized by the vector representation of its vertices. Vector algebra is used to calculate all desired geometric properties of grid elements. The properties are used to determine the shape factor between the element and an area element in space. The grid generation can be graphically displayed using any software with three dimensional features. DISSPLA was used to view the grids.
IGES transformer and NURBS in grid generation
NASA Technical Reports Server (NTRS)
Yu, Tzu-Yi; Soni, Bharat K.
1993-01-01
In the field of Grid Generation and the CAD/CAM, there are numerous geometry output formats which require the designer to spend a great deal of time manipulating geometrical entities in order to achieve a useful sculptured geometrical description for grid generation. Also in this process, there is a danger of losing fidelity of the geometry under consideration. This stresses the importance of a standard geometry definition for the communication link between varying CAD/CAM and grid system. The IGES (Initial Graphics Exchange Specification) file is a widely used communication between CAD/CAM and the analysis tools. The scientists at NASA Research Centers - including NASA Ames, NASA Langley, NASA Lewis, NASA Marshall - have recognized this importance and, therefore, in 1992 they formed the committee of the 'NASA-IGES' which is the subset of the standard IGES. This committee stresses the importance and encourages the CFD community to use the standard IGES file for the interface between the CAD/CAM and CFD analysis. Also, two of the IGES entities -- the NURBS Curve (Entity 126) and NURBS Surface (Entity 128) -- which have many useful geometric properties -- like the convex hull property, local control property and affine invariance, also widely utilized analytical geometries can be accurately represented using NURBS. This is important in today grid generation tools because of the emphasis of the interactive design. To satisfy the geometry transformation between the CAD/CAM system and Grid Generation field, the CAGI (Computer Aided Geometry Design) developed, which include the Geometry Transformation, Geometry Manipulation and Geometry Generation as well as the user interface. This paper will present the successful development IGES file transformer and application of NURBS definition in the grid generation.
Batch mode grid generation: An endangered species
NASA Technical Reports Server (NTRS)
Schuster, David M.
1992-01-01
Non-interactive grid generation schemes should thrive as emphasis shifts from development of numerical analysis and design methods to application of these tools to real engineering problems. A strong case is presented for the continued development and application of non-interactive geometry modeling methods. Guidelines, strategies, and techniques for developing and implementing these tools are presented using current non-interactive grid generation methods as examples. These schemes play an important role in the development of multidisciplinary analysis methods and some of these applications are also discussed.
A three-dimensional grid generation method for gas-turbine combustor flow computations
NASA Astrophysics Data System (ADS)
Shyy, Wei; Braaten, Mark E.; Sober, Janet S.
1987-02-01
A special-purpose code suitable for generating a curvilinear nonorthogonal grid system for gas-turbine combustor flow computations has been produced. The code is capable of handling an arbitrary number of dilution holes with any radii as well as film-cooling slots on the top and bottom surfaces. A zonal approach has been developed to handle the fast length scale variations imposed by the geometric constraints and to minimize the overall computational efforts needed to generate the grids. The code combines partial differential equation and algebraic interpolation methods to generate the grid system. The salient features of the grid characteristics are discussed. Also included are sample results of a 3-D turbulent combusting flow field calculated on the grid system produced by this methodology.
NASA Technical Reports Server (NTRS)
Smith, R. E.; Everton, E. L.; Weilmuenster, K. J.; Weise, M. R.; Farr, N.
1990-01-01
The surface definition and grid generation about an Assured Crew Return Vehicle (ACRV) for the Space Station Freedom are described. The purpose of the surface definition and grid generation is to provide the necessary geometry information for CFD calculations about the vehicle. There are two salient features in this description. The first is that the numerical model representing the ACRV configuration is obtained from the measurement of an existing wind tunnel model. The method for smoothing the measured data and obtaining the numerical model is described. The second feature is the description of the algebraic grid generation method and software to compute volume grids about the ACRV. The methods and software allow rapid computation of volume grids for a wide range of flow conditions.
Katz, Jessica; Cochran, Jaquelin
2015-05-27
Greening the Grid provides technical assistance to energy system planners, regulators, and grid operators to overcome challenges associated with integrating variable renewable energy into the grid. This document, part of a Greening the Grid toolkit, provides power system planners with tips to help secure and sustain investment in new renewable energy generation by aligning renewable energy policy targets and incentives with grid integration considerations.
Generation Of Surface Grids From Data Points
NASA Technical Reports Server (NTRS)
Luh, Raymond Ching-Chung
1991-01-01
Computational procedure generates grids on complicated three-dimensional surfaces from sets of data points that lie on and specify those surfaces. Starting with grouping of possibly sparse surface points into lines and/or patches, procedure involves interpolation within and blending of lines and/or patches and possibly redistribution and reassembly of patches to obtain finished system of zonal patch grids that match at boundaries between them. Procedure semiautomated via computer program that performs all steps except selection of patches and interpolation points, left to discretion of user.
Integrated geometry and grid generation system for complex configurations
NASA Technical Reports Server (NTRS)
Akdag, Vedat; Wulf, Armin
1992-01-01
A grid generation system was developed that enables grid generation for complex configurations. The system called ICEM/CFD is described and its role in computational fluid dynamics (CFD) applications is presented. The capabilities of the system include full computer aided design (CAD), grid generation on the actual CAD geometry definition using robust surface projection algorithms, interfacing easily with known CAD packages through common file formats for geometry transfer, grid quality evaluation of the volume grid, coupling boundary condition set-up for block faces with grid topology generation, multi-block grid generation with or without point continuity and block to block interface requirement, and generating grid files directly compatible with known flow solvers. The interactive and integrated approach to the problem of computational grid generation not only substantially reduces manpower time but also increases the flexibility of later grid modifications and enhancements which is required in an environment where CFD is integrated into a product design cycle.
Three-dimensional elliptic grid generation with fully automatic boundary constraints
NASA Astrophysics Data System (ADS)
Kaul, Upender K.
2010-08-01
A new procedure for generating smooth uniformly clustered three-dimensional structured elliptic grids is presented here which formulates three-dimensional boundary constraints by extending the two-dimensional counterpart presented by the author earlier. This fully automatic procedure obviates the need for manual specification of decay parameters over the six bounding surfaces of a given volume grid. The procedure has been demonstrated here for the Mars Science Laboratory (MSL) geometries such as aeroshell and canopy, as well as the Inflatable Aerodynamic Decelerator (IAD) geometry and a 3D analytically defined geometry. The new procedure also enables generation of single-block grids for such geometries because the automatic boundary constraints permit the decay parameters to evolve as part of the solution to the elliptic grid system of equations. These decay parameters are no longer just constants, as specified in the conventional approach, but functions of generalized coordinate variables over a given bounding surface. Since these decay functions vary over a given boundary, orthogonal grids around any arbitrary simply-connected boundary can be clustered automatically without having to break up the boundaries and the corresponding interior or exterior domains into various blocks for grid generation. The new boundary constraints are not limited to the simply-connected regions only, but can also be formulated around multiply-connected and isolated regions in the interior. The proposed method is superior to other methods of grid generation such as algebraic and hyperbolic techniques in that the grids obtained here are C2 continuous, whereas simple elliptic smoothing of algebraic or hyperbolic grids to enforce C2 continuity destroys the grid clustering near the boundaries. US patent 7231329.
An interactive grid generation procedure for axial and radial flow turbomachinery
NASA Technical Reports Server (NTRS)
Beach, Timothy A.
1989-01-01
A combination algebraic/elliptic technique is presented for the generation of three dimensional grids about turbo-machinery blade rows for both axial and radial flow machinery. The technique is built around use of an advanced engineering workstation to construct several two dimensional grids interactively on predetermined blade-to-blade surfaces. A three dimensional grid is generated by interpolating these surface grids onto an axisymmetric grid. On each blade-to-blade surface, a grid is created using algebraic techniques near the blade to control orthogonality within the boundary layer region and elliptic techniques in the mid-passage to achieve smoothness. The interactive definition of bezier curves as internal boundaries is the key to simple construction. This procedure lends itself well to zonal grid construction, an important example being the tip clearance region. Calculations done to date include a space shuttle main engine turbopump blade, a radial inflow turbine blade, and the first stator of the United Technologies Research Center large scale rotating rig. A finite Navier-Stokes solver was used in each case.
An interactive grid generation procedure for axial and radial flow turbomachinery
NASA Astrophysics Data System (ADS)
Beach, T. A.
1990-01-01
A combination algebraic/elliptic technique is presented for the generation of three dimensional grids about turbo-machinery blade rows for both axial and radial flow machinery. The technique is built around use of an advanced engineering workstation to construct several two dimensional grids interactively on predetermined blade-to-blade surfaces. A three dimensional grid is generated by interpolating these surface grids onto an axisymmetric grid. On each blade-to-blade surface, a grid is created using algebraic techniques near the blade to control orthogonality within the boundary layer region and elliptic techniques in the mid-passage to achieve smoothness. The interactive definition of bezier curves as internal boundaries is the key to simple construction. This procedure lends itself well to zonal grid construction, an important example being the tip clearance region. Calculations done to date include a space shuttle main engine turbopump blade, a radial inflow turbine blade, and the first stator of the United Technologies Research Center large scale rotating rig. A finite Navier-Stokes solver was used in each case.
Criteria for evaluation of grid generation systems
NASA Technical Reports Server (NTRS)
Ascoli, Edward P.; Barson, Steven L.; Decroix, Michele E.; Hsu, Wayne W.
1993-01-01
Many CFD grid generation systems are in use nationally, but few comparative studies have been performed to quantify their relative merits. A study was undertaken to systematically evaluate and select the best CFD grid generation codes available. Detailed evaluation criteria were established as the basis for the evaluation conducted. Descriptions of thirty-four separate criteria, grouped into eight general categories are provided. Benchmark test cases, developed to test basic features of selected codes, are described in detail. Scoring guidelines were generated to establish standards for measuring code capabilities, ensuring uniformity of ratings, and minimizing personal bias among the three code evaluators. Ten candidate codes were identified from government, industry, universities, and commercial software companies. A three phase evaluation was conducted. In Phase 1, ten codes identified were screened through conversations with code authors and other industry experts. Seven codes were carried forward into a Phase 2 evaluation in which all codes were scored according to the predefined criteria. Two codes emerged as being significantly better than the others: RAGGS and GRIDGEN. Finally, these two codes were carried forward into a Phase 3 evaluation in which complex 3-D multizone grids were generated to verify capability.
Grid generation and flow computation about a Martian entry vehicle
NASA Technical Reports Server (NTRS)
Stewart, J. E.; Tiwari, S. N.
1990-01-01
A number of vehicles are currently being proposed for a manned mission to Mars. One of these vehicles has a modified blunt-nosed cone configuration. Experimental results were obtained for this vehicle in 1968. They show lift-over-drag ratios comparable to those needed for Mars entry. Computations are performed to verify the earlier results and to further describe the flight characteristics of this vehicle. An analytical method is used to define the surface of this vehicle. A single-block volume grid is generated around the vehicle using the algebraic Two-Boundary Grid Generation algorithm (TBGG) and transfinite interpolation. Euler solutions are then obtained from a Langley Aerodynamic Upward Relaxation Algorithm (LAURA) at Mach 6.0 and angles of attack of 0, 6, and 12 deg. The lift coefficient determined from the LAURA code agree very well with the experimental results. The drag and pitching moment coefficients, however, are underestimated by the code since viscous effects are not considered. Contour plots of the flowfield show no evidence of separation for angles of attack up to 12 deg.
Automatic structured grid generation using Gridgen (some restrictions apply)
NASA Technical Reports Server (NTRS)
Chawner, John R.; Steinbrenner, John P.
1995-01-01
The authors have noticed in the recent grid generation literature an emphasis on the automation of structured grid generation. The motivation behind such work is clear; grid generation is easily the most despised task in the grid-analyze-visualize triad of computational analysis (CA). However, because grid generation is closely coupled to both the design and analysis software and because quantitative measures of grid quality are lacking, 'push button' grid generation usually results in a compromise between speed, control, and quality. Overt emphasis on automation obscures the substantive issues of providing users with flexible tools for generating and modifying high quality grids in a design environment. In support of this paper's tongue-in-cheek title, many features of the Gridgen software are described. Gridgen is by no stretch of the imagination an automatic grid generator. Despite this fact, the code does utilize many automation techniques that permit interesting regenerative features.
Flames in fractal grid generated turbulence
NASA Astrophysics Data System (ADS)
Goh, K. H. H.; Geipel, P.; Hampp, F.; Lindstedt, R. P.
2013-12-01
Twin premixed turbulent opposed jet flames were stabilized for lean mixtures of air with methane and propane in fractal grid generated turbulence. A density segregation method was applied alongside particle image velocimetry to obtain velocity and scalar statistics. It is shown that the current fractal grids increase the turbulence levels by around a factor of 2. Proper orthogonal decomposition (POD) was applied to show that the fractal grids produce slightly larger turbulent structures that decay at a slower rate as compared to conventional perforated plates. Conditional POD (CPOD) was also implemented using the density segregation technique and the results show that CPOD is essential to segregate the relative structures and turbulent kinetic energy distributions in each stream. The Kolmogorov length scales were also estimated providing values ∼0.1 and ∼0.5 mm in the reactants and products, respectively. Resolved profiles of flame surface density indicate that a thin flame assumption leading to bimodal statistics is not perfectly valid under the current conditions and it is expected that the data obtained will be of significant value to the development of computational methods that can provide information on the conditional structure of turbulence. It is concluded that the increase in the turbulent Reynolds number is without any negative impact on other parameters and that fractal grids provide a route towards removing the classical problem of a relatively low ratio of turbulent to bulk strain associated with the opposed jet configuration.
Advancing-layers method for generation of unstructured viscous grids
NASA Technical Reports Server (NTRS)
Pirzadeh, Shahyar
1993-01-01
A novel approach for generating highly stretched grids which is based on a modified advancing-front technique and benefits from the generality, flexibility, and grid quality of the conventional advancing-front-based Euler grid generators is presented. The method is self-sufficient for the insertion of grid points in the boundary layer and beyond. Since it is based on a totally unstructured grid strategy, the method alleviates the difficulties stemming from the structural limitations of the prismatic techniques.
NASA Technical Reports Server (NTRS)
Bailey, R. T.; Shih, T. I.-P.; Nguyen, H. L.; Roelke, R. J.
1990-01-01
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
Hyperbolic Prismatic Grid Generation and Solution of Euler Equations on Prismatic Grids
NASA Technical Reports Server (NTRS)
Pandya, S. A.; Chattot, JJ; Hafez, M. M.; Kutler, Paul (Technical Monitor)
1994-01-01
A hyperbolic grid generation method is used to generate prismatic grids and an approach using prismatic grids to solve the Euler equations is presented. The theory of the stability and feasibility of the hyperbolic grid generation method is presented. The hyperbolic grid generation method of Steger et al for structured grids is applied to a three dimensional triangularized surface definition to generate a grid that is unstructured on each successive layer. The grid, however, retains structure in the body-normal direction and has a computational cell shaped like a triangular prism. In order to take advantage of the structure in the normal direction, a finite-volume scheme that treats the unknowns along the normal direction implicitly is introduced and the flow over a sphere is simulated.
Three-dimensional elliptic grid generation for an F-16
NASA Technical Reports Server (NTRS)
Sorenson, Reese L.
1988-01-01
A case history depicting the effort to generate a computational grid for the simulation of transonic flow about an F-16 aircraft at realistic flight conditions is presented. The flow solver for which this grid is designed is a zonal one, using the Reynolds averaged Navier-Stokes equations near the surface of the aircraft, and the Euler equations in regions removed from the aircraft. A body conforming global grid, suitable for the Euler equation, is first generated using 3-D Poisson equations having inhomogeneous terms modeled after the 2-D GRAPE code. Regions of the global grid are then designated for zonal refinement as appropriate to accurately model the flow physics. Grid spacing suitable for solution of the Navier-Stokes equations is generated in the refinement zones by simple subdivision of the given coarse grid intervals. That grid generation project is described, with particular emphasis on the global coarse grid.
Unstructured viscous grid generation by advancing-front method
NASA Technical Reports Server (NTRS)
Pirzadeh, Shahyar
1993-01-01
A new method of generating unstructured triangular/tetrahedral grids with high-aspect-ratio cells is proposed. The method is based on new grid-marching strategy referred to as 'advancing-layers' for construction of highly stretched cells in the boundary layer and the conventional advancing-front technique for generation of regular, equilateral cells in the inviscid-flow region. Unlike the existing semi-structured viscous grid generation techniques, the new procedure relies on a totally unstructured advancing-front grid strategy resulting in a substantially enhanced grid flexibility and efficiency. The method is conceptually simple but powerful, capable of producing high quality viscous grids for complex configurations with ease. A number of two-dimensional, triangular grids are presented to demonstrate the methodology. The basic elements of the method, however, have been primarily designed with three-dimensional problems in mind, making it extendible for tetrahedral, viscous grid generation.
Software Surface Modeling and Grid Generation Steering Committee
NASA Technical Reports Server (NTRS)
Smith, Robert E. (Editor)
1992-01-01
It is a NASA objective to promote improvements in the capability and efficiency of computational fluid dynamics. Grid generation, the creation of a discrete representation of the solution domain, is an essential part of computational fluid dynamics. However, grid generation about complex boundaries requires sophisticated surface-model descriptions of the boundaries. The surface modeling and the associated computation of surface grids consume an extremely large percentage of the total time required for volume grid generation. Efficient and user friendly software systems for surface modeling and grid generation are critical for computational fluid dynamics to reach its potential. The papers presented here represent the state-of-the-art in software systems for surface modeling and grid generation. Several papers describe improved techniques for grid generation.
NASA Technical Reports Server (NTRS)
Rostand, Philippe
1989-01-01
The incorporation of algebraic turbulence models in a solver for the 2-D compressible Navier-Stokes equations using triangular grids is described. A practial way to use the Cebeci Smith model, and to modify it in separated regions is proposed. The ability of the model to predict high speed, perfect gas boundary layers is investigated from a numerical point of view.
An algebra for spatio-temporal information generation
NASA Astrophysics Data System (ADS)
Pebesma, Edzer; Scheider, Simon; Gräler, Benedikt; Stasch, Christoph; Hinz, Matthias
2016-04-01
When we accept the premises of James Frew's laws of metadata (Frew's first law: scientists don't write metadata; Frew's second law: any scientist can be forced to write bad metadata), but also assume that scientists try to maximise the impact of their research findings, can we develop our information infrastructures such that useful metadata is generated automatically? Currently, sharing of data and software to completely reproduce research findings is becoming standard, e.g. in the Journal of Statistical Software [1]. The reproduction (e.g. R) scripts however convey correct syntax, but still limited semantics. We propose [2] a new, platform-neutral way to algebraically describe how data is generated, e.g. by observation, and how data is derived, e.g. by processing observations. It starts with forming functions composed of four reference system types (space, time, quality, entity), which express for instance continuity of objects over time, and continuity of fields over space and time. Data, which is discrete by definition, is generated by evaluating such functions at discrete space and time instances, or by evaluating a convolution (aggregation) over them. Derived data is obtained by inputting data to data derivation functions, which for instance interpolate, estimate, aggregate, or convert fields into objects and vice versa. As opposed to the traditional when, where and what semantics of data sets, our algebra focuses on describing how a data set was generated. We argue that it can be used to discover data sets that were derived from a particular source x, or derived by a particular procedure y. It may also form the basis for inferring meaningfulness of derivation procedures [3]. Current research focuses on automatically generating provenance documentation from R scripts. [1] http://www.jstatsoft.org/ (open access) [2] http://www.meaningfulspatialstatistics.org has the full paper (in review) [3] Stasch, C., S. Scheider, E. Pebesma, W. Kuhn, 2014. Meaningful
Asymptotics of bivariate generating functions with algebraic singularities
NASA Astrophysics Data System (ADS)
Greenwood, Torin
Flajolet and Odlyzko (1990) derived asymptotic formulae the coefficients of a class of uni- variate generating functions with algebraic singularities. Gao and Richmond (1992) and Hwang (1996, 1998) extended these results to classes of multivariate generating functions, in both cases by reducing to the univariate case. Pemantle and Wilson (2013) outlined new multivariate ana- lytic techniques and used them to analyze the coefficients of rational generating functions. After overviewing these methods, we use them to find asymptotic formulae for the coefficients of a broad class of bivariate generating functions with algebraic singularities. Beginning with the Cauchy integral formula, we explicity deform the contour of integration so that it hugs a set of critical points. The asymptotic contribution to the integral comes from analyzing the integrand near these points, leading to explicit asymptotic formulae. Next, we use this formula to analyze an example from current research. In the following chapter, we apply multivariate analytic techniques to quan- tum walks. Bressler and Pemantle (2007) found a (d + 1)-dimensional rational generating function whose coefficients described the amplitude of a particle at a position in the integer lattice after n steps. Here, the minimal critical points form a curve on the (d + 1)-dimensional unit torus. We find asymptotic formulae for the amplitude of a particle in a given position, normalized by the number of steps n, as n approaches infinity. Each critical point contributes to the asymptotics for a specific normalized position. Using Groebner bases in Maple again, we compute the explicit locations of peak amplitudes. In a scaling window of size the square root of n near the peaks, each amplitude is asymptotic to an Airy function.
Computing Aerodynamic Performance of a 2D Iced Airfoil: Blocking Topology and Grid Generation
NASA Technical Reports Server (NTRS)
Chi, X.; Zhu, B.; Shih, T. I.-P.; Slater, J. W.; Addy, H. E.; Choo, Yung K.; Lee, Chi-Ming (Technical Monitor)
2002-01-01
The ice accrued on airfoils can have enormously complicated shapes with multiple protruded horns and feathers. In this paper, several blocking topologies are proposed and evaluated on their ability to produce high-quality structured multi-block grid systems. A transition layer grid is introduced to ensure that jaggedness on the ice-surface geometry do not to propagate into the domain. This is important for grid-generation methods based on hyperbolic PDEs (Partial Differential Equations) and algebraic transfinite interpolation. A 'thick' wrap-around grid is introduced to ensure that grid lines clustered next to solid walls do not propagate as streaks of tightly packed grid lines into the interior of the domain along block boundaries. For ice shapes that are not too complicated, a method is presented for generating high-quality single-block grids. To demonstrate the usefulness of the methods developed, grids and CFD solutions were generated for two iced airfoils: the NLF0414 airfoil with and without the 623-ice shape and the B575/767 airfoil with and without the 145m-ice shape. To validate the computations, the computed lift coefficients as a function of angle of attack were compared with available experimental data. The ice shapes and the blocking topologies were prepared by NASA Glenn's SmaggIce software. The grid systems were generated by using a four-boundary method based on Hermite interpolation with controls on clustering, orthogonality next to walls, and C continuity across block boundaries. The flow was modeled by the ensemble-averaged compressible Navier-Stokes equations, closed by the shear-stress transport turbulence model in which the integration is to the wall. All solutions were generated by using the NPARC WIND code.
Interactive grid generation program for CAP-TSD
NASA Technical Reports Server (NTRS)
Bland, Samuel R.
1990-01-01
A grid generation program for use with the CAP-TSD transonic small disturbance code is described. The program runs interactively in FORTRAN on the Sun Workstation. A fifth-degree polynomial is used to map the grid index onto the computational coordinate. The grid is plotted to aid in the assessment of its quality and may be saved on file in NAMELIST format.
NASA Technical Reports Server (NTRS)
Chan, William M.; Akien, Edwin (Technical Monitor)
2002-01-01
For many years, generation of overset grids for complex configurations has required the use of a number of different independently developed software utilities. Results created by each step were then visualized using a separate visualization tool before moving on to the next. A new software tool called OVERGRID was developed which allows the user to perform all the grid generation steps and visualization under one environment. OVERGRID provides grid diagnostic functions such as surface tangent and normal checks as well as grid manipulation functions such as extraction, extrapolation, concatenation, redistribution, smoothing, and projection. Moreover, it also contains hyperbolic surface and volume grid generation modules that are specifically suited for overset grid generation. It is the first time that such a unified interface existed for the creation of overset grids for complex geometries. New concepts on automatic overset surface grid generation around surface discontinuities will also be briefly presented. Special control curves on the surface such as intersection curves, sharp edges, open boundaries, are called seam curves. The seam curves are first automatically extracted from a multiple panel network description of the surface. Points where three or more seam curves meet are automatically identified and are called seam corners. Seam corner surface grids are automatically generated using a singular axis topology. Hyperbolic surface grids are then grown from the seam curves that are automatically trimmed away from the seam corners.
Evaluation of the Dornier Gmbh interactive grid generation system
NASA Technical Reports Server (NTRS)
Brown, Robert L.
1989-01-01
An interactive grid generation program, INGRID, is investigated and evaluated. A description of the task and work performed, a description and evaluation of INGRID, and a discussion of the possibilities for bringing INGRID into the NASA and Numerical Aerodynamic Simulator (NAS) computing environments is included. The interactive grid generation program was found to be a viable approach for grid generation and determined that it could be converted to work in the NAS environment but that INGRID does not solve the fundamentally hard problems associated with grid generation, specifically, domain decomposition.
DRAGON Grid: A Three-Dimensional Hybrid Grid Generation Code Developed
NASA Technical Reports Server (NTRS)
Liou, Meng-Sing
2000-01-01
Because grid generation can consume 70 percent of the total analysis time for a typical three-dimensional viscous flow simulation for a practical engineering device, payoffs from research and development could reduce costs and increase throughputs considerably. In this study, researchers at the NASA Glenn Research Center at Lewis Field developed a new hybrid grid approach with the advantages of flexibility, high-quality grids suitable for an accurate resolution of viscous regions, and a low memory requirement. These advantages will, in turn, reduce analysis time and increase accuracy. They result from an innovative combination of structured and unstructured grids to represent the geometry and the computation domain. The present approach makes use of the respective strengths of both the structured and unstructured grid methods, while minimizing their weaknesses. First, the Chimera grid generates high-quality, mostly orthogonal meshes around individual components. This process is flexible and can be done easily. Normally, these individual grids are required overlap each other so that the solution on one grid can communicate with another. However, when this communication is carried out via a nonconservative interpolation procedure, a spurious solution can result. Current research is aimed at entirely eliminating this undesired interpolation by directly replacing arbitrary grid overlapping with a nonstructured grid called a DRAGON grid, which uses the same set of conservation laws over the entire region, thus ensuring conservation everywhere. The DRAGON grid is shown for a typical film-cooled turbine vane with 33 holes and 3 plenum compartments. There are structured grids around each geometrical entity and unstructured grids connecting them. In fiscal year 1999, Glenn researchers developed and tested the three-dimensional DRAGON grid-generation tools. A flow solver suitable for the DRAGON grid has been developed, and a series of validation tests are underway.
NASA Technical Reports Server (NTRS)
Eriksson, L. E.
1980-01-01
A direct algebraic method was developed and applied to generate three dimensional grids around wing-body configurations. The method used is a generalized transfinite interpolation method which generates the desired coordinate transformation using geometric data only on the boundaries of the domain of interest. The geometric data that can be specified includes not only coordinates on the boundaries but also out-of-surface parametric derivatives that give a very precise control over the transformation in the vicinity of the surface. In addition to this, the method gives good control over the stretching of the mesh between different boundaries.
Structured background grids for generation of unstructured grids by advancing front method
NASA Technical Reports Server (NTRS)
Pirzadeh, Shahyar
1991-01-01
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.
Generating functions and multiplicity formulas: The case of rank two simple Lie algebras
NASA Astrophysics Data System (ADS)
Fernández Núñez, José; García Fuertes, Wifredo; Perelomov, Askold M.
2015-09-01
A procedure is described that makes use of the generating function of characters to obtain a new generating function H giving the multiplicities of each weight in all the representations of a simple Lie algebra. The way to extract from H explicit multiplicity formulas for particular weights is explained and the results corresponding to rank two simple Lie algebras are shown.
Surface grid generation for wing-fuselage bodies
NASA Technical Reports Server (NTRS)
Smith, R. E.; Kudlinski, R. A.; Pitts, J. I.
1984-01-01
In the application of finite-difference methods to obtain numerical solutions of viscous compressible fluid flow about wing-fuselage bodies, it is advantageous to transform the governing equations to an idealized boundary-fitted coordinate system. The advantages are reduced computational complexity and added accuracy in the application of boundary conditions. The solution process requires that a grid be superimposed on the physical solution domain which corresponds to a uniform grid on a rectangular computational domain (uniform rectangular parallel-epiped). Grid generation is the determination of a one to one relationship between grid points in the physical domain and grid points in the computational domain. A technique for computing wing-fuselage surface grids using the Harris geometry and software for smooth-surface representation is described. Grid spacing control concepts which govern the relationship between the wing-fuselage surface and the computational grid are also presented.
Advanced Unstructured Grid Generation for Complex Aerodynamic Applications
NASA Technical Reports Server (NTRS)
Pirzadeh, Shahyar Z.
2008-01-01
A new approach for distribution of grid points on the surface and in the volume has been developed and implemented in the NASA unstructured grid generation code VGRID. In addition to the point and line sources of prior work, the new approach utilizes surface and volume sources for automatic curvature-based grid sizing and convenient point distribution in the volume. A new exponential growth function produces smoother and more efficient grids and provides superior control over distribution of grid points in the field. All types of sources support anisotropic grid stretching which not only improves the grid economy but also provides more accurate solutions for certain aerodynamic applications. The new approach does not require a three-dimensional background grid as in the previous methods. Instead, it makes use of an efficient bounding-box auxiliary medium for storing grid parameters defined by surface sources. The new approach is less memory-intensive and more efficient computationally. The grids generated with the new method either eliminate the need for adaptive grid refinement for certain class of problems or provide high quality initial grids that would enhance the performance of many adaptation methods.
NASA Technical Reports Server (NTRS)
Warsi, Saif A.
1989-01-01
A detailed operating manual is presented for a grid generating program that produces 3-D meshes for advanced turboprops. The code uses both algebraic and elliptic partial differential equation methods to generate single rotation and counterrotation, H or C type meshes for the z - r planes and H type for the z - theta planes. The code allows easy specification of geometrical constraints (such as blade angle, location of bounding surfaces, etc.), mesh control parameters (point distribution near blades and nacelle, number of grid points desired, etc.), and it has good runtime diagnostics. An overview is provided of the mesh generation procedure, sample input dataset with detailed explanation of all input, and example meshes.
MESH2D GRID GENERATOR DESIGN AND USE
Flach, G.; Smith, F.
2012-01-20
Mesh2d is a Fortran90 program designed to generate two-dimensional structured grids of the form [x(i),y(i,j)] where [x,y] are grid coordinates identified by indices (i,j). The x(i) coordinates alone can be used to specify a one-dimensional grid. Because the x-coordinates vary only with the i index, a two-dimensional grid is composed in part of straight vertical lines. However, the nominally horizontal y(i,j{sub 0}) coordinates along index i are permitted to undulate or otherwise vary. Mesh2d also assigns an integer material type to each grid cell, mtyp(i,j), in a user-specified manner. The complete grid is specified through three separate input files defining the x(i), y(i,j), and mtyp(i,j) variations. The overall mesh is constructed from grid zones that are typically then subdivided into a collection of smaller grid cells. The grid zones usually correspond to distinct materials or larger-scale geometric shapes. The structured grid zones are identified through uppercase indices (I,J). Subdivision of zonal regions into grid cells can be done uniformly, or nonuniformly using either a polynomial or geometric skewing algorithm. Grid cells may be concentrated backward, forward, or toward both ends. Figure 1 illustrates the above concepts in the context of a simple four zone grid.
Surface and Volume Grid Generation in Parametric Form
NASA Technical Reports Server (NTRS)
Yu, Tzuyi; Soni, Bharat K.; Benjamin, Ted; Williams, Robert
1996-01-01
The algorithm for surface modeling and volume grid generation using parametric Non-Uniform Rational B-splines (NURBS) geometric representation are presented. The enhanced re-parameterization algorithm which can yield a desired physical distribution on the curve, surface, and volume is also presented. This approach bridges the gap between computer aided design surface/volume definition and surface/volume grid generation.
Grid generation on trimmed Bezier and NURBS quilted surfaces
NASA Technical Reports Server (NTRS)
Woan, Chung-Jin; Clever, Willard C.; Tam, Clement K.
1995-01-01
This paper presents some recently added capabilities to RAGGS, Rockwell Automated Grid Generation System. Included are the trimmed surface handling and display capability and structures and unstructured grid generation on trimmed Bezier and NURBS (non-uniform rational B-spline surfaces) quilted surfaces. Samples are given to demonstrate the new capabilities.
S3D: An interactive surface grid generation tool
NASA Technical Reports Server (NTRS)
Luh, Raymond Ching-Chung; Pierce, Lawrence E.; Yip, David
1992-01-01
S3D, an interactive software tool for surface grid generation, is described. S3D provides the means with which a geometry definition based either on a discretized curve set or a rectangular set can be quickly processed towards the generation of a surface grid for computational fluid dynamics (CFD) applications. This is made possible as a result of implementing commonly encountered surface gridding tasks in an environment with a highly efficient and user friendly graphical interface. Some of the more advanced features of S3D include surface-surface intersections, optimized surface domain decomposition and recomposition, and automated propagation of edge distributions to surrounding grids.
TCGRID: A three dimensional C-grid generator for turbomachinery
NASA Technical Reports Server (NTRS)
Chima, Rodrick V.
1992-01-01
A fast 3-D grid code for turbomachinery was developed. The code, TCGRID (Turbomachinery C-GRID), can generate either C or H type grids for fairly arbitrary axial or radical turbomachinery geometries. The code also has limited blocked grid capability and can generate an axisymmetric H type grid upstream of the blade row or an O type grid within the tip clearance region. Hub and tip geometries are input as a simple list of pairs. All geometric data is handled using parametric splines so that geometries that turn 90 degrees can be handled without difficulty. Blade input is in standard MERIDL or Lewis compressor design code format. TCGRID adds leading and trailing edge circles to MERIDL geometries and intersects the blade with the hub and tip if necessary using a novel intersection algorithm. The procedure used to generate the grid is given. Output is in PLOT3D format, which can also be read by the RVC3D (Rotor Viscous Code 3-D) Navier-Stokes code for turbomachinery. Intermediate 2-D or 3-D grids useful for debug and other purposes can also be output using a convenient output flag. A grid generated figure is given.
Three-dimensional hybrid grid generation using advancing front techniques
NASA Technical Reports Server (NTRS)
Steinbrenner, John P.; Noack, Ralph W.
1995-01-01
A new 3-dimensional hybrid grid generation technique has been developed, based on ideas of advancing fronts for both structured and unstructured grids. In this approach, structured grids are first generate independently around individual components of the geometry. Fronts are initialized on these structure grids, and advanced outward so that new cells are extracted directly from the structured grids. Employing typical advancing front techniques, cells are rejected if they intersect the existing front or fail other criteria When no more viable structured cells exist further cells are advanced in an unstructured manner to close off the overall domain, resulting in a grid of 'hybrid' form. There are two primary advantages to the hybrid formulation. First, generating blocks with limited regard to topology eliminates the bottleneck encountered when a multiple block system is used to fully encapsulate a domain. Individual blocks may be generated free of external constraints, which will significantly reduce the generation time. Secondly, grid points near the body (presumably with high aspect ratio) will still maintain a structured (non-triangular or tetrahedral) character, thereby maximizing grid quality and solution accuracy near the surface.
Advanced Unstructured Grid Generation for Complex Aerodynamic Applications
NASA Technical Reports Server (NTRS)
Pirzadeh, Shahyar
2010-01-01
A new approach for distribution of grid points on the surface and in the volume has been developed. In addition to the point and line sources of prior work, the new approach utilizes surface and volume sources for automatic curvature-based grid sizing and convenient point distribution in the volume. A new exponential growth function produces smoother and more efficient grids and provides superior control over distribution of grid points in the field. All types of sources support anisotropic grid stretching which not only improves the grid economy but also provides more accurate solutions for certain aerodynamic applications. The new approach does not require a three-dimensional background grid as in the previous methods. Instead, it makes use of an efficient bounding-box auxiliary medium for storing grid parameters defined by surface sources. The new approach is less memory-intensive and more efficient computationally. The grids generated with the new method either eliminate the need for adaptive grid refinement for certain class of problems or provide high quality initial grids that would enhance the performance of many adaptation methods.
An interactive grid generator for TOUGH family code
2004-01-09
WinGridder has been developed for designing, generating, and visualizing (at various spatial scales) numerical grids used in reservoir simulations and groundwater modeling studies. It can save mesh files for TOUGH family codes and output additional grid information for various purposes in either graphic format or plain text format, many important features, such as inclined faults and offset, layering structure, local refinements, and embedded engineering structures, can be represented in the grid. The main advantages ofmore » this grid-generation software are its user friendly graphical interfaces, flexible grid design capabilities, efficient grid generation, and powerful searching and post-processing capability, especially for large size grid (e.g., a grid of million grid cells). The main improvements of the version 2.0 are (1) to add a capability of handling a repository with multiple sub-regions and specified drifts, (2) to use an interpolation method, instead of picking the nearest point, in calculating the geological data from the given digital geological model, and (3) enhanced searching and other capability.« less
NASA Technical Reports Server (NTRS)
Choo, Yung K.; Soh, Woo-Yung; Yoon, Seokkwan
1989-01-01
A finite-volume lower-upper (LU) implicit scheme is used to simulate an inviscid flow in a turbine cascade. This approximate factorization scheme requires only the inversion of sparse lower and upper triangular matrices, which can be done efficiently without extensive storage. As an implicit scheme it allows a large time step to reach the steady state. An interactive grid generation program (TURBO), which is being developed, is used to generate grids. This program uses the control point form of algebraic grid generation which uses a sparse collection of control points from which the shape and position of coordinate curves can be adjusted. A distinct advantage of TURBO compared with other grid generation programs is that it allows the easy change of local mesh structure without affecting the grid outside the domain of dependence. Sample grids are generated by TURBO for a compressor rotor blade and a turbine cascade. The turbine cascade flow is simulated by using the LU implicit scheme on the grid generated by TURBO.
NASA Technical Reports Server (NTRS)
Choo, Yung K.; Soh, Woo-Yung; Yoon, Seokkwan
1989-01-01
A finite-volume lower-upper (LU) implicit scheme is used to simulate an inviscid flow in a tubine cascade. This approximate factorization scheme requires only the inversion of sparse lower and upper triangular matrices, which can be done efficiently without extensive storage. As an implicit scheme it allows a large time step to reach the steady state. An interactive grid generation program (TURBO), which is being developed, is used to generate grids. This program uses the control point form of algebraic grid generation which uses a sparse collection of control points from which the shape and position of coordinate curves can be adjusted. A distinct advantage of TURBO compared with other grid generation programs is that it allows the easy change of local mesh structure without affecting the grid outside the domain of independence. Sample grids are generated by TURBO for a compressor rotor blade and a turbine cascade. The turbine cascade flow is simulated by using the LU implicit scheme on the grid generated by TURBO.
A generalized scheme for three-dimensional hyperbolic grid generation
NASA Technical Reports Server (NTRS)
Chan, William M.; Steger, Joseph L.
1991-01-01
A hyperbolic grid generation scheme formulated from grid orthogonality and cell volume specification is generalized such that high quality three-dimensional grids can be obtained for a wide variety of geometries. The speed of the scheme is one to two orders of magnitude faster than typical elliptic grid generation methods. The robustness of the scheme is significantly enhanced by several new techniques. By using a spatially variable smoothing coefficient, orthogonality and smoothness of the grid are maintained around complex concave and convex surface topologies. A metric correction procedure is employed to guarantee that the grid marches out of a corner by bisecting the angles subtended by the neighboring points. Extra robustness at severe convex corners is achieved by special local treatments. Different extrapolation methods are used to provide smoothness at floating edges and axis regions. The versatility of the new hyperbolic grid generation scheme is demonstrated by three-dimensional grids generated for external components of the intergrated Space Shuttle vehicle and the SOFIA telescope.
Methods for prismatic/tetrahedral grid generation and adaptation
NASA Astrophysics Data System (ADS)
Kallinderis, Y.
1995-10-01
The present work involves generation of hybrid prismatic/tetrahedral grids for complex 3-D geometries including multi-body domains. The prisms cover the region close to each body's surface, while tetrahedra are created elsewhere. Two developments are presented for hybrid grid generation around complex 3-D geometries. The first is a new octree/advancing front type of method for generation of the tetrahedra of the hybrid mesh. The main feature of the present advancing front tetrahedra generator that is different from previous such methods is that it does not require the creation of a background mesh by the user for the determination of the grid-spacing and stretching parameters. These are determined via an automatically generated octree. The second development is a method for treating the narrow gaps in between different bodies in a multiply-connected domain. This method is applied to a two-element wing case. A High Speed Civil Transport (HSCT) type of aircraft geometry is considered. The generated hybrid grid required only 170 K tetrahedra instead of an estimated two million had a tetrahedral mesh been used in the prisms region as well. A solution adaptive scheme for viscous computations on hybrid grids is also presented. A hybrid grid adaptation scheme that employs both h-refinement and redistribution strategies is developed to provide optimum meshes for viscous flow computations. Grid refinement is a dual adaptation scheme that couples 3-D, isotropic division of tetrahedra and 2-D, directional division of prisms.
Best Practices in Overset Grid Generation
NASA Technical Reports Server (NTRS)
Gomez, Reynaldo J., III
2002-01-01
Accurate geometry + high quality grids are necessary for an accurate solution. Other requirements include a) Verified/validated solver with appropriate physics b) Convergence criteria consistent with application: 1) Aerodynamics - forces and moments; 2) Heat transfer - maximum and minimum heat transfer coefficients.
3D Structured Grid Generation Codes for Turbomachinery
NASA Technical Reports Server (NTRS)
Loellbach, James; Tsung, Fu-Lin
1999-01-01
This report describes the research tasks during the past year. The research was mainly in the area of computational grid generation in support of CFD analyses of turbomachinery components. In addition to the grid generation work, a numerical simulation was obtained for the flow through a centrifugal gas compressor using an unstructured Navier-Stokes solver. Other tasks involved many different turbomachinery component analyses. These analyses were performed for NASA projects or for industrial applications. The work includes both centrifugal and axial machines, single and multiple blade rows, and steady and unsteady analyses. Over the past five years, a set of structured grid generation codes were developed that allow grids to be obtained fairly quickly for the large majority of configurations we encounter. These codes do not comprise a generalized grid generation package; they are noninteractive codes specifically designed for turbomachinery blade row geometries. But because of this limited scope, the codes are small, fast, and portable, and they can be run in the batch mode on small workstations. During the past year, these programs were used to generate computational grids were modified for a wide variety of configurations. In particular, the codes or wrote supplementary codes to improve our grid generation capabilities for multiple blade row configurations. This involves generating separate grids for each blade row, and then making them match and overlap by a few grid points at their common interface so that fluid properties are communicated across the interface. Unsteady rotor/stator analyses were performed for an axial turbine, a centrifugal compressor, and a centrifugal pump. Steady-state single-blade-row analyses were made for a study of blade sweep in transonic compressors. There was also cooperation on the application of an unstructured Navier-Stokes solver for turbomachinery flow simulations. In particular, the unstructured solver was used to analyze the
Incompressible and anelastic flow simulations on numerically generated grids
NASA Technical Reports Server (NTRS)
Sharman, R. D.; Keller, T. L.; Wurtele, M. G.
1988-01-01
In the numerical simulation of incompressible and anelastic flows, it is necessary to solve an elliptic equation at each time step. When the boundaries of such flows are nonrectangular, it may be advantageous to solve the equations on a new, numerically generated coordinate grid, in which the property of orthogonality has been preserved. Flow equations in general curvilinear coordinates maintaining the conservative form are given for both anelastic models using the momentum equations, and for incompressible models, using the vorticity equation. The general problem of grid-generation in two dimensions is presented, and a quasi-conformal transformation technique is discussed in detail. Some examples of grids generated by this technique are exhibited. Three examples of the flow of a stratified fluid over obstacles are presented, in which the grid-generation permits some new results to be obtained.
Grid generation and inviscid flow computation about aircraft geometries
NASA Technical Reports Server (NTRS)
Smith, Robert E.
1989-01-01
Grid generation and Euler flow about fighter aircraft are described. A fighter aircraft geometry is specified by an area ruled fuselage with an internal duct, cranked delta wing or strake/wing combinations, canard and/or horizontal tail surfaces, and vertical tail surfaces. The initial step before grid generation and flow computation is the determination of a suitable grid topology. The external grid topology that has been applied is called a dual-block topology which is a patched C (exp 1) continuous multiple-block system where inner blocks cover the highly-swept part of a cranked wing or strake, rearward inner-part of the wing, and tail components. Outer-blocks cover the remainder of the fuselage, outer-part of the wing, canards and extend to the far field boundaries. The grid generation is based on transfinite interpolation with Lagrangian blending functions. This procedure has been applied to the Langley experimental fighter configuration and a modified F-18 configuration. Supersonic flow between Mach 1.3 and 2.5 and angles of attack between 0 degrees and 10 degrees have been computed with associated Euler solvers based on the finite-volume approach. When coupling geometric details such as boundary layer diverter regions, duct regions with inlets and outlets, or slots with the general external grid, imposing C (exp 1) continuity can be extremely tedious. The approach taken here is to patch blocks together at common interfaces where there is no grid continuity, but enforce conservation in the finite-volume solution. The key to this technique is how to obtain the information required for a conservative interface. The Ramshaw technique which automates the computation of proportional areas of two overlapping grids on a planar surface and is suitable for coding was used. Researchers generated internal duct grids for the Langley experimental fighter configuration independent of the external grid topology, with a conservative interface at the inlet and outlet.
Surface modeling and grid generation for aeropropulsion CFD
NASA Technical Reports Server (NTRS)
Choo, Yung K.; Slater, John W.; Loellbach, James; Lee, Jinho
1995-01-01
The efforts in geometry modeling and grid generation at the NASA Lewis Research Center, as applied to the computational fluid dynamic (CFD) analysis of aeropropulsion systems, are presented. The efforts are mainly characterized by a focus on the analysis of components of an aeropropulsion system, which involve turbulent viscous flow with heat transfer and chemistry. Thus, this discussion will follow that characterization and will sequence through the components of typical propulsion systems consisting of inlets, compressors, combustors, turbines, and nozzles. For each component, some applications of CFD analysis will be presented to show how CFD is used to compute the desired performance information, how geometry modeling and grid generation are performed, and what issues have developed related to geometry modeling and grid generation. The discussion will illustrate the following needs related to geometry modeling and grid generation as observed in aeropropulsion analysis: (1) accurate and efficient resolution of turbulent viscous and chemically-reacting flowfields; (2) easy-to-use interfaces with CAD data for automated grid generation about complex geometries; and (3) automated batch grid generation software for use with design and optimization software.
Some effects of vortex shedding in grid-generated turbulence
NASA Astrophysics Data System (ADS)
Melina, Gianfrancesco; Bruce, Paul J. K.; Vassilicos, John Christos
2015-11-01
We perform hot-wire measurements in a wind tunnel downstream of different types of turbulence-generating grids: a regular grid (RG60), a fractal square grid (FSG17) and a single square grid (SSG). We characterize the flow highlighting similarities and differences between the grids and between the production and the decay regions of turbulence. We focus on the effects of vortex shedding from the bars of the grids. For this purpose we design a novel 3D configuration formed by the SSG and a set of four splitter plates detached from the grid. We show that, by placing the splitter plates, the peak of turbulence intensity on the centerline is reduced and its location is moved downstream. We compare data from the different turbulence generators and find that a reduction of vortex shedding energy correlates with an increase in the magnitudes of the skewness and flatness of the turbulent velocity fluctuations in the production region. The authors acknowledge support form the EU through the FP7 Marie Curie MULTISOLVE project (grant agreement No. 317269).
Marshall Space Flight Center surface modeling and grid generation applications
NASA Technical Reports Server (NTRS)
Williams, Robert W.; Benjamin, Theodore G.; Cornelison, Joni W.
1995-01-01
The Solid Rocket Motors (SRM) used by NASA to propel the Space Shuttle employ gimballing nozzles as a means for vehicular guidance during launch and ascent. Gimballing a nozzle renders the pressure field of the exhaust gases nonaxisymmetric. This has two effects: (1) it exerts a torque and side load on the nozzle; and (2) the exhaust gases flow circumferentially in the aft-dome region, thermally loading the flexible boot, case-to-nozzle joint, and casing insulation. The use of CFD models to simulate such flows is imperative in order to assess SRM design. The grids for these problems were constructed by obtaining information from drawings and tabulated coordinates. The 2D axisymmetric grids were designed and generated using the EZ-Surf and GEN2D surface and grid generation codes. These 2D grids were solved using codes such as FDNS, GASP, and MINT. These axisymmetric grids were rotated around the center-line to form 3D nongimballed grids. These were then gimballed around the pivot point and the gaps or overlaps resurfaced to obtain the final domains, which contained approximately 366,000 grid points. The 2D solutions were then rotated and manipulated as appropriate for geometry and used as initial guesses in the final solution. The analyses were used in answering questions about flight criteria.
Marshall Space Flight Center surface modeling and grid generation applications
NASA Astrophysics Data System (ADS)
Williams, Robert W.; Benjamin, Theodore G.; Cornelison, Joni W.
1995-03-01
The Solid Rocket Motors (SRM) used by NASA to propel the Space Shuttle employ gimballing nozzles as a means for vehicular guidance during launch and ascent. Gimballing a nozzle renders the pressure field of the exhaust gases nonaxisymmetric. This has two effects: (1) it exerts a torque and side load on the nozzle; and (2) the exhaust gases flow circumferentially in the aft-dome region, thermally loading the flexible boot, case-to-nozzle joint, and casing insulation. The use of CFD models to simulate such flows is imperative in order to assess SRM design. The grids for these problems were constructed by obtaining information from drawings and tabulated coordinates. The 2D axisymmetric grids were designed and generated using the EZ-Surf and GEN2D surface and grid generation codes. These 2D grids were solved using codes such as FDNS, GASP, and MINT. These axisymmetric grids were rotated around the center-line to form 3D nongimballed grids. These were then gimballed around the pivot point and the gaps or overlaps resurfaced to obtain the final domains, which contained approximately 366,000 grid points. The 2D solutions were then rotated and manipulated as appropriate for geometry and used as initial guesses in the final solution. The analyses were used in answering questions about flight criteria.
Ray tracing for point distribution in unstructured grid generation
Khamayseh, A.; Ortega, F.; Trease, H.
1995-12-31
We present a procedure by which grid points are generated on surfaces or within three-dimensional volumes to produce high quality unstructed grids for complex geometries. The virtue of this method is based on ray-tracing approach for curved polyhedra whose faces may lie on natural quadrics (planes, cylinders, cones, or spheres) or triangular faceted surfaces. We also present an efficient point location algorithm for identifying points relative to various regions with classification of inside/on/outside.
Triangle geometry processing for surface modeling and cartesian grid generation
Aftosmis, Michael J [San Mateo, CA; Melton, John E [Hollister, CA; Berger, Marsha J [New York, NY
2002-09-03
Cartesian mesh generation is accomplished for component based geometries, by intersecting components subject to mesh generation to extract wetted surfaces with a geometry engine using adaptive precision arithmetic in a system which automatically breaks ties with respect to geometric degeneracies. During volume mesh generation, intersected surface triangulations are received to enable mesh generation with cell division of an initially coarse grid. The hexagonal cells are resolved, preserving the ability to directionally divide cells which are locally well aligned.
Triangle Geometry Processing for Surface Modeling and Cartesian Grid Generation
NASA Technical Reports Server (NTRS)
Aftosmis, Michael J. (Inventor); Melton, John E. (Inventor); Berger, Marsha J. (Inventor)
2002-01-01
Cartesian mesh generation is accomplished for component based geometries, by intersecting components subject to mesh generation to extract wetted surfaces with a geometry engine using adaptive precision arithmetic in a system which automatically breaks ties with respect to geometric degeneracies. During volume mesh generation, intersected surface triangulations are received to enable mesh generation with cell division of an initially coarse grid. The hexagonal cells are resolved, preserving the ability to directionally divide cells which are locally well aligned.
Geometry definition and grid generation for a complete fighter aircraft
NASA Technical Reports Server (NTRS)
Edwards, T. A.
1986-01-01
Recent advances in computing power and numerical solution procedures have enabled computational fluid dynamicists to attempt increasingly difficult problems. In particular, efforts are focusing on computations of complex three-dimensional flow fields about realistic aerodynamic bodies. To perform such computations, a very accurate and detailed description of the surface geometry must be provided, and a three-dimensional grid must be generated in the space around the body. The geometry must be supplied in a format compatible with the grid generation requirements, and must be verified to be free of inconsistencies. This paper presents a procedure for performing the geometry definition of a fighter aircraft that makes use of a commercial computer-aided design/computer-aided manufacturing system. Furthermore, visual representations of the geometry are generated using a computer graphics system for verification of the body definition. Finally, the three-dimensional grids for fighter-like aircraft are generated by means of an efficient new parabolic grid generation method. This method exhibits good control of grid quality.
A Richer Understanding of Algebra
ERIC Educational Resources Information Center
Foy, Michelle
2008-01-01
Algebra is one of those hard-to-teach topics where pupils seem to struggle to see it as more than a set of rules to learn, but this author recently used the software "Grid Algebra" from ATM, which engaged her Year 7 pupils in exploring algebraic concepts for themselves. "Grid Algebra" allows pupils to experience number, pre-algebra, and algebra…
Grid generation and flow solution method for Euler equations on unstructured grids
NASA Technical Reports Server (NTRS)
Anderson, W. Kyle
1992-01-01
A grid generation and flow solution algorithm for the Euler equations on unstructured grids is presented. The grid generation scheme, which uses Delaunay triangulation, generates the field points for the mesh based on cell aspect ratios and allows clustering of grid points near solid surfaces. The flow solution method is an implicit algorithm in which the linear set of equations arising at each time step is solved using a Gauss-Seidel procedure that is completely vectorizable. Also, a study is conducted to examine the number of subiterations required for good convergence of the overall algorithm. Grid generation results are shown in two dimensions for an NACA 0012 airfoil as well as a two element configuration. Flow solution results are shown for a two dimensional flow over the NACA 0012 airfoil and for a two element configuration in which the solution was obtained through an adaptation procedure and compared with an exact solution. Preliminary three dimensional results also are shown in which the subsonic flow over a business jet is computed.
Variational method for adaptive grid generation
Brackbill, J.U.
1983-01-01
A variational method for generating adaptive meshes is described. Functionals measuring smoothness, skewness, orientation, and the Jacobian are minimized to generate a mapping from a rectilinear domain in natural coordinate to an arbitrary domain in physical coordinates. From the mapping, a mesh is easily constructed. In using the method to adaptively zone computational problems, as few as one third the number of mesh points are required in each coordinate direction compared with a uniformly zoned mesh.
NASA Technical Reports Server (NTRS)
Smith, R. E.
1981-01-01
A grid generation technique called the two boundary technique is developed and applied for the solution of the three dimensional Navier-Stokes equations. The Navier-Stokes equations are transformed from a cartesian coordinate system to a computational coordinate system, and the grid generation technique provides the Jacobian matrix describing the transformation. The two boundary technique is based on algebraically defining two distinct boundaries of a flow domain and the distribution of the grid is achieved by applying functions to the uniform computational grid which redistribute the computational independent variables and consequently concentrate or disperse the grid points in the physical domain. The Navier-Stokes equations are solved using a MacCormack time-split technique. Grids and supersonic laminar flow solutions are obtained for a family of three dimensional corners and two spike-nosed bodies.
NASA Technical Reports Server (NTRS)
Dulikravich, D. S.
1982-01-01
A fast computer program, GRID3C, was developed for accurately generating periodic, boundary conforming, three dimensional, consecutively refined computational grids applicable to realistic axial turbomachinery geometries. The method is based on using two functions to generate two dimensional grids on a number of coaxial axisymmetric surfaces positioned between the centerbody and the outer radial boundary. These boundary fitted grids are of the C type and are characterized by quasi-orthogonality and geometric periodicity. The built in nonorthogonal coordinate stretchings and shearings cause the grid clustering in the regions of interest. The stretching parameters are part of the input to GRID3C. In its present version GRID3C can generate and store a maximum of four consecutively refined three dimensional grids. The output grid coordinates can be calculated either in the Cartesian or in the cylindrical coordinate system.
Enhanced Product Generation at NASA Data Centers Through Grid Technology
NASA Technical Reports Server (NTRS)
Barkstrom, Bruce R.; Hinke, Thomas H.; Gavali, Shradha; Seufzer, William J.
2003-01-01
This paper describes how grid technology can support the ability of NASA data centers to provide customized data products. A combination of grid technology and commodity processors are proposed to provide the bandwidth necessary to perform customized processing of data, with customized data subsetting providing the initial example. This customized subsetting engine can be used to support a new type of subsetting, called phenomena-based subsetting, where data is subsetted based on its association with some phenomena, such as mesoscale convective systems or hurricanes. This concept is expanded to allow the phenomena to be detected in one type of data, with the subsetting requirements transmitted to the subsetting engine to subset a different type of data. The subsetting requirements are generated by a data mining system and transmitted to the subsetter in the form of an XML feature index that describes the spatial and temporal extent of the phenomena. For this work, a grid-based mining system called the Grid Miner is used to identify the phenomena and generate the feature index. This paper discusses the value of grid technology in facilitating the development of a high performance customized product processing and the coupling of a grid mining system to support phenomena-based subsetting.
Mixed Element Type Unstructured Grid Generation for Viscous Flow Applications
NASA Technical Reports Server (NTRS)
Marcum, David L.; Gaither, J. Adam
2000-01-01
A procedure is presented for efficient generation of high-quality unstructured grids suitable for CFD simulation of high Reynolds number viscous flow fields. Layers of anisotropic elements are generated by advancing along prescribed normals from solid boundaries. The points are generated such that either pentahedral or tetrahedral elements with an implied connectivity can be be directly recovered. As points are generated they are temporarily attached to a volume triangulation of the boundary points. This triangulation allows efficient local search algorithms to be used when checking merging layers, The existing advancing-front/local-reconnection procedure is used to generate isotropic elements outside of the anisotropic region. Results are presented for a variety of applications. The results demonstrate that high-quality anisotropic unstructured grids can be efficiently and consistently generated for complex configurations.
Recent enhancements to the GRIDGEN structured grid generation system
NASA Technical Reports Server (NTRS)
Steinbrenner, John P.; Chawner, John R.
1992-01-01
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.
NASA Astrophysics Data System (ADS)
Schertzer, Daniel; Tchiguirinskaia, Ioulia
2014-05-01
A complex key feature of turbulence is that the velocity is a vector field, whereas intermittency, another key feature, has been mostly understood, analysed and simulated in scalar frameworks. This gap has prevented many developments. Some years ago, the general framework of 'Lie cascades' was introduced (Schertzer and Lovejoy, 1993) to deal with both features by considering cascades generated by stochastic Lie algebra. However, the theoretical efforts were mostly concentrated on the decomposition of this algebra into its radical and a semi-simple algebra and faced too many degrees of freedom. In this communication, we show that the class of Clifford algebra is already wide enough, very convenient and physically meaningful to understand, analyse and simulate intermittent vector fields.
Grid generation and surface modeling for CFD
NASA Technical Reports Server (NTRS)
Connell, Stuart D.; Sober, Janet S.; Lamson, Scott H.
1995-01-01
When computing the flow around complex three dimensional configurations, the generation of the mesh is the most time consuming part of any calculation. With some meshing technologies this can take of the order of a man month or more. The requirement for a number of design iterations coupled with ever decreasing time allocated for design leads to the need for a significant acceleration of this process. Of the two competing approaches, block-structured and unstructured, only the unstructured approach will allow fully automatic mesh generation directly from a CAD model. Using this approach coupled with the techniques described in this paper, it is possible to reduce the mesh generation time from man months to a few hours on a workstation. The desire to closely couple a CFD code with a design or optimization algorithm requires that the changes to the geometry be performed quickly and in a smooth manner. This need for smoothness necessitates the use of Bezier polynomials in place of the more usual NURBS or cubic splines. A two dimensional Bezier polynomial based design system is described.
NASA Technical Reports Server (NTRS)
Houston, Johnny L.
1989-01-01
Program EAGLE (Eglin Arbitrary Geometry Implicit Euler) Numerical Grid Generation System is a composite (multi-block) algebraic or elliptic grid generation system designed to discretize the domain in and/or around any arbitrarily shaped three dimensional regions. This system combines a boundary conforming surface generation scheme and includes plotting routines designed to take full advantage of the DISSPLA Graphics Package (Version 9.0). Program EAGLE is written to compile and execute efficiently on any Cray machine with or without solid state disk (SSD) devices. Also, the code uses namelist inputs which are supported by all Cray machines using the FORTRAN compiler CFT77. The namelist inputs makes it easier for the user to understand the inputs and operation of Program EAGLE. EAGLE's numerical grid generator is constructed in the following form: main program, EGG (executive routine); subroutine SURFAC (surface generation routine); subroutine GRID (grid generation routine); and subroutine GRDPLOT (grid plotting routines). The EAGLE code was modified to use on the NASA-LaRC SNS computer (Cray 2S) system. During the modification a conversion program was developed for the output data of EAGLE's subroutine GRID to permit the data to be graphically displayed by IRIS workstations, using Plot3D. The code of program EAGLE was modified to make operational subroutine GRDPLOT (using DI-3000 Graphics Software Packages) on the NASA-LaRC SNS Computer System. How to implement graphically, the output data of subroutine GRID was determined on any NASA-LaRC graphics terminal that has access to the SNS Computer System DI-300 Graphics Software Packages. A Quick Reference User Guide was developed for the use of program EAGLE on the NASA-LaRC SNS Computer System. One or more application program(s) was illustrated using program EAGLE on the NASA LaRC SNS Computer System, with emphasis on graphics illustrations.
A grid generation and flow solution method for the Euler equations on unstructured grids
NASA Technical Reports Server (NTRS)
Anderson, W. Kyle
1994-01-01
A grid generation and flow solution algorithm for the Euler equations on unstructured grids is presented. The grid generation scheme utilizes Delaunay triangulation and self-generates the field points for the mesh based on cell aspect ratios and allows for clustering near solid surfaces. The flow solution method is an implicit algorithm in which the linear set of equations arising at each time step is solved using a Gauss Seidel procedure which is completely vectorizable. In addition, a study is conducted to examine the number of subiterations required for good convergence of the overall algorithm. Grid generation results are shown in two dimensions for a National Advisory Committee for Aeronautics (NACA) 0012 airfoil as well as a two-element configuration. Flow solution results are shown for two-dimensional flow over the NACA 0012 airfoil and for a two-element configuration in which the solution has been obtained through an adaptation procedure and compared to an exact solution. Preliminary three-dimensional results are also shown in which subsonic flow over a business jet is computed.
A grid generation and flow solution method for the Euler equations on unstructured grids
Anderson, W.K. )
1994-01-01
A grid generation and flow solution algorithm for the Euler equations on unstructured grids is presented. The grid generation scheme utilizes Delaunay triangulation and self-generates the field points for the mesh based on cell aspect ratios and allows for clustering near solid surfaces. The flow solution method is an implicit algorithm in which the linear set or equations arising at each time step is solved using a Gauss Seidel procedure which is completely vectorizable. In addition, a study is conducted to examine the number of subiterations required for good convergence of the overall algorithm. Grid generation results are shown in two dimensions for a NACA 0012 airfoil as well as two-element configuration. Flow solution results are shown for two-dimensional flow over the NACA 0012 airfoil and for a two-element configuration in which the solution has been obtained through an adaptation procedure and compared to an exact solution. Preliminary three-dimensional results are also shown in which subsonic flow over a business jet is computed. 31 refs. 30 figs.
Quantum entanglement in states generated by bilocal group algebras
Hamma, Alioscia; Ionicioiu, Radu; Zanardi, Paolo
2005-07-15
Given a finite group G with a bilocal representation, we investigate the bipartite entanglement in the state constructed from the group algebra of G acting on a separable reference state. We find an upper bound for the von Neumann entropy for a bipartition (A,B) of a quantum system and conditions to saturate it. We show that these states can be interpreted as ground states of generic Hamiltonians or as the physical states in a quantum gauge theory and that under specific conditions their geometric entropy satisfies the entropic area law. If G is a group of spin flips acting on a set of qubits, these states are locally equivalent to 2-colorable (i.e., bipartite) graph states and they include Greenberger-Horne-Zeilinger, cluster states, etc. Examples include an application to qudits and a calculation of the n-tangle for 2-colorable graph states.
Feynman graph generation and calculations in the Hopf algebra of Feynman graphs
NASA Astrophysics Data System (ADS)
Borinsky, Michael
2014-12-01
Two programs for the computation of perturbative expansions of quantum field theory amplitudes are provided. feyngen can be used to generate Feynman graphs for Yang-Mills, QED and φk theories. Using dedicated graph theoretic tools feyngen can generate graphs of comparatively high loop orders. feyncop implements the Hopf algebra of those Feynman graphs which incorporates the renormalization procedure necessary to calculate finite results in perturbation theory of the underlying quantum field theory. feyngen is validated by comparison to explicit calculations of zero dimensional quantum field theories and feyncop is validated using a combinatorial identity on the Hopf algebra of graphs.
GridMan: A grid manipulation system
NASA Technical Reports Server (NTRS)
Eiseman, Peter R.; Wang, Zhu
1992-01-01
GridMan is an interactive grid manipulation system. It operates on grids to produce new grids which conform to user demands. The input grids are not constrained to come from any particular source. They may be generated by algebraic methods, elliptic methods, hyperbolic methods, parabolic methods, or some combination of methods. The methods are included in the various available structured grid generation codes. These codes perform the basic assembly function for the various elements of the initial grid. For block structured grids, the assembly can be quite complex due to a large number of clock corners, edges, and faces for which various connections and orientations must be properly identified. The grid generation codes are distinguished among themselves by their balance between interactive and automatic actions and by their modest variations in control. The basic form of GridMan provides a much more substantial level of grid control and will take its input from any of the structured grid generation codes. The communication link to the outside codes is a data file which contains the grid or section of grid.
Surface Modeling and Grid Generation of Orbital Sciences X34 Vehicle. Phase 1
NASA Technical Reports Server (NTRS)
Alter, Stephen J.
1997-01-01
The surface modeling and grid generation requirements, motivations, and methods used to develop Computational Fluid Dynamic volume grids for the X34-Phase 1 are presented. The requirements set forth by the Aerothermodynamics Branch at the NASA Langley Research Center serve as the basis for the final techniques used in the construction of all volume grids, including grids for parametric studies of the X34. The Integrated Computer Engineering and Manufacturing code for Computational Fluid Dynamics (ICEM/CFD), the Grid Generation code (GRIDGEN), the Three-Dimensional Multi-block Advanced Grid Generation System (3DMAGGS) code, and Volume Grid Manipulator (VGM) code are used to enable the necessary surface modeling, surface grid generation, volume grid generation, and grid alterations, respectively. All volume grids generated for the X34, as outlined in this paper, were used for CFD simulations within the Aerothermodynamics Branch.
A method for generating volumetric fault zone grids for pillar gridded reservoir models
NASA Astrophysics Data System (ADS)
Qu, Dongfang; Røe, Per; Tveranger, Jan
2015-08-01
The internal structure and petrophysical property distribution of fault zones are commonly exceedingly complex compared to the surrounding host rock from which they are derived. This in turn produces highly complex fluid flow patterns which affect petroleum migration and trapping as well as reservoir behavior during production and injection. Detailed rendering and forecasting of fluid flow inside fault zones require high-resolution, explicit models of fault zone structure and properties. A fundamental requirement for achieving this is the ability to create volumetric grids in which modeling of fault zone structures and properties can be performed. Answering this need, a method for generating volumetric fault zone grids which can be seamlessly integrated into existing standard reservoir modeling tools is presented. The algorithm has been tested on a wide range of fault configurations of varying complexity, providing flexible modeling grids which in turn can be populated with fault zone structures and properties.
Automatic code generation in SPARK: Applications of computer algebra and compiler-compilers
Nataf, J.M.; Winkelmann, F.
1992-09-01
We show how computer algebra and compiler-compilers are used for automatic code generation in the Simulation Problem Analysis and Research Kernel (SPARK), an object oriented environment for modeling complex physical systems that can be described by differential-algebraic equations. After a brief overview of SPARK, we describe the use of computer algebra in SPARK's symbolic interface, which generates solution code for equations that are entered in symbolic form. We also describe how the Lex/Yacc compiler-compiler is used to achieve important extensions to the SPARK simulation language, including parametrized macro objects and steady-state resetting of a dynamic simulation. The application of these methods to solving the partial differential equations for two-dimensional heat flow is illustrated.
Automatic code generation in SPARK: Applications of computer algebra and compiler-compilers
Nataf, J.M.; Winkelmann, F.
1992-09-01
We show how computer algebra and compiler-compilers are used for automatic code generation in the Simulation Problem Analysis and Research Kernel (SPARK), an object oriented environment for modeling complex physical systems that can be described by differential-algebraic equations. After a brief overview of SPARK, we describe the use of computer algebra in SPARK`s symbolic interface, which generates solution code for equations that are entered in symbolic form. We also describe how the Lex/Yacc compiler-compiler is used to achieve important extensions to the SPARK simulation language, including parametrized macro objects and steady-state resetting of a dynamic simulation. The application of these methods to solving the partial differential equations for two-dimensional heat flow is illustrated.
A novel hyperbolic grid generation procedure with inherent adaptive dissipation
Tai, C.H.; Yin, S.L.; Soong, C.Y.
1995-01-01
This paper reports a novel hyperbolic grid-generation with an inherent adaptive dissipation (HGAD), which is capable of improving the oscillation and overlapping of grid lines. In the present work upwinding differencing is applied to discretize the hyperbolic system and, thereby, to develop the adaptive dissipation coefficient. Complex configurations with the features of geometric discontinuity, exceptional concavity and convexity are used as the test cases for comparison of the present HGAD procedure with the conventional hyerbolic and elliptic ones. The results reveal that the HGAD method is superior in orthogonality and smoothness of the grid system. In addition, the computational efficiency of the flow solver may be improved by using the present HGAD procedure. 15 refs., 8 figs.
On Generating Discrete Integrable Systems via Lie Algebras and Commutator Equations
NASA Astrophysics Data System (ADS)
Zhang, Yu-Feng; Honwah, Tam
2016-03-01
In the paper, we introduce the Lie algebras and the commutator equations to rewrite the Tu-d scheme for generating discrete integrable systems regularly. By the approach the various loop algebras of the Lie algebra A1 are defined so that the well-known Toda hierarchy and a novel discrete integrable system are obtained, respectively. A reduction of the later hierarchy is just right the famous Ablowitz-Ladik hierarchy. Finally, via two different enlarging Lie algebras of the Lie algebra A1, we derive two resulting differential-difference integrable couplings of the Toda hierarchy, of course, they are all various discrete expanding integrable models of the Toda hierarchy. When the introduced spectral matrices are higher degrees, the way presented in the paper is more convenient to generate discrete integrable equations than the Tu-d scheme by using the software Maple. Supported by the National Natural Science Foundation of China under Grant No. 11371361, the Innovation Team of Jiangsu Province hosted by China University of Mining and Technology (2014), and Hong Kong Research Grant Council under Grant No. HKBU202512, as well as the Natural Science Foundation of Shandong Province under Grant No. ZR2013AL016
On Generating Discrete Integrable Systems via Lie Algebras and Commutator Equations
NASA Astrophysics Data System (ADS)
Zhang, Yu-Feng; Tam, Honwah
2016-03-01
In the paper, we introduce the Lie algebras and the commutator equations to rewrite the Tu-d scheme for generating discrete integrable systems regularly. By the approach the various loop algebras of the Lie algebra A1 are defined so that the well-known Toda hierarchy and a novel discrete integrable system are obtained, respectively. A reduction of the later hierarchy is just right the famous Ablowitz–Ladik hierarchy. Finally, via two different enlarging Lie algebras of the Lie algebra A1, we derive two resulting differential-difference integrable couplings of the Toda hierarchy, of course, they are all various discrete expanding integrable models of the Toda hierarchy. When the introduced spectral matrices are higher degrees, the way presented in the paper is more convenient to generate discrete integrable equations than the Tu-d scheme by using the software Maple. Supported by the National Natural Science Foundation of China under Grant No. 11371361, the Innovation Team of Jiangsu Province hosted by China University of Mining and Technology (2014), and Hong Kong Research Grant Council under Grant No. HKBU202512, as well as the Natural Science Foundation of Shandong Province under Grant No. ZR2013AL016
Grid generation about complex three-dimensional aircraft configurations
NASA Technical Reports Server (NTRS)
Klopfer, Goetz H.
1991-01-01
The problem of obtaining three dimensional grids with sufficient resolution to resolve all the flow or other physical features of interest is addressed. The generation of a computational grid involves a series of compromises to resolve several conflicting requirements. On one hand, one would like the grid to be fine enough and not too skewed to reduce the numerical errors and to adequately resolve the pertinent physical features of the flow field about the aircraft. On the other hand, the capabilities of present or even future supercomputers are finite and the number of mesh points must be limited to a reasonable number: one which is usually much less than desired for numerical accuracy. One technique to overcome this limitation is the 'zonal' grid approach. In this method, the overall field is subdivided into smaller zones or blocks in each of which an independent grid is generated with enough grid density to resolve the flow features in that zone. The zonal boundaries or interfaces require special boundary conditions such that the conservation properties of the governing equations are observed. Much work was done in 3-D zonal approaches with nonconservative zonal interfaces. A 3-D zonal conservative interfacing method that is efficient and easy to implement was developed during the past year. During the course of the work, it became apparent that it would be much more feasible to do the conservative interfacing with cell-centered finite volume codes instead of the originally planned finite difference codes. Accordingly, the CNS code was converted to finite volume form. This new version of the code is named CNSFV. The original multi-zonal interfacing capability of the CNS code was enhanced by generalizing the procedure to allow for completely arbitrarily shaped zones with no mesh continuity between the zones. While this zoning capability works well for most flow situations, it is, however, still nonconservative. The conservative interface algorithm was also
Grid Generation Issues and CFD Simulation Accuracy for the X33 Aerothermal Simulations
NASA Technical Reports Server (NTRS)
Polsky, Susan; Papadopoulos, Periklis; Davies, Carol; Loomis, Mark; Prabhu, Dinesh; Langhoff, Stephen R. (Technical Monitor)
1997-01-01
Grid generation issues relating to the simulation of the X33 aerothermal environment using the GASP code are explored. Required grid densities and normal grid stretching are discussed with regards to predicting the fluid dynamic and heating environments with the desired accuracy. The generation of volume grids is explored and includes discussions of structured grid generation packages such as GRIDGEN, GRIDPRO and HYPGEN. Volume grid manipulation techniques for obtaining desired outer boundary and grid clustering using the OUTBOUND code are examined. The generation of the surface grid with the required surface grid with the required surface grid topology is also discussed. Utilizing grids without singular axes is explored as a method of avoiding numerical difficulties at the singular line.
Algebras Generated by Geometric Scalar Forms and their Applications in Physics and Social Sciences
Keller, Jaime
2008-09-17
The present paper analyzes the consequences of defining that the geometric scalar form is not necessarily quadratic, but in general K-atic, that is obtained from the K{sup th} power of the linear form, requiring {l_brace}e{sub i};i = 1,...,N;(e{sub i}){sup K} = 1{r_brace} and d-vector {sigma}{sub i}x{sub i}e{sub i}. We consider the algebras which are thus generated, for positive integer K, a generalization of the geometric algebras we know under the names of Clifford or Grassmann algebras. We then obtain a set of geometric K-algebras. We also consider the generalization of special functions of geometry which corresponds to the K-order scalar forms (as trigonometric functions and other related geometric functions which are based on the use of quadratic forms). We present an overview of the use of quadratic forms in physics as in our general theory, we have called START. And, in order to give an introduction to the use of the more general K-algebras and to the possible application to sciences other than physics, the application to social sciences is considered.For the applications to physics we show that quadratic spaces are a fundamental clue to understand the structure of theoretical physics (see, for example, Keller in ICNAAM 2005 and 2006)
Vortex shedding effects in grid-generated turbulence
NASA Astrophysics Data System (ADS)
Melina, G.; Bruce, P. J. K.; Vassilicos, J. C.
2016-08-01
The flow on the centerline of grid-generated turbulence is characterized via hot-wire anemometry for three grids with different geometry: a regular grid (RG60), a fractal grid (FSG17), and a single-square grid (SSG). Due to a higher value of the thickness t0 of its bars, SSG produces greater values of turbulence intensity Tu than FSG17, despite SSG having a smaller blockage ratio. However, the higher Tu for SSG is mainly due to a more pronounced vortex shedding contribution. The effects of vortex shedding suppression along the streamwise direction x are studied by testing a three-dimensional configuration, formed by SSG and a set of four splitter plates detached from the grid (SSG+SP). When vortex shedding is damped, the centerline location of the peak of turbulence intensity xpeak moves downstream and Tu considerably decreases in the production region. For FSG17 the vortex shedding is less intense and it disappears more quickly, in terms of x /xpeak , when compared to all the other configurations. When vortex shedding is attenuated, the integral length scale Lu grows more slowly in the streamwise direction, this being verified both for FSG17 and for SSG+SP. In the production region, there is a correlation between the vortex shedding energy and the skewness and the flatness of the velocity fluctuations. When vortex shedding is not significant, the skewness is highly negative and the flatness is much larger than 3. On the opposite side, when vortex shedding is prominent, the non-Gaussian behavior of the velocity fluctuations becomes masked.
Hydrogen ionic plasma generated using Al plasma grid
NASA Astrophysics Data System (ADS)
Oohara, W.; Anegawa, N.; Egawa, M.; Kawata, K.; Kamikawa, T.
2016-08-01
Negative hydrogen ions are produced in the apertures of a plasma grid made of aluminum under the irradiation of positive ions, generating an ionic plasma consisting of positive and negative ions. The saturation current ratio obtained using a Langmuir probe reflects the existence ratio of electrons and is found to increase in connection with the diffusion of the ionic plasma. The local increment of the current ratio suggests the collapse of negative ions and the replacement of detached electrons.
A finite volume method for numerical grid generation
NASA Astrophysics Data System (ADS)
Beale, S. B.
1999-07-01
A novel method to generate body-fitted grids based on the direct solution for three scalar functions is derived. The solution for scalar variables , and is obtained with a conventional finite volume method based on a physical space formulation. The grid is adapted or re-zoned to eliminate the residual error between the current solution and the desired solution, by means of an implicit grid-correction procedure. The scalar variables are re-mapped and the process is reiterated until convergence is obtained. Calculations are performed for a variety of problems by assuming combined Dirichlet-Neumann and pure Dirichlet boundary conditions involving the use of transcendental control functions, as well as functions designed to effect grid control automatically on the basis of boundary values. The use of dimensional analysis to build stable exponential functions and other control functions is demonstrated. Automatic procedures are implemented: one based on a finite difference approximation to the Cristoffel terms assuming local-boundary orthogonality, and another designed to procure boundary orthogonality. The performance of the new scheme is shown to be comparable with that of conventional inverse methods when calculations are performed on benchmark problems through the application of point-by-point and whole-field solution schemes. Advantages and disadvantages of the present method are critically appraised. Copyright
Multilevel elliptic smoothing of large three-dimensional grids
NASA Technical Reports Server (NTRS)
Mastin, C. Wayne
1995-01-01
Elliptic grid generation methods have been used for many years to smooth and improve grids generated by algebraic interpolation schemes. However, the elliptic system that must be solved is nonlinear and convergence is generally very slow for large grids. In an attempt to make elliptic methods practical for large three-dimensional grids, a two-stage implementation is developed where the overall grid point locations are set using a coarse grid generated by the elliptic system. The coarse grid is then interpolated to generate a finer grid which is smoothed using only a few iterations of the elliptic system.
Geometry Modeling and Grid Generation for Design and Optimization
NASA Technical Reports Server (NTRS)
Samareh, Jamshid A.
1998-01-01
Geometry modeling and grid generation (GMGG) have played and will continue to play an important role in computational aerosciences. During the past two decades, tremendous progress has occurred in GMGG; however, GMGG is still the biggest bottleneck to routine applications for complicated Computational Fluid Dynamics (CFD) and Computational Structures Mechanics (CSM) models for analysis, design, and optimization. We are still far from incorporating GMGG tools in a design and optimization environment for complicated configurations. It is still a challenging task to parameterize an existing model in today's Computer-Aided Design (CAD) systems, and the models created are not always good enough for automatic grid generation tools. Designers may believe their models are complete and accurate, but unseen imperfections (e.g., gaps, unwanted wiggles, free edges, slivers, and transition cracks) often cause problems in gridding for CSM and CFD. Despite many advances in grid generation, the process is still the most labor-intensive and time-consuming part of the computational aerosciences for analysis, design, and optimization. In an ideal design environment, a design engineer would use a parametric model to evaluate alternative designs effortlessly and optimize an existing design for a new set of design objectives and constraints. For this ideal environment to be realized, the GMGG tools must have the following characteristics: (1) be automated, (2) provide consistent geometry across all disciplines, (3) be parametric, and (4) provide sensitivity derivatives. This paper will review the status of GMGG for analysis, design, and optimization processes, and it will focus on some emerging ideas that will advance the GMGG toward the ideal design environment.
Chemical image generation with a grid-gate device
NASA Astrophysics Data System (ADS)
Filippini, D.; Gunnarsson, J.; Lundström, I.
2004-12-01
Scanning light pulse technique generating distinctive chemical images of diverse gases is demonstrated using a sensing arrangement that allows unrestricted choice of sensing materials, disregarding its conductivity or morphology. The present device, a metal oxide semiconductor structure, disentangles biasing from chemical functions by providing an inert grid as a gate that supplies the proper biasing, while functional materials even in the form of disconnected clusters can be used for sensing. The reading of conductimetric chemical responses of clustered materials, in nominal operating conditions, is demonstrated by the generation of chemical images acquired for inversion biasing conditions.
NASA Technical Reports Server (NTRS)
Samareh, Jamshid A.
2000-01-01
The purpose of this paper is to discuss grid generation issues and to challenge the grid generation community to develop tools suitable for automated multidisciplinary analysis and design optimization of aerospace vehicles. Special attention is given to the grid generation issues of computational fluid dynamics and computational structural mechanics disciplines.
A geometry-based adaptive unstructured grid generation algorithm for complex geological media
NASA Astrophysics Data System (ADS)
Bahrainian, Seyed Saied; Dezfuli, Alireza Daneh
2014-07-01
In this paper a novel unstructured grid generation algorithm is presented that considers the effect of geological features and well locations in grid resolution. The proposed grid generation algorithm presents a strategy for definition and construction of an initial grid based on the geological model, geometry adaptation of geological features, and grid resolution control. The algorithm is applied to seismotectonic map of the Masjed-i-Soleiman reservoir. Comparison of grid results with the “Triangle” program shows a more suitable permeability contrast. Immiscible two-phase flow solutions are presented for a fractured porous media test case using different grid resolutions. Adapted grid on the fracture geometry gave identical results with that of a fine grid. The adapted grid employed 88.2% less CPU time when compared to the solutions obtained by the fine grid.
An automatic, unstructured grid-generation system for geologically complex reservoirs
Kocberber, S.
1995-10-01
This paper presents an automatic, 3D, locally unstructured hybrid-grid generation system for sloping faults. This gridding system replaces a portion of an existing finite-difference grid around sloping faults with a finite-element grid made of tetrahedrons. This innovative approach retains the finite-difference character of the grid and minimizes the decrease in computational efficiency. This paper discusses the details of the gridding techniques used and provides several example grids that demonstrate that locally unstructured grids can accurately represent geologically complex reservoirs.
NASA Technical Reports Server (NTRS)
Choo, Yung K.; Slater, John W.; Henderson, Todd L.; Bidwell, Colin S.; Braun, Donald C.; Chung, Joongkee
1998-01-01
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.
Three-dimensional grid generation about a submarine
NASA Technical Reports Server (NTRS)
Abolhassani, Jamshid Samareh; Smith, Robert E.
1988-01-01
A systematic multiple-block grid method has been developed to compute grids about submarines. Several topologies are proposed, and an oscillatory transfinite interpolation is used in the grid construction.
Spectrum generating algebra for the continuous spectrum of a free particle in Lobachevski space
Gadella, M.; Negro, J.; Santander, M.; Pronko, G. P.
2013-02-15
In this paper, we construct a Spectrum Generating Algebra (SGA) for a quantum system with purely continuous spectrum: the quantum free particle in a Lobachevski space with constant negative curvature. The SGA contains the geometrical symmetry algebra of the system plus a subalgebra of operators that give the spectrum of the system and connects the eigenfunctions of the Hamiltonian among themselves. In our case, the geometrical symmetry algebra is so(3,1) and the SGA is so(4,2). We start with a representation of so(4,2) by functions on a realization of the Lobachevski space given by a two-sheeted hyperboloid, where the Lie algebra commutators are the usual Poisson-Dirac brackets. Then, we introduce a quantized version of the representation in which functions are replaced by operators on a Hilbert space and Poisson-Dirac brackets by commutators. Eigenfunctions of the Hamiltonian are given and 'naive' ladder operators are identified. The previously defined 'naive' ladder operators shift the eigenvalues by a complex number so that an alternative approach is necessary. This is obtained by a non-self-adjoint function of a linear combination of the ladder operators, which gives the correct relation among the eigenfunctions of the Hamiltonian. We give an eigenfunction expansion of functions over the upper sheet of a two-sheeted hyperboloid in terms of the eigenfunctions of the Hamiltonian.
Development of an Automatic Grid Generator for Multi-Element High-Lift Wings
NASA Technical Reports Server (NTRS)
Eberhardt, Scott; Wibowo, Pratomo; Tu, Eugene
1996-01-01
The procedure to generate the grid around a complex wing configuration is presented in this report. The automatic grid generation utilizes the Modified Advancing Front Method as a predictor and an elliptic scheme as a corrector. The scheme will advance the surface grid one cell outward and the newly obtained grid is corrected using the Laplace equation. The predictor-corrector step ensures that the grid produced will be smooth for every configuration. The predictor-corrector scheme is extended for a complex wing configuration. A new technique is developed to deal with the grid generation in the wing-gaps and on the flaps. It will create the grids that fill the gap on the wing surface and the gap created by the flaps. The scheme recognizes these configurations automatically so that minimal user input is required. By utilizing an appropriate sequence in advancing the grid points on a wing surface, the automatic grid generation for complex wing configurations is achieved.
Application of the multigrid method to grid generation
NASA Technical Reports Server (NTRS)
Ohring, S.
1980-01-01
The multigrid method (MGM), used to numerically solve the pair of nonlinear elliptic equations commonly used to generate two dimensional boundary-fitted coordinate systems is discussed. Two different geometries are considered: one involving a coordinate system fitted about a circle and the other selected for an impinging jet flow problem. Two different relaxation schemes are tried: one is successive point overrelaxation and the other is a four-color scheme vectorizeable to take advantage of a parallel processor computer for greater computational speed. Results using MGM are compared with those using SOR (doing successive overrelaxations with the corresponding relaxation scheme on the fine grid only). It is found that MGM becomes significantly more effective than SOR as more accuracy is demanded and as more corrective grids, or more grid points, are used. For the accuracy required, it is found that MGM is two to three times faster than SOR in computing time. With the four-color relaxation scheme as applied to the impinging jet problem, the advantage of MGM over SOR is not as great. This may be due to the effect of a poor initial guess on MGM for this problem.
Automated, Parametric Geometry Modeling and Grid Generation for Turbomachinery Applications
NASA Technical Reports Server (NTRS)
Harrand, Vincent J.; Uchitel, Vadim G.; Whitmire, John B.
2000-01-01
The objective of this Phase I project is to develop a highly automated software system for rapid geometry modeling and grid generation for turbomachinery applications. The proposed system features a graphical user interface for interactive control, a direct interface to commercial CAD/PDM systems, support for IGES geometry output, and a scripting capability for obtaining a high level of automation and end-user customization of the tool. The developed system is fully parametric and highly automated, and, therefore, significantly reduces the turnaround time for 3D geometry modeling, grid generation and model setup. This facilitates design environments in which a large number of cases need to be generated, such as for parametric analysis and design optimization of turbomachinery equipment. In Phase I we have successfully demonstrated the feasibility of the approach. The system has been tested on a wide variety of turbomachinery geometries, including several impellers and a multi stage rotor-stator combination. In Phase II, we plan to integrate the developed system with turbomachinery design software and with commercial CAD/PDM software.
Anisotropic Solution Adaptive Unstructured Grid Generation Using AFLR
NASA Technical Reports Server (NTRS)
Marcum, David L.
2007-01-01
An existing volume grid generation procedure, AFLR3, was successfully modified to generate anisotropic tetrahedral elements using a directional metric transformation defined at source nodes. The procedure can be coupled with a solver and an error estimator as part of an overall anisotropic solution adaptation methodology. It is suitable for use with an error estimator based on an adjoint, optimization, sensitivity derivative, or related approach. This offers many advantages, including more efficient point placement along with robust and efficient error estimation. It also serves as a framework for true grid optimization wherein error estimation and computational resources can be used as cost functions to determine the optimal point distribution. Within AFLR3 the metric transformation is implemented using a set of transformation vectors and associated aspect ratios. The modified overall procedure is presented along with details of the anisotropic transformation implementation. Multiple two-and three-dimensional examples are also presented that demonstrate the capability of the modified AFLR procedure to generate anisotropic elements using a set of source nodes with anisotropic transformation metrics. The example cases presented use moderate levels of anisotropy and result in usable element quality. Future testing with various flow solvers and methods for obtaining transformation metric information is needed to determine practical limits and evaluate the efficacy of the overall approach.
SUSY QM, symmetries and spectrum generating algebras for two-dimensional systems
Martinez, D. Mota, R.D.
2008-04-15
We show in a systematic and clear way how factorization methods can be used to construct the generators for hidden and dynamical symmetries. This is shown by studying the 2D problems of hydrogen atom, the isotropic harmonic oscillator and the radial potential A{rho}{sup 2{zeta}}{sup -2} - B{rho}{sup {zeta}}{sup -2}. We show that in these cases the non-compact (compact) algebra corresponds to so(2, 1) (su(2))
Noniterative three-dimensional grid generation using parabolic partial differential equations
NASA Technical Reports Server (NTRS)
Edwards, T. A.
1985-01-01
A new algorithm for generating three-dimensional grids has been developed and implemented which numerically solves a parabolic partial differential equation (PDE). The solution procedure marches outward in two coordinate directions, and requires inversion of a scalar tridiagonal system in the third. Source terms have been introduced to control the spacing and angle of grid lines near the grid boundaries, and to control the outer boundary point distribution. The method has been found to generate grids about 100 times faster than comparable grids generated via solution of elliptic PDEs, and produces smooth grids for finite-difference flow calculations.
NASA Technical Reports Server (NTRS)
Steger, Joseph L.
1989-01-01
Hyperbolic grid generation procedures are described which have been used in external flow simulations about complex configurations. For many practical applications a single well-ordered (i.e., structured) grid can be used to mesh an entire configuration, in other problems, composite or unstructured grid procedures are needed. Although the hyperbolic partial differential equation grid generation procedure has mainly been utilized to generate structured grids, an extension of the procedure to semiunstructured grids is briefly described. Extensions of the methodology are also described using two-dimensional equations.
Grid-generated isotropic homogeneous turbulence at high Reynolds numbers
NASA Technical Reports Server (NTRS)
Rosen, G.
1981-01-01
Consideration is given to an empirical formula for the longitudinal correlation function for grid-generated incompressible fluid turbulence at Reynolds numbers above 12,800. The formula, which relates the longitudinal correlation function to the inverse cube of a dimensionless geometrical ratio, is shown to minimize the global correlation integrals into which the two-point velocity correlation tensor has been substituted subject to a global constraint on the Sobolev concomitent of the longitudinal correlation function. Furthermore, the energy spectrum function associated with the empirical formula is shown to satisfy a tertiary Helmholtz-type linear condition throughout the initial period of decay.
Parallel and Streaming Generation of Ghost Data for Structured Grids
Isenburg, M; Lindstrom, P; Childs, H
2008-04-15
Parallel simulations decompose large domains into many blocks. A fundamental requirement for subsequent parallel analysis and visualization is the presence of ghost data that supplements each block with a layer of adjacent data elements from neighboring blocks. The standard approach for generating ghost data requires all blocks to be in memory at once. This becomes impractical when there are fewer processors - and thus less aggregate memory - available for analysis than for simulation. We describe an algorithm for generating ghost data for structured grids that uses many fewer processors than previously possible. Our algorithm stores as little as one block per processor in memory and can run on as few processors as are available (possibly just one). The key idea is to slightly change the size of the original blocks by declaring parts of them to be ghost data, and by later padding adjacent blocks with this data.
NASA Astrophysics Data System (ADS)
Korf, Lisa A.; Schroeck, Franklin E.
2015-12-01
We consider an effect algebra of phase space localization operators for a quantum mechanical Hilbert space that contains no non-trivial projections, and the C*-algebra generated by it. This C∗-algebra forms an informationally complete set in the original Hilbert space. Its elements are shown to have singular-value-based decompositions that permit their characterization in terms of limits of linear combinations of products of pairs of the phase space fuzzy localization operators. Through these results, it is shown that the informational completeness of the C*-algebra can be greatly reduced to the informational completeness of the set of products of pairs formed from the elements of the effect algebra.
NASA Astrophysics Data System (ADS)
Chen, Hsian-Yang; Lam, Ching Hung
2014-06-01
In this paper, we construct explicitly certain moonshine type vertex operator algebras generated by a set of Ising vectors I such that (1) for any e ≠ f ∈ I, the subVOA VOA(e, f) generated by e and f is isomorphic to either U2B or U3C; and (2) the subgroup generated by the corresponding Miyamoto involutions {τe | e ∈ I} is isomorphic to the Weyl group of a root system of type An, Dn, E6, E7 or E8. The structures of the corresponding vertex operator algebras and their Griess algebras are also studied. In particular, the central charge of these vertex operator algebras are determined.
Direct numerical simulation of turbulent mixing in grid-generated turbulence
NASA Astrophysics Data System (ADS)
Nagata, Kouji; Suzuki, Hiroki; Sakai, Yasuhiko; Hayase, Toshiyuki; Kubo, Takashi
2008-12-01
Turbulent mixing of passive scalar (heat) in grid-generated turbulence (GGT) is simulated by means of direct numerical simulation (DNS). A turbulence-generating grid, on which the velocity components are set to zero, is located downstream of the channel entrance, and it is numerically constructed on the staggered mesh arrangement using the immersed boundary method. The grid types constructed are: (a) square-mesh biplane grid, (b) square-mesh single-plane grid, (c) composite grid consisting of parallel square-bars and (d) fractal grid. Two fluids with different temperatures are provided separately in the upper and lower streams upstream of the turbulence-generating grids, generating the thermal mixing layer behind the grids. For the grid (a), simulations for two different Prandtl numbers of 0.71 and 7.1, corresponding to air and water flows, are conducted to investigate the effect of the Prandtl number. The results show that the typical grid turbulence and shearless mixing layer are generated downstream of the grids. The results of the scalar field show that a typical thermal mixing layer is generated as well, and the effects of the Prandtl numbers on turbulent heat transfer are observed.
Numerical grid generation and flow simulation in SSME thrust chamber
Gross, K.W.; Daley, P.L.; Przekwas, A.J.
1987-01-01
The development of liquid and solid rocket engines for future space projects demands a detailed optimization process for highly efficient performance and cost reasons. Also, testing of full size engines may not be feasible when the large size requires test facilities which are cost prohibitive or if vacuum operation cannot be acquired. For such situations only scaling from small test scale measurements or accurate analytical predictions will provide the performance prior to actually flying the mission. A rigorous approach for simulating the combustion processes in liquid rocket engines by employing a direct solution of Navier-Stokes equations within the entire volume of the thrust chambers is presented. This method is illustrated in the solution of reactive flow in the Space Shuttle Main Engine (SSME) thrust chamber. The objective is to review recent improvements in the mathematical model and to present the grid generation methodology suitable for rocket thrust chamber geometries.
Knowledge-based zonal grid generation for computational fluid dynamics
NASA Technical Reports Server (NTRS)
Andrews, Alison E.
1988-01-01
Automation of flow field zoning in two dimensions is an important step towards reducing the difficulty of three-dimensional grid generation in computational fluid dynamics. Using a knowledge-based approach makes sense, but problems arise which are caused by aspects of zoning involving perception, lack of expert consensus, and design processes. These obstacles are overcome by means of a simple shape and configuration language, a tunable zoning archetype, and a method of assembling plans from selected, predefined subplans. A demonstration system for knowledge-based two-dimensional flow field zoning has been successfully implemented and tested on representative aerodynamic configurations. The results show that this approach can produce flow field zonings that are acceptable to experts with differing evaluation criteria.
Unstructured Grid Generation for Complex 3D High-Lift Configurations
NASA Technical Reports Server (NTRS)
Pirzadeh, Shahyar Z.
1999-01-01
The application of an unstructured grid methodology on a three-dimensional high-lift configuration is presented. The focus of this paper is on the grid generation aspect of an integrated effort for the development of an unstructured-grid computational fluid dynamics (CFD) capability at the NASA Langley Research Center. The meshing approach is based on tetrahedral grids generated by the advancing-front and the advancing-layers procedures. The capability of the method for solving high-lift problems is demonstrated on an aircraft model referred to as the energy efficient transport configuration. The grid generation issues, including the pros and cons of the present approach, are discussed in relation to the high-lift problems. Limited viscous flow results are presented to demonstrate the viability of the generated grids. A corresponding Navier-Stokes solution capability, along with further computations on the present grid, is presented in a companion SAE paper.
Bgridi - Interactive three-dimensional turbomachinery grid generation system with applications
Shoemaker, J.M.; Hah, C. NASA, Lewis Research Center, Cleveland, OH )
1993-01-01
An interactive, graphics-based grid generation system for 3D turbomachinery geometries has been developed. The system consists of separate modules for geometry modeling and grid generation. The grid generation method generates a series of 2D grids in the blade-to-blade passage to build up the 3D grid. A Poisson equation with forcing functions selected to control orthogonality and spacing on all boundaries is solved to generate the grid. Interactive definition of Bezier curves and surfaces as internal boundaries is used to improve control of grid quality. A multi-block data structure simpifies the creation of structured H-grids about complex turbomachinery geometries. The multi-block strategy facilitates the creation of a grid in the tip flow region, which is an important contributor to losses within the passage. The grid generation system is applied to several complex geometries including a simple radial impeller, a conventional turbine rotor, the SSME LOX turbine rotor with and without a tip flow grid, a multi-passage inducer-impeller, and a tip-flow cascade. In addition, a calculation of the tip-flow cascade flow field is shown. 17 refs.
Bgridi - Interactive three-dimensional turbomachinery grid generation system with applications
NASA Technical Reports Server (NTRS)
Shoemaker, J. M.; Hah, Chunill
1993-01-01
An interactive, graphics-based grid generation system for 3D turbomachinery geometries has been developed. The system consists of separate modules for geometry modeling and grid generation. The grid generation method generates a series of 2D grids in the blade-to-blade passage to build up the 3D grid. A Poisson equation with forcing functions selected to control orthogonality and spacing on all boundaries is solved to generate the grid. Interactive definition of Bezier curves and surfaces as internal boundaries is used to improve control of grid quality. A multi-block data structure simpifies the creation of structured H-grids about complex turbomachinery geometries. The multi-block strategy facilitates the creation of a grid in the tip flow region, which is an important contributor to losses within the passage. The grid generation system is applied to several complex geometries including a simple radial impeller, a conventional turbine rotor, the SSME LOX turbine rotor with and without a tip flow grid, a multi-passage inducer-impeller, and a tip-flow cascade. In addition, a calculation of the tip-flow cascade flow field is shown.
NASA Technical Reports Server (NTRS)
Spekreijse, S. P.; Boerstoel, J. W.; Vitagliano, P. L.; Kuyvenhoven, J. L.
1992-01-01
About five years ago, a joint development was started of a flow simulation system for engine-airframe integration studies on propeller as well as jet aircraft. The initial system was based on the Euler equations and made operational for industrial aerodynamic design work. The system consists of three major components: a domain modeller, for the graphical interactive subdivision of flow domains into an unstructured collection of blocks; a grid generator, for the graphical interactive computation of structured grids in blocks; and a flow solver, for the computation of flows on multi-block grids. The industrial partners of the collaboration and NLR have demonstrated that the domain modeller, grid generator and flow solver can be applied to simulate Euler flows around complete aircraft, including propulsion system simulation. Extension to Navier-Stokes flows is in progress. Delft Hydraulics has shown that both the domain modeller and grid generator can also be applied successfully for hydrodynamic configurations. An overview is given about the main aspects of both domain modelling and grid generation.
Specialized CFD Grid Generation Methods for Near-Field Sonic Boom Prediction
NASA Technical Reports Server (NTRS)
Park, Michael A.; Campbell, Richard L.; Elmiligui, Alaa; Cliff, Susan E.; Nayani, Sudheer N.
2014-01-01
Ongoing interest in analysis and design of low sonic boom supersonic transports re- quires accurate and ecient Computational Fluid Dynamics (CFD) tools. Specialized grid generation techniques are employed to predict near- eld acoustic signatures of these con- gurations. A fundamental examination of grid properties is performed including grid alignment with ow characteristics and element type. The issues a ecting the robustness of cylindrical surface extrusion are illustrated. This study will compare three methods in the extrusion family of grid generation methods that produce grids aligned with the freestream Mach angle. These methods are applied to con gurations from the First AIAA Sonic Boom Prediction Workshop.
NGP: Defining a grid generation paradigm based on NURBS and solid modeling topology
Gaither, A.; Jean, B.; Remotigue, M.; Whitmire, J.
1996-12-31
A grid generation paradigm is presented that allows a user to build both structured and unstructured grids within the same environment. It provides the user with a flexible, efficient and accurate way to generate these grids. The paradigm utilizes a Boundary Representation (B-rep) radial edge non-manifold solid modeling topology data structure for all geometric and grid interrogations. Non-Uniform Rational B-Splines (NURBS) are utilized as the geometric representation to ensure accuracy and provide generality for both geometric and grid manipulations.
Three-dimensional adaptive grid generation for body-fitted coordinate system
NASA Astrophysics Data System (ADS)
Chen, S. C.
1988-08-01
This report describes a numerical method for generating 3-D grids for general configurations. The basic method involves the solution of a set of quasi-linear elliptic partial differential equations via pointwise relaxation with a local relaxation factor. It allows specification of the grid spacing off the boundary surfaces and the grid orthogonality at the boundary surfaces. It includes adaptive mechanisms to improve smoothness, orthogonality, and flow resolution in the grid interior.
Three-dimensional adaptive grid generation for body-fitted coordinate system
NASA Astrophysics Data System (ADS)
Chen, S. C.
This report describes a numerical method for generating 3-D grids for general configurations. The basic method involves the solution of a set of quasi-linear elliptic partial differential equations via pointwise relaxation with a local relaxation factor. It allows specification of the grid spacing off the boundary surfaces and the grid orthogonality at the boundary surfaces. It includes adaptive mechanisms to improve smoothness, orthogonality, and flow resolution in the grid interior.
Domain decomposition by the advancing-partition method for parallel unstructured grid generation
NASA Technical Reports Server (NTRS)
Pirzadeh, Shahyar Z. (Inventor); Banihashemi, legal representative, Soheila (Inventor)
2012-01-01
In a method for domain decomposition for generating unstructured grids, a surface mesh is generated for a spatial domain. A location of a partition plane dividing the domain into two sections is determined. Triangular faces on the surface mesh that intersect the partition plane are identified. A partition grid of tetrahedral cells, dividing the domain into two sub-domains, is generated using a marching process in which a front comprises only faces of new cells which intersect the partition plane. The partition grid is generated until no active faces remain on the front. Triangular faces on each side of the partition plane are collected into two separate subsets. Each subset of triangular faces is renumbered locally and a local/global mapping is created for each sub-domain. A volume grid is generated for each sub-domain. The partition grid and volume grids are then merged using the local-global mapping.
WinGridder - An interactive grid generator for TOUGH - A user's manual (Version 1.0)
Pan, Lehua; Hinds, Jennifer; Haukwa, Charles; Wu, Yu-Shu; Bodvarsson, Gudmundur
2001-07-18
WinGridder is a Windows-based software package for designing, generating, and visualizing at various spatial scales numerical grids used in reservoir simulations and groundwater modeling studies. Development of this software was motivated by the requirements of the TOUGH (Transport of Unsaturated Groundwater and Heat) family of codes (Pruess 1987, 1991) for simulating subsurface processes related to high-level nuclear waste isolation in partially saturated geological media. Although the TOUGH family of codes has great flexibility in handling the variety of grid information required to describe complex objects, designing and generating a suitable irregular grid can be a tedious and error-prone process, even with the help of existing grid generating programs. This is especially true when the number of cells and connections is very large. The processes of inspecting the quality of the grid or extracting sub-grids or other specific grid information are also complex. The mesh maker embedded within TOUGH2 generates only uniform numerical grids and handles only one set of uniform fracture and matrix properties throughout the model domain. This is not suitable for grid generation in complex flow and transport simulations (such as those of Yucca Mountain, which have heterogeneity in both fracture and matrix media). As a result, the software program Amesh (Haukwa 2000) was developed to generate irregular, effective-continuum (ECM) grids.
ON 3D, AUTOMATED, SELF-CONTAINED GRID GENERATION WITHIN THE RAGE CAMR HYDROCODE
Oakes, W.R.; Henning, P.J.; Gittings, M.L.; Weaver, R.P.
2000-06-01
We discuss using the inherent grid manipulation capability within a Continuously Adaptive Mesh Refinement hydrodynamics code, RAGE, to implement parallel, automated, self-contained grid generation. We show how arbitrarily complex 3D geometries specified in any unambiguous form can be used. The RAGE computational environment is any of several massively parallel computers being developed under the Department Of Energy's Accelerated Strategic Computing Initiative. A typical 3D RAGE analysis may contain 100 million cells and occupy 2000 processors for several weeks. RAGE grid generation is embarrassingly parallel. The RAGE computational grid is an octree decomposition of the model space. The problem domain is subdivided into as many subdomains as the number of processors assigned to the problem. The grid for each subdomain is then generated independently, except for occasional adjustments. Geometry used for initial grid generation includes CSG combinations of NURBS-based boundary representation models, stereo lithography (STL) files, implicit surfaces, and functionally perturbed surfaces.
Structured grid generation using a CAD solid model for an aero-gas turbine combustion system
Eccles, N.C.; Manners, A.P.
1996-12-31
An aero-gas turbine combustion system was used to demonstrate the problems of creating a single block structured grid suitable for CFD predictions from a designer`s parametric solid model. The solid model had to be filtered of sub-grid detail and computational fluid volumes generated from the solid model of the metal. Alternative methods of transferring the geometry from the CAD package to the grid generator were considered. The type and method of grid generation was found to influence all stages in manipulating the geometry.
Generation and adaptation of 3-D unstructured grids for transient problems
NASA Technical Reports Server (NTRS)
Loehner, Rainald
1990-01-01
Grid generation and adaptive refinement techniques suitable for the simulation of strongly unsteady flows past geometrically complex bodies in 3-D are described. The grids are generated using the advancing front technique. Emphasis is placed not to generate elements that are too small, as this would severely increase the cost of simulations with explicit flow solvers. The grids are adapted to an evolving flowfield using simple h-refinement. A grid change is performed every 5 to 10 timesteps, and only one level of refinement/coarsening is allowed per mesh change.
Automated grid generation from models of complex geologic structure and stratigraphy
Gable, C.; Trease, H.; Cherry, T.
1996-04-01
The construction of computational grids which accurately reflect complex geologic structure and stratigraphy for flow and transport models poses a formidable task. With an understanding of stratigraphy, material properties and boundary and initial conditions, the task of incorporating this data into a numerical model can be difficult and time consuming. Most GIS tools for representing complex geologic volumes and surfaces are not designed for producing optimal grids for flow and transport computation. We have developed a tool, GEOMESH, for generating finite element grids that maintain the geometric integrity of input volumes, surfaces, and geologic data and produce an optimal (Delaunay) tetrahedral grid that can be used for flow and transport computations. GEOMESH also satisfies the constraint that the geometric coupling coefficients of the grid are positive for all elements. GEOMESH generates grids for two dimensional cross sections, three dimensional regional models, represents faults and fractures, and has the capability of including finer grids representing tunnels and well bores into grids. GEOMESH also permits adaptive grid refinement in three dimensions. The tools to glue, merge and insert grids together demonstrate how complex grids can be built from simpler pieces. The resulting grid can be utilized by unstructured finite element or integrated finite difference computational physics codes.
Domain Decomposition By the Advancing-Partition Method for Parallel Unstructured Grid Generation
NASA Technical Reports Server (NTRS)
Pirzadeh, Shahyar Z.; Zagaris, George
2009-01-01
A new method of domain decomposition has been developed for generating unstructured grids in subdomains either sequentially or using multiple computers in parallel. Domain decomposition is a crucial and challenging step for parallel grid generation. Prior methods are generally based on auxiliary, complex, and computationally intensive operations for defining partition interfaces and usually produce grids of lower quality than those generated in single domains. The new technique, referred to as "Advancing Partition," is based on the Advancing-Front method, which partitions a domain as part of the volume mesh generation in a consistent and "natural" way. The benefits of this approach are: 1) the process of domain decomposition is highly automated, 2) partitioning of domain does not compromise the quality of the generated grids, and 3) the computational overhead for domain decomposition is minimal. The new method has been implemented in NASA's unstructured grid generation code VGRID.
Geometry modeling and grid generation using 3D NURBS control volume
NASA Technical Reports Server (NTRS)
Yu, Tzu-Yi; Soni, Bharat K.; Shih, Ming-Hsin
1995-01-01
The algorithms for volume grid generation using NURBS geometric representation are presented. The parameterization algorithm is enhanced to yield a desired physical distribution on the curve, surface and volume. This approach bridges the gap between CAD surface/volume definition and surface/volume grid generation. Computational examples associated with practical configurations have shown the utilization of these algorithms.
Gable, C.W.; Trease, H.E.; Cherry, T.A.
1996-04-01
The construction of grids that accurately reflect geologic structure and stratigraphy for computational flow and transport models poses a formidable task. Even with a complete understanding of stratigraphy, material properties, boundary and initial conditions, the task of incorporating data into a numerical model can be difficult and time consuming. Furthermore, most tools available for representing complex geologic surfaces and volumes are not designed for producing optimal grids for flow and transport computation. We have developed a modeling tool, GEOMESH, for automating finite element grid generation that maintains the geometric integrity of geologic structure and stratigraphy. The method produces an optimal (Delaunay) tetrahedral grid that can be used for flow and transport computations. The process of developing a flow and transport model can be divided into three parts: (1) Developing accurate conceptual models inclusive of geologic interpretation, material characterization and construction of a stratigraphic and hydrostratigraphic framework model, (2) Building and initializing computational frameworks; grid generation, boundary and initial conditions, (3) Computational physics models of flow and transport. Process (1) and (3) have received considerable attention whereas (2) has not. This work concentrates on grid generation and its connections to geologic characterization and process modeling. Applications of GEOMESH illustrate grid generation for two dimensional cross sections, three dimensional regional models, and adaptive grid refinement in three dimensions. Examples of grid representation of wells and tunnels with GEOMESH can be found in Cherry et al. The resulting grid can be utilized by unstructured finite element or integrated finite difference models.
Adaptive grid generation in a patient-specific cerebral aneurysm.
Hodis, Simona; Kallmes, David F; Dragomir-Daescu, Dan
2013-11-01
Adapting grid density to flow behavior provides the advantage of increasing solution accuracy while decreasing the number of grid elements in the simulation domain, therefore reducing the computational time. One method for grid adaptation requires successive refinement of grid density based on observed solution behavior until the numerical errors between successive grids are negligible. However, such an approach is time consuming and it is often neglected by the researchers. We present a technique to calculate the grid size distribution of an adaptive grid for computational fluid dynamics (CFD) simulations in a complex cerebral aneurysm geometry based on the kinematic curvature and torsion calculated from the velocity field. The relationship between the kinematic characteristics of the flow and the element size of the adaptive grid leads to a mathematical equation to calculate the grid size in different regions of the flow. The adaptive grid density is obtained such that it captures the more complex details of the flow with locally smaller grid size, while less complex flow characteristics are calculated on locally larger grid size. The current study shows that kinematic curvature and torsion calculated from the velocity field in a cerebral aneurysm can be used to find the locations of complex flow where the computational grid needs to be refined in order to obtain an accurate solution. We found that the complexity of the flow can be adequately described by velocity and vorticity and the angle between the two vectors. For example, inside the aneurysm bleb, at the bifurcation, and at the major arterial turns the element size in the lumen needs to be less than 10% of the artery radius, while at the boundary layer, the element size should be smaller than 1% of the artery radius, for accurate results within a 0.5% relative approximation error. This technique of quantifying flow complexity and adaptive remeshing has the potential to improve results accuracy and reduce
Adaptive grid generation in a patient-specific cerebral aneurysm
NASA Astrophysics Data System (ADS)
Hodis, Simona; Kallmes, David F.; Dragomir-Daescu, Dan
2013-11-01
Adapting grid density to flow behavior provides the advantage of increasing solution accuracy while decreasing the number of grid elements in the simulation domain, therefore reducing the computational time. One method for grid adaptation requires successive refinement of grid density based on observed solution behavior until the numerical errors between successive grids are negligible. However, such an approach is time consuming and it is often neglected by the researchers. We present a technique to calculate the grid size distribution of an adaptive grid for computational fluid dynamics (CFD) simulations in a complex cerebral aneurysm geometry based on the kinematic curvature and torsion calculated from the velocity field. The relationship between the kinematic characteristics of the flow and the element size of the adaptive grid leads to a mathematical equation to calculate the grid size in different regions of the flow. The adaptive grid density is obtained such that it captures the more complex details of the flow with locally smaller grid size, while less complex flow characteristics are calculated on locally larger grid size. The current study shows that kinematic curvature and torsion calculated from the velocity field in a cerebral aneurysm can be used to find the locations of complex flow where the computational grid needs to be refined in order to obtain an accurate solution. We found that the complexity of the flow can be adequately described by velocity and vorticity and the angle between the two vectors. For example, inside the aneurysm bleb, at the bifurcation, and at the major arterial turns the element size in the lumen needs to be less than 10% of the artery radius, while at the boundary layer, the element size should be smaller than 1% of the artery radius, for accurate results within a 0.5% relative approximation error. This technique of quantifying flow complexity and adaptive remeshing has the potential to improve results accuracy and reduce
Finite difference time domain grid generation from AMC helicopter models
NASA Technical Reports Server (NTRS)
Cravey, Robin L.
1992-01-01
A simple technique is presented which forms a cubic grid model of a helicopter from an Aircraft Modeling Code (AMC) input file. The AMC input file defines the helicopter fuselage as a series of polygonal cross sections. The cubic grid model is used as an input to a Finite Difference Time Domain (FDTD) code to obtain predictions of antenna performance on a generic helicopter model. The predictions compare reasonably well with measured data.
Three-dimensional elliptic grid generation technique with application to turbomachinery cascades
NASA Technical Reports Server (NTRS)
Chen, S. C.; Schwab, J. R.
1988-01-01
Described is a numerical method for generating 3-D grids for turbomachinery computational fluid dynamic codes. The basic method is general and involves the solution of a quasi-linear elliptic partial differential equation via pointwise relaxation with a local relaxation factor. It allows specification of the grid point distribution on the boundary surfaces, the grid spacing off the boundary surfaces, and the grid orthogonality at the boundary surfaces. A geometry preprocessor constructs the grid point distributions on the boundary surfaces for general turbomachinery cascades. Representative results are shown for a C-grid and an H-grid for a turbine rotor. Two appendices serve as user's manuals for the basic solver and the geometry preprocessor.
Three-dimensional elliptic grid generation technique with application to turbomachinery cascades
NASA Astrophysics Data System (ADS)
Chen, S. C.; Schwab, J. R.
1988-08-01
Described is a numerical method for generating 3-D grids for turbomachinery computational fluid dynamic codes. The basic method is general and involves the solution of a quasi-linear elliptic partial differential equation via pointwise relaxation with a local relaxation factor. It allows specification of the grid point distribution on the boundary surfaces, the grid spacing off the boundary surfaces, and the grid orthogonality at the boundary surfaces. A geometry preprocessor constructs the grid point distributions on the boundary surfaces for general turbomachinery cascades. Representative results are shown for a C-grid and an H-grid for a turbine rotor. Two appendices serve as user's manuals for the basic solver and the geometry preprocessor.
Generation of a composite grid for turbine flows and consideration of a numerical scheme
NASA Technical Reports Server (NTRS)
Choo, Y.; Yoon, S.; Reno, C.
1986-01-01
A composite grid was generated for flows in turbines. It consisted of the C-grid (or O-grid) in the immediate vicinity of the blade and the H-grid in the middle of the blade passage between the C-grids and in the upstream region. This new composite grid provides better smoothness, resolution, and orthogonality than any single grid for a typical turbine blade with a large camber and rounded leading and trailing edges. The C-H (or O-H) composite grid has an unusual grid point that is connected to more than four neighboring nodes in two dimensions (more than six neighboring nodes in three dimensions). A finite-volume lower-upper (LU) implicit scheme to be used on this grid poses no problem and requires no special treatment because each interior cell of this composite grid has only four neighboring cells in two dimensions (six cells in three dimensions). The LU implicit scheme was demonstrated to be efficient and robust for external flows in a broad flow regime and can be easily applied to internal flows and extended from two to three dimensions.
Cell volume control at a surface for three-dimensional grid generation packages
NASA Technical Reports Server (NTRS)
Alter, Stephen J.; Weilmuenster, Kenneth J.
1992-01-01
An alternate method of calculating the cell size for orthogonality control in the solution of Poisson's 3D space equations is presented. The method provides the capability to enforce a better initial guess for the grid distribution required for boundary layer resolution. This grid point distribution is accomplished by enforcing grid spacing from a grid block boundary where orthogonality is required. The actual grid spacing or cell size for that boundary is determined by the two or four adjacent boundaries in the grid block definition, which are two dimensional grids. These two dimensional grids are in turn defined by the user using insight into the flow field and boundary layer characteristics. The adjoining boundaries are extended using a multifunctional blending scheme, with user control of the blending and interpolating functions to be used. This grid generation procedure results in an enhanced computational fluid dynamics calculation by allowing a quicker resolution of the configuration's boundary layer and flow field and by limiting the number of grid re-adaptations. The cell size specification calculation was applied to a variety of configurations ranging from axisymmetric to complex three-dimensional configurations. Representative grids are shown for the Space Shuttle and the Langley Lifting Body (HL-20).
Automatic computation of Euler-marching and subsonic grids for wing-fuselage configurations
NASA Technical Reports Server (NTRS)
Barger, Raymond L.; Adams, Mary S.; Krishnan, Ramki R.
1994-01-01
Algebraic procedures are described for the automatic generation of structured, single-block flow computation grids for relatively simple configurations (wing, fuselage, and fin). For supersonic flows, a quasi two-dimensional grid for Euler-marching codes is developed, and some sample results in graphical form are included. A type of grid for subsonic flow calculation is also described. The techniques are algebraic and are based on a generalization of the method of transfinite interpolation.
Federal Register 2010, 2011, 2012, 2013, 2014
2012-08-07
... From the Federal Register Online via the Government Publishing Office DEPARTMENT OF ENERGY Federal Energy Regulatory Commission The Incorporated Village of Port Jefferson v. National Grid Generation LLC... Jefferson (Complainant) filed a formal complaint against the National Grid Generation LLC...
Generator algebra of the asymptotic Poincare group in the general theory of relativity
Solovev, V.O.
1986-06-01
This paper obtains the Poisson brackets of the generators of the Hamiltonian formalism for general relativity with allowance for surface terms of aritrary form. For Minkowski space, there exists the asymptotic Poincare group, which is the semi-direct product of the Poincare group and an infinite subgroup for which the algebra of generators with surface terms closes. A criterion invariant with respect to the choice of the coordinate system on the hypersurfaces is obtained for realization of the Poincare group in asymptotically flat space-time. The ''background'' flat metric on the hypersurfaces and Poincare group that preserve it are determined nonuniquely; however, the numerical values of the generators do not depend on the freedom of this choice on solutions of the constraint equations. For an asymptotically Galilean metric, the widely used boundary cnoditins are determined more accurately. A prescription is given for application of the Arnowitt-Deser-Misner decomposition in the case of a slowly decreasing contribution from coordinate and time transformations.
NASA Technical Reports Server (NTRS)
Arthur, Trey; Bockelie, Michael J.
1993-01-01
Efforts to parallelize the VGRIDSG unstructured surface grid generation program are described. The inherent parallel nature of the grid generation algorithm used in VGRIDSG was exploited on a cluster of Silicon Graphics IRIS 4D workstations using the message passing libraries Application Portable Parallel Library (APPL) and Parallel Virtual Machine (PVM). Comparisons of speed up are presented for generating the surface grid of a unit cube and a Mach 3.0 High Speed Civil Transport. It was concluded that for this application, both APPL and PVM give approximately the same performance, however, APPL is easier to use.
NASA Astrophysics Data System (ADS)
Roache, P. J.
1982-08-01
A computational effort to develop computer codes for rapidly and accurately modeling the electric fields within laser cavities is described. Semidirect/marching methods are used both for the generation of two dimensional boundary fitted grids using the elliptic generating equation approach, and for the solution of electric field problems in those coordinate systems. The efficiency of the semidirect/marching methods makes possible interactive design of the laser electrodes using a modest computer. Also described are techniques for high order accuracy, a method for precise grid control at interior points, and applications to the elliptic grid generation problem of computer symbolic manipulation.
BGRID: A block-structured grid generation code for wing sections
NASA Technical Reports Server (NTRS)
Chen, H. C.; Lee, K. D.
1981-01-01
The operation of the BGRID computer program is described for generating block-structured grids. Examples are provided to illustrate the code input and output. The application of a fully implicit AF (approximation factorization)-based computer code, called TWINGB (Transonic WING), for solving the 3D transonic full potential equation in conservation form on block-structured grids is also discussed.
Applications of Lagrangian blending functions for grid generation around airplane geometries
NASA Technical Reports Server (NTRS)
Abolhassani, Jamshid S.; Sadrehaghighi, Ideen; Tiwari, Surendra N.; Smith, Robert E.
1990-01-01
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.
Geometry acquisition and grid generation: Recent experiences with complex aircraft configurations
NASA Technical Reports Server (NTRS)
Gatzke, Timothy D.; Labozzetta, Walter F.; Cooley, John W.; Finfrock, Gregory P.
1992-01-01
Important issues involved in working with complex geometries are discussed. Approaches taken to address complex geometry issues in the McDonnell Aircraft Computational Grid System and related geometry processing tools are discussed. The efficiency of acquiring a suitable geometry definition, the need to manipulate the geometry, and the time and skill level required to generate the grid while preserving geometric fidelity are discussed.
Application of Lagrangian blending functions for grid generation around airplane geometries
NASA Technical Reports Server (NTRS)
Abolhassani, Jamshid S.; Sadrehaghighi, Ideen; Tiwari, Surendra N.
1990-01-01
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.
An analytical approach to grid sensitivity analysis for NACA four-digit wing sections
NASA Technical Reports Server (NTRS)
Sadrehaghighi, I.; Tiwari, S. N.
1992-01-01
Sensitivity analysis in computational fluid dynamics with emphasis on grids and surface parameterization is described. An interactive algebraic grid-generation technique is employed to generate C-type grids around NACA four-digit wing sections. An analytical procedure is developed for calculating grid sensitivity with respect to design parameters of a wing section. A comparison of the sensitivity with that obtained using a finite difference approach is made. Grid sensitivity with respect to grid parameters, such as grid-stretching coefficients, are also investigated. Using the resultant grid sensitivity, aerodynamic sensitivity is obtained using the compressible two-dimensional thin-layer Navier-Stokes equations.
NASA Astrophysics Data System (ADS)
Konstein, S. E.; Tyutin, I. V.
2016-05-01
The associative algebra of symplectic reflections H: = {H_{1,{v_{1,}}{v_2}}}( {{I_2}( {2m} )} ) based on the group generated by the root system I 2(2m) depends on two parameters, ν 1 and ν 2. For each value of these parameters, the algebra admits an m-dimensional space of traces. A trace tr is said to be degenerate if the corresponding symmetric bilinear form B tr( x, y) = tr( xy) is degenerate. We find all values of the parameters ν 1 and ν 2 for which the space of traces contains degenerate traces and the algebra H consequently has a two-sided ideal. It turns out that a linear combination of degenerate traces is also a degenerate trace. For the ν 1 and ν 2 values corresponding to degenerate traces, we find the dimensions of the space of degenerate traces.
GENIE - Generation of computational geometry-grids for internal-external flow configurations
NASA Technical Reports Server (NTRS)
Soni, B. K.
1988-01-01
Progress realized in the development of a master geometry-grid generation code GENIE is presented. The grid refinement process is enhanced by developing strategies to utilize bezier curves/surfaces and splines along with weighted transfinite interpolation technique and by formulating new forcing function for the elliptic solver based on the minimization of a non-orthogonality functional. A two step grid adaptation procedure is developed by optimally blending adaptive weightings with weighted transfinite interpolation technique. Examples of 2D-3D grids are provided to illustrate the success of these methods.
Computational Needs for the Next Generation Electric Grid Proceedings
Birman, Kenneth; Ganesh, Lakshmi; Renessee, Robbert van; Ferris, Michael; Hofmann, Andreas; Williams, Brian; Sztipanovits, Janos; Hemingway, Graham; University, Vanderbilt; Bose, Anjan; Stivastava, Anurag; Grijalva, Santiago; Grijalva, Santiago; Ryan, Sarah M.; McCalley, James D.; Woodruff, David L.; Xiong, Jinjun; Acar, Emrah; Agrawal, Bhavna; Conn, Andrew R.; Ditlow, Gary; Feldmann, Peter; Finkler, Ulrich; Gaucher, Brian; Gupta, Anshul; Heng, Fook-Luen; Kalagnanam, Jayant R; Koc, Ali; Kung, David; Phan, Dung; Singhee, Amith; Smith, Basil
2011-10-05
The April 2011 DOE workshop, 'Computational Needs for the Next Generation Electric Grid', was the culmination of a year-long process to bring together some of the Nation's leading researchers and experts to identify computational challenges associated with the operation and planning of the electric power system. The attached papers provide a journey into these experts' insights, highlighting a class of mathematical and computational problems relevant for potential power systems research. While each paper defines a specific problem area, there were several recurrent themes. First, the breadth and depth of power system data has expanded tremendously over the past decade. This provides the potential for new control approaches and operator tools that can enhance system efficiencies and improve reliability. However, the large volume of data poses its own challenges, and could benefit from application of advances in computer networking and architecture, as well as data base structures. Second, the computational complexity of the underlying system problems is growing. Transmitting electricity from clean, domestic energy resources in remote regions to urban consumers, for example, requires broader, regional planning over multi-decade time horizons. Yet, it may also mean operational focus on local solutions and shorter timescales, as reactive power and system dynamics (including fast switching and controls) play an increasingly critical role in achieving stability and ultimately reliability. The expected growth in reliance on variable renewable sources of electricity generation places an exclamation point on both of these observations, and highlights the need for new focus in areas such as stochastic optimization to accommodate the increased uncertainty that is occurring in both planning and operations. Application of research advances in algorithms (especially related to optimization techniques and uncertainty quantification) could accelerate power system software tool
Multi-scale grid generated turbulence in an internal flow application
NASA Astrophysics Data System (ADS)
Ranade, Piyush; Morris, Scott
2013-11-01
Turbulence generation using multi-scale, or fractal grids, is a method of creating high turbulence intensity flows passively by utilizing the intrinsic scales associated with the grid. This has become the topic of research in many external flow applications. In turbomachinery, the flow at the exit of the combustor and into the first nozzle stage is highly turbulent. In order to create high turbulence intensities in a lab setting passively, multi-scale turbulence generation grids are proposed. The presence of multiple length scales in the grid geometry innately gives rise to turbulent motions of a wide spectrum being shed immediately downstream of the grid, leading to high turbulence intensity flow. The biggest challenge with using such a grid in an internal flow, however, is to achieve spatial uniformity. In this research, three grid geometries commonly found in literature were tested in an experimental set-up consisting of flow between two flat plates. In addition, several other fractal grid geometries were created and tested in an attempt to maximize turbulence intensity while maintaining spatial homogeneity. This research hopes to begin giving insight into the development of turbulence downstream of a multi-scale grid in an internal flow setting.
Makris, Evangelos; Neofytou, Panagiotis; Tsangaris, Sokrates; Housiadas, Christos
2012-10-01
In this study a description of a new approach, for the generation of multi-block structured computational grids on patient-specific bifurcation geometries is presented. The structured grid generation technique is applied to data obtained by medical imaging examination, resulting in a surface conforming, high quality, multi-block structured grid of the branching geometry. As a case study application a patient specific abdominal aorta bifurcation is selected. For the evaluation of the grid produced by the novel method, a grid convergence study and a comparison between the grid produced by the method and unstructured grids produced by commercial meshing software are carried out. PMID:22209311
NASA Technical Reports Server (NTRS)
Papadopoulos, Periklis; Venkatapathy, Ethiraj; Prabhu, Dinesh; Loomis, Mark P.; Olynick, Dave; Arnold, James O. (Technical Monitor)
1998-01-01
Recent advances in computational power enable computational fluid dynamic modeling of increasingly complex configurations. A review of grid generation methodologies implemented in support of the computational work performed for the X-38 and X-33 are presented. In strategizing topological constructs and blocking structures factors considered are the geometric configuration, optimal grid size, numerical algorithms, accuracy requirements, physics of the problem at hand, computational expense, and the available computer hardware. Also addressed are grid refinement strategies, the effects of wall spacing, and convergence. The significance of grid is demonstrated through a comparison of computational and experimental results of the aeroheating environment experienced by the X-38 vehicle. Special topics on grid generation strategies are also addressed to model control surface deflections, and material mapping.
NASA Surface-Modeling and Grid-Generation (SM/GG) activities
NASA Technical Reports Server (NTRS)
Choo, Yung K.
1992-01-01
A NASA Steering Committee was formed to carry out the recommendations from the NASA Workshop on Future Directions in Surface Modeling and Grid Generation. Its function is to communicate and coordinate within NASA the acquisition and distribution of geometry/grid generation software/data, establish geometry data exchange standards, and interface with other government, university, and industry efforts. Two speakers present the committee's activities in viewgraph format.
Online Optimization Method for Operation of Generators in a Micro Grid
NASA Astrophysics Data System (ADS)
Hayashi, Yasuhiro; Miyamoto, Hideki; Matsuki, Junya; Iizuka, Toshio; Azuma, Hitoshi
Recently a lot of studies and developments about distributed generator such as photovoltaic generation system, wind turbine generation system and fuel cell have been performed under the background of the global environment issues and deregulation of the electricity market, and the technique of these distributed generators have progressed. Especially, micro grid which consists of several distributed generators, loads and storage battery is expected as one of the new operation system of distributed generator. However, since precipitous load fluctuation occurs in micro grid for the reason of its smaller capacity compared with conventional power system, high-accuracy load forecasting and control scheme to balance of supply and demand are needed. Namely, it is necessary to improve the precision of operation in micro grid by observing load fluctuation and correcting start-stop schedule and output of generators online. But it is not easy to determine the operation schedule of each generator in short time, because the problem to determine start-up, shut-down and output of each generator in micro grid is a mixed integer programming problem. In this paper, the authors propose an online optimization method for the optimal operation schedule of generators in micro grid. The proposed method is based on enumeration method and particle swarm optimization (PSO). In the proposed method, after picking up all unit commitment patterns of each generators satisfied with minimum up time and minimum down time constraint by using enumeration method, optimal schedule and output of generators are determined under the other operational constraints by using PSO. Numerical simulation is carried out for a micro grid model with five generators and photovoltaic generation system in order to examine the validity of the proposed method.
A Software Demonstration of 'rap': Preparing CAD Geometries for Overlapping Grid Generation
Anders Petersson, N.
2002-02-15
We demonstrate the application code ''rap'' which is part of the ''Overture'' library. A CAD geometry imported from an IGES file is first cleaned up and simplified to suit the needs of mesh generation. Thereafter, the topology of the model is computed and a water-tight surface triangulation is created on the CAD surface. This triangulation is used to speed up the projection of points onto the CAD surface during the generation of overlapping surface grids. From each surface grid, volume grids are grown into the domain using a hyperbolic marching procedure. The final step is to fill any remaining parts of the interior with background meshes.
Elliptic grid generation with orthogonality and spacing control on an arbitrary number of boundaries
NASA Technical Reports Server (NTRS)
White, J. A.
1990-01-01
A procedure for the generation of two and quasi-three-dimensional grids with control of orthogonality and spacing with respect to any and/or all boundaries of the domain is described. The elliptic grid generation equations of Thompson are solved implicitly. Control of the grid behavior is achieved through the introduction of forcing functions terms in the manner of Steger and Sorenson or in a modification of the method of Hilgenstock. The forcing function terms are constructed on the boundaries and propagated into the domain using transfinite Lagrangian bivariate interpolation. An anisotropic transfinite stencil is introduced and is shown to produce excellent grid behavior particularly in the vicinity of corner singularities. Emphasis is placed on the generation of viscous grids and the method is shown to be suited for use in the generation of grids for internal as well as external flow geometries. A FORTRAN program named PISCES has been written to implement the algorithm. Examples of grids for internal and external flows are given that highlight the characteristics and behavior of the algorithm.
NASA Technical Reports Server (NTRS)
Steger, Joseph L.
1989-01-01
Hyperbolic grid generation procedures are described which have been used in external flow simulations about complex configurations. For many practical applications a single well-ordered (i.e., structured) grid can be used to mesh an entire configuration, in other problems, composite or unstructured grid procedures are needed. Although the hyperbolic partial differential equation grid generation procedure has mainly been utilized to generate structured grids, extension of the procedure to semiunstructured grids is briefly described. Extensions of the methodology are also described using two-dimensional equations.
NASA Technical Reports Server (NTRS)
Steinbrenner, John P.; Chawner, John R.
1992-01-01
GRIDGEN is a government domain software package for interactive generation of multiple block grids around general configurations. Though it has been freely available since 1989, it has not been widely embraced by the internal flow community due to a misconception that it was designed for external flow use only. In reality GRIDGEN has always worked for internal flow applications, and GRIDGEN ongoing enhancements are increasing the quality of and efficiency with which grids for external and internal flow problems may be constructed. The software consists of four codes used to perform the four steps of the grid generation process. GRIDBLOCK is first used to decompose the flow domain into a collection of component blocks and then to establish interblock connections and flow solver boundary conditions. GRIDGEN2D is then used to generate surface grids on the outer shell of each component block. GRIDGEN3D generates grid points on the interior of each block, and finally GRIDVUE3D is used to inspect the resulting multiple block grid. Three of these codes (GRIDBLOCK, GRIDGEN2D, and GRIDVUE3D) are highly interactive and graphical in nature, and currently run on Silicon Graphics, Inc., and IBM RS/6000 workstations. The lone batch code (GRIDGEN3D) may be run on any of several Unix based platforms. Surface grid generation in GRIDGEN2D is being improved with the addition of higher order surface definitions (NURBS and parametric surfaces input in IGES format and bicubic surfaces input in PATRAN Neutral File format) and double precision mathematics. In addition, two types of automation have been added to GRIDGEN2D that reduce the learning curve slope for new users and eliminate work for experienced users. Volume grid generation using GRIDGEN3D has been improved via the addition of an advanced hybrid control function formulation that provides both orthogonality and clustering control at the block faces and clustering control on the block interior.
A gridded multisite weather generator and synchronization to observed weather data
NASA Astrophysics Data System (ADS)
Wilks, Daniel S.
2009-10-01
Procedures are described for constructing a daily multisite weather generator at a collection of arbitrary (e.g., gridded) locations and for synchronizing the gridded generator to observed weather series at a set of reference stations. The gridded generator is constructed by interpolating conventional single-station weather generator parameters using locally weighted regressions and producing coherent simulations of daily weather from them using spatial correlation functions. When implemented, the synchronization algorithm results in simulated spatial weather fields at the grid points that are consistent with daily weather observations at nearby locations for particular years. The synchronization is achieved by exploiting the latent multivariate Gaussian structure of the spatially distributed weather generator and making use of well-known statistical results that define conditional multivariate Gaussian distributions given known values for a subset of variables from the larger joint distribution. The primary focus is on precipitation, but the nonprecipitation variables in the weather generator are also amenable to gridding and to synchronization with nearby observed weather series. The motivating idea is to allow calibration of spatially distributed hydrological models consistent with the climate of the spatial weather generator, potentially allowing more realistic hydrological simulation, but the procedure may also be useful for interpolation of missing daily weather data.
Message passing for integrating and assessing renewable generation in a redundant power grid
Zdeborova, Lenka; Backhaus, Scott; Chertkov, Michael
2009-01-01
A simplified model of a redundant power grid is used to study integration of fluctuating renewable generation. The grid consists of large number of generator and consumer nodes. The net power consumption is determined by the difference between the gross consumption and the level of renewable generation. The gross consumption is drawn from a narrow distribution representing the predictability of aggregated loads, and we consider two different distributions representing wind and solar resources. Each generator is connected to D consumers, and redundancy is built in by connecting R {le} D of these consumers to other generators. The lines are switchable so that at any instance each consumer is connected to a single generator. We explore the capacity of the renewable generation by determining the level of 'firm' generation capacity that can be displaced for different levels of redundancy R. We also develop message-passing control algorithm for finding switch sellings where no generator is overloaded.
Scenario generation for stochastic optimization problems via the sparse grid method
Chen, Michael; Mehrotra, Sanjay; Papp, David
2015-04-19
We study the use of sparse grids in the scenario generation (or discretization) problem in stochastic programming problems where the uncertainty is modeled using a continuous multivariate distribution. We show that, under a regularity assumption on the random function involved, the sequence of optimal objective function values of the sparse grid approximations converges to the true optimal objective function values as the number of scenarios increases. The rate of convergence is also established. We treat separately the special case when the underlying distribution is an affine transform of a product of univariate distributions, and show how the sparse grid method can be adapted to the distribution by the use of quadrature formulas tailored to the distribution. We numerically compare the performance of the sparse grid method using different quadrature rules with classic quasi-Monte Carlo (QMC) methods, optimal rank-one lattice rules, and Monte Carlo (MC) scenario generation, using a series of utility maximization problems with up to 160 random variables. The results show that the sparse grid method is very efficient, especially if the integrand is sufficiently smooth. In such problems the sparse grid scenario generation method is found to need several orders of magnitude fewer scenarios than MC and QMC scenario generation to achieve the same accuracy. As a result, it is indicated that the method scales well with the dimension of the distribution--especially when the underlying distribution is an affine transform of a product of univariate distributions, in which case the method appears scalable to thousands of random variables.
On the use of Schwarz-Christoffel conformal mappings to the grid generation for global ocean models
NASA Astrophysics Data System (ADS)
Xu, S.; Wang, B.; Liu, J.
2015-02-01
In this article we propose two conformal mapping based grid generation algorithms for global ocean general circulation models (OGCMs). Contrary to conventional, analytical forms based dipolar or tripolar grids, the new algorithms are based on Schwarz-Christoffel (SC) conformal mapping with prescribed boundary information. While dealing with the basic grid design problem of pole relocation, these new algorithms also address more advanced issues such as smoothed scaling factor, or the new requirements on OGCM grids arisen from the recent trend of high-resolution and multi-scale modeling. The proposed grid generation algorithm could potentially achieve the alignment of grid lines to coastlines, enhanced spatial resolution in coastal regions, and easier computational load balance. Since the generated grids are still orthogonal curvilinear, they can be readily utilized in existing Bryan-Cox-Semtner type ocean models. The proposed methodology can also be applied to the grid generation task for regional ocean modeling where complex land-ocean distribution is present.
A grid quality manipulation system
NASA Technical Reports Server (NTRS)
Lu, Ning; Eiseman, Peter R.
1991-01-01
A grid quality manipulation system is described. The elements of the system are the measures by which quality is assessed, the computer graphic display of those measures, and the local grid manipulation to provide a response to the viewed quality indication. The display is an overlaid composite where the region is first covered with colors to reflect the values of the quality indicator, the grid is then placed on top of those colors, and finally a control net is placed on top of everything. The net represents the grid in terms of the control point form of algebraic grid generation. As a control point is moved, both the grid and the colored quality measures also move. This is a real time dynamic action so that the consequences of the manipulation are continuously seen.
NASA Technical Reports Server (NTRS)
kaul, Upender K.
2008-01-01
A procedure for generating smooth uniformly clustered single-zone grids using enhanced elliptic grid generation has been demonstrated here for the Mars Science Laboratory (MSL) geometries such as aeroshell and canopy. The procedure obviates the need for generating multizone grids for such geometries, as reported in the literature. This has been possible because the enhanced elliptic grid generator automatically generates clustered grids without manual prescription of decay parameters needed with the conventional approach. In fact, these decay parameters are calculated as decay functions as part of the solution, and they are not constant over a given boundary. Since these decay functions vary over a given boundary, orthogonal grids near any arbitrary boundary can be clustered automatically without having to break up the boundaries and the corresponding interior domains into various zones for grid generation.
The three-dimensional Multi-Block Advanced Grid Generation System (3DMAGGS)
NASA Technical Reports Server (NTRS)
Alter, Stephen J.; Weilmuenster, Kenneth J.
1993-01-01
As the size and complexity of three dimensional volume grids increases, there is a growing need for fast and efficient 3D volumetric elliptic grid solvers. Present day solvers are limited by computational speed and do not have all the capabilities such as interior volume grid clustering control, viscous grid clustering at the wall of a configuration, truncation error limiters, and convergence optimization residing in one code. A new volume grid generator, 3DMAGGS (Three-Dimensional Multi-Block Advanced Grid Generation System), which is based on the 3DGRAPE code, has evolved to meet these needs. This is a manual for the usage of 3DMAGGS and contains five sections, including the motivations and usage, a GRIDGEN interface, a grid quality analysis tool, a sample case for verifying correct operation of the code, and a comparison to both 3DGRAPE and GRIDGEN3D. Since it was derived from 3DGRAPE, this technical memorandum should be used in conjunction with the 3DGRAPE manual (NASA TM-102224).
NASA Astrophysics Data System (ADS)
Crowe, A. S.; Shikaze, S. G.; Schwartz, F. W.
An algorithm is presented for generating finite element grids that can be used to calculate the position of a fluctuating water table and the formation of seepage faces within a heterogeneous unconfined aquifer. Our approach overcomes limitations with existing techniques by allowing the water table to rise or decline through hydrostratigraphic boundaries yet maintains numerical and conceptual accuracy with respect to hydrostratigraphic geometry. The algorithm involves (1) limited stretching or shrinking of elements along the water table if the change in the position of the water table is small with respect to the vertical grid spacing, and (2) the addition or removal of nodes and elements in the finite element mesh along the water table as the change becomes large with respect to the vertical grid spacing. This technique is applicable to any 2-D or 3-D finite element code that contains an automatic finite-element grid generator.
Generalized Monge-Kantorovich optimization for grid generation and adaptation in LP
Delzanno, G L; Finn, J M
2009-01-01
The Monge-Kantorovich grid generation and adaptation scheme of is generalized from a variational principle based on L{sub 2} to a variational principle based on L{sub p}. A generalized Monge-Ampere (MA) equation is derived and its properties are discussed. Results for p > 1 are obtained and compared in terms of the quality of the resulting grid. We conclude that for the grid generation application, the formulation based on L{sub p} for p close to unity leads to serious problems associated with the boundary. Results for 1.5 {approx}< p {approx}< 2.5 are quite good, but there is a fairly narrow range around p = 2 where the results are close to optimal with respect to grid distortion. Furthermore, the Newton-Krylov methods used to solve the generalized MA equation perform best for p = 2.
Elliptic Grid Generation of Spiral-Bevel Pinion Gear Typical of OH-58 Helicopter Transmission
NASA Technical Reports Server (NTRS)
Kaul, Upender K.; Huff, Edward M.
2002-01-01
This paper discusses the source term treatment in the numerical solution of elliptic partial differential equations for an interior grid generation problem in generalized curvilinear coordinates. The geometry considered is that of a planar cross-section of a generic spiral-bevel gear tooth typical of a pinion in the OH-58 helicopter transmission. The source terms used are appropriate for an interior grid domain where all the boundaries are prescribed via a combination of Dirichlet and Neumann boundary conditions. New constraints based on the Green's Theorem are derived which uniquely determine the coefficients in the source terms. These constraints are designed for boundary clustered grids where gradients in physical quantities need to be resolved adequately. However, it is seen that the present formulation works satisfactorily for mild clustering also. Thus, a fully automated elliptic grid generation technique is made possible where there is no need for a parametric study of these parameters since the new relations fix these free parameters uniquely.
An assessment of ASTER surface reflectance products generated by GEO Grid
NASA Astrophysics Data System (ADS)
Yamamoto, Hirokazu; Kamei, Akihide; Moriyama, Masao; Tsuchida, Satoshi
2010-08-01
The GEO Grid is an e-infrastructure, which is capable in archiving large amount of satellite data and conducting higher level processing using the advanced grid technologies.1 The Advanced Space-borne Thermal Emission and Reflection Radiometer (ASTER) Level 0 data are stored in a cluster system on GEO Grid, and ASTER ortho-rectified radiance and Digital Elevation Model (DEM) products are able to be generated on this system globally since 2000. This research shows validation of new ASTER surface reflectance products generated by the GEO Grid system, which can apply the radiometric and atmospheric correction to ASTER ortho-rectified radiance data of Visible and Near Infrared (VNIR) and Shortwave Infrared (SWIR).
NASA Astrophysics Data System (ADS)
Khawaja, Aly Salim
A general prismatic mesh generator capable of discretizing flow domains for arbitrary 3-D geometries is presented. The overall project objective was to be able to perform routine viscous flow simulations for engineering design and analysis. The suitability of the hybrid prismatic/tetrahedral grid generation approach for numerical computations of flow phenomena over complex bodies was to be authenticated. The prismatic elements are used in close proximity to the body surface to resolve the viscous stresses whereas tetrahedral elements tessellate the rest of the domain. Such an approach allows the exploitation of the best of both, structured and unstructured grid generation approaches. A special algorithm is developed to allow the prisms to march along general splined boundary surfaces. The method uses a 2-D marching scheme in the parametric domain and performs coordinate transfers to the real space. The inclusion of such a scheme allows the use of periodic boundary conditions to reduce solver memory requirements and broaden the range of applicability of the grid generator. The work also introduces the novel ideas of multi-zone and unstructured prismatic mesh generation to allow different levels of grid resolution within the same geometry and to treat disparate length scales. Both these developments are aimed at optimizing the discretized flow domain with the fewest elements and reducing the time step restrictions of the solver by increasing the volumes of the individual cells. Several quality enhancement and validity checks are presented along with an automatic mesh regeneration mechanism for improved overall quality. The combination of the developed algorithms allows for the discretization of realistic 3-D geometries without much user intervention. Applications of the hybrid prismatic/tetrahedral grid generator are presented from various fields such as the aerospace, turbomachinery and offshore industries. The robustness and efficiency of the prismatic grid
On the use of Schwarz-Christoffel conformal mappings to the grid generation for global ocean models
NASA Astrophysics Data System (ADS)
Xu, S.; Wang, B.; Liu, J.
2015-10-01
In this article we propose two grid generation methods for global ocean general circulation models. Contrary to conventional dipolar or tripolar grids, the proposed methods are based on Schwarz-Christoffel conformal mappings that map areas with user-prescribed, irregular boundaries to those with regular boundaries (i.e., disks, slits, etc.). The first method aims at improving existing dipolar grids. Compared with existing grids, the sample grid achieves a better trade-off between the enlargement of the latitudinal-longitudinal portion and the overall smooth grid cell size transition. The second method addresses more modern and advanced grid design requirements arising from high-resolution and multi-scale ocean modeling. The generated grids could potentially achieve the alignment of grid lines to the large-scale coastlines, enhanced spatial resolution in coastal regions, and easier computational load balance. Since the grids are orthogonal curvilinear, they can be easily utilized by the majority of ocean general circulation models that are based on finite difference and require grid orthogonality. The proposed grid generation algorithms can also be applied to the grid generation for regional ocean modeling where complex land-sea distribution is present.
Generation and use of unstructured grids for turbomachinery calculations
NASA Technical Reports Server (NTRS)
Lindquist, Dana R.; Giles, Michael B.
1991-01-01
A wavefront mesh generator for two dimensional triangular meshes as well as a brief description of the solution method used with these meshes are presented. The interest is in creating meshes for solving the equations of fluid mechanics in complex turbomachinery problems, although the mesh generator and flow solver may be used for a larger variety of applications. The focus is on the flexibility and power of the mesh generation method for triangulating extremely complex geometries and in changing the geometry to create a new mesh. Two turbomachinery applications are presented which take advantage of this method: the analysis of pylon/strut and pylon/OGV interaction in the bypass of a turbofan.
NASA Technical Reports Server (NTRS)
Kathong, Monchai; Tiwari, Surendra N.
1988-01-01
In the computation of flowfields about complex configurations, it is very difficult to construct a boundary-fitted coordinate system. An alternative approach is to use several grids at once, each of which is generated independently. This procedure is called the multiple grids or zonal grids approach; its applications are investigated. The method conservative providing conservation of fluxes at grid interfaces. The Euler equations are solved numerically on such grids for various configurations. The numerical scheme used is the finite-volume technique with a three-stage Runge-Kutta time integration. The code is vectorized and programmed to run on the CDC VPS-32 computer. Steady state solutions of the Euler equations are presented and discussed. The solutions include: low speed flow over a sphere, high speed flow over a slender body, supersonic flow through a duct, and supersonic internal/external flow interaction for an aircraft configuration at various angles of attack. The results demonstrate that the multiple grids approach along with the conservative interfacing is capable of computing the flows about the complex configurations where the use of a single grid system is not possible.
Multi-Resolution Unstructured Grid-Generation for Geophysical Applications on the Sphere
NASA Technical Reports Server (NTRS)
Engwirda, Darren
2015-01-01
An algorithm for the generation of non-uniform unstructured grids on ellipsoidal geometries is described. This technique is designed to generate high quality triangular and polygonal meshes appropriate for general circulation modelling on the sphere, including applications to atmospheric and ocean simulation, and numerical weather predication. Using a recently developed Frontal-Delaunay-refinement technique, a method for the construction of high-quality unstructured ellipsoidal Delaunay triangulations is introduced. A dual polygonal grid, derived from the associated Voronoi diagram, is also optionally generated as a by-product. Compared to existing techniques, it is shown that the Frontal-Delaunay approach typically produces grids with near-optimal element quality and smooth grading characteristics, while imposing relatively low computational expense. Initial results are presented for a selection of uniform and non-uniform ellipsoidal grids appropriate for large-scale geophysical applications. The use of user-defined mesh-sizing functions to generate smoothly graded, non-uniform grids is discussed.
New Boundary Constraints for Elliptic Systems used in Grid Generation Problems
NASA Technical Reports Server (NTRS)
Kaul, Upender K.; Clancy, Daniel (Technical Monitor)
2002-01-01
This paper discusses new boundary constraints for elliptic partial differential equations as used in grid generation problems in generalized curvilinear coordinate systems. These constraints, based on the principle of local conservation of thermal energy in the vicinity of the boundaries, are derived using the Green's Theorem. They uniquely determine the so called decay parameters in the source terms of these elliptic systems. These constraints' are designed for boundary clustered grids where large gradients in physical quantities need to be resolved adequately. It is observed that the present formulation also works satisfactorily for mild clustering. Therefore, a closure for the decay parameter specification for elliptic grid generation problems has been provided resulting in a fully automated elliptic grid generation technique. Thus, there is no need for a parametric study of these decay parameters since the new constraints fix them uniquely. It is also shown that for Neumann type boundary conditions, these boundary constraints uniquely determine the solution to the internal elliptic problem thus eliminating the non-uniqueness of the solution of an internal Neumann boundary value grid generation problem.
NASA Workshop on future directions in surface modeling and grid generation
NASA Technical Reports Server (NTRS)
Vandalsem, W. R.; Smith, R. E.; Choo, Y. K.; Birckelbaw, L. D.; Vogel, A. A.
1992-01-01
Given here is a summary of the paper sessions and panel discussions of the NASA Workshop on Future Directions in Surface Modeling and Grid Generation held a NASA Ames Research Center, Moffett Field, California, December 5-7, 1989. The purpose was to assess U.S. capabilities in surface modeling and grid generation and take steps to improve the focus and pace of these disciplines within NASA. The organization of the workshop centered around overviews from NASA centers and expert presentations from U.S. corporations and universities. Small discussion groups were held and summarized by group leaders. Brief overviews and a panel discussion by representatives from the DoD were held, and a NASA-only session concluded the meeting. In the NASA Program Planning Session summary there are five recommended steps for NASA to take to improve the development and application of surface modeling and grid generation.
Algorithms for the automatic generation of 2-D structured multi-block grids
NASA Technical Reports Server (NTRS)
Schoenfeld, Thilo; Weinerfelt, Per; Jenssen, Carl B.
1995-01-01
Two different approaches to the fully automatic generation of structured multi-block grids in two dimensions are presented. The work aims to simplify the user interactivity necessary for the definition of a multiple block grid topology. The first approach is based on an advancing front method commonly used for the generation of unstructured grids. The original algorithm has been modified toward the generation of large quadrilateral elements. The second method is based on the divide-and-conquer paradigm with the global domain recursively partitioned into sub-domains. For either method each of the resulting blocks is then meshed using transfinite interpolation and elliptic smoothing. The applicability of these methods to practical problems is demonstrated for typical geometries of fluid dynamics.
SmaggIce 2.0: Additional Capabilities for Interactive Grid Generation of Iced Airfoils
NASA Technical Reports Server (NTRS)
Kreeger, Richard E.; Baez, Marivell; Braun, Donald C.; Schilling, Herbert W.; Vickerman, Mary B.
2008-01-01
The Surface Modeling and Grid Generation for Iced Airfoils (SmaggIce) software toolkit has been extended to allow interactive grid generation for multi-element iced airfoils. The essential phases of an icing effects study include geometry preparation, block creation and grid generation. SmaggIce Version 2.0 now includes these main capabilities for both single and multi-element airfoils, plus an improved flow solver interface and a variety of additional tools to enhance the efficiency and accuracy of icing effects studies. An overview of these features is given, especially the new multi-element blocking strategy using the multiple wakes method. Examples are given which illustrate the capabilities of SmaggIce for conducting an icing effects study for both single and multi-element airfoils.
An Automatic K-Point Grid Generation Scheme for Enhanced Efficiency and Accuracy in DFT Calculations
NASA Astrophysics Data System (ADS)
Mohr, Jennifer A.-F.; Shepherd, James J.; Alavi, Ali
2013-03-01
We seek to create an automatic k-point grid generation scheme for density functional theory (DFT) calculations that improves the efficiency and accuracy of the calculations and is suitable for use in high-throughput computations. Current automated k-point generation schemes often result in calculations with insufficient k-points, which reduces the reliability of the results, or too many k-points, which can significantly increase computational cost. By controlling a wider range of k-point grid densities for the Brillouin zone based upon factors of conductivity and symmetry, a scalable k-point grid generation scheme can lower calculation runtimes and improve the accuracy of energy convergence. Johns Hopkins University
GENERATING ON-THE-FLY LARGE SAMPLES OF THEORETICAL SPECTRA THROUGH AN N-DIMENSIONAL GRID
Yip, C.-W.
2010-02-15
Many analyses and parameter estimations undertaken in astronomy require a large set ({approx}>10{sup 5}) of non-analytical, theoretical spectra, each of these defined by multiple parameters. We describe the construction of an N-dimensional grid which is suitable for generating such spectra. The theoretical spectra are designed to correspond to a targeted parameter grid but otherwise to random positions in the parameter space, and they are interpolated on the fly through a pre-calculated grid of spectra. The initial grid is designed to be relatively low in parameter resolution and small in occupied hard disk space and therefore can be updated efficiently when a new model is desired. In a pilot study of stellar population synthesis of galaxies, the mean square errors on the estimated parameters are found to decrease with the targeted grid resolution. This scheme of generating a large model grid is general for other areas of studies, particularly if they are based on multi-dimensional parameter space and are focused on contrasting model differences.
Mitigation of Power Quality Problems in Grid-Interactive Distributed Generation System
NASA Astrophysics Data System (ADS)
Bhende, C. N.; Kalam, A.; Malla, S. G.
2016-04-01
Having an inter-tie between low/medium voltage grid and distributed generation (DG), both exposes to power quality (PQ) problems created by each other. This paper addresses various PQ problems arise due to integration of DG with grid. The major PQ problems are due to unbalanced and non-linear load connected at DG, unbalanced voltage variations on transmission line and unbalanced grid voltages which severely affect the performance of the system. To mitigate the above mentioned PQ problems, a novel integrated control of distribution static shunt compensator (DSTATCOM) is presented in this paper. DSTATCOM control helps in reducing the unbalance factor of PCC voltage. It also eliminates harmonics from line currents and makes them balanced. Moreover, DSTATCOM supplies the reactive power required by the load locally and hence, grid need not to supply the reactive power. To show the efficacy of the proposed controller, several operating conditions are considered and verified through simulation using MATLAB/SIMULINK.
NASA Technical Reports Server (NTRS)
Kamhawi, Hilmi N.
2012-01-01
This report documents the work performed from March 2010 to March 2012. The Integrated Design and Engineering Analysis (IDEA) environment is a collaborative environment based on an object-oriented, multidisciplinary, distributed framework using the Adaptive Modeling Language (AML) as a framework and supporting the configuration design and parametric CFD grid generation. This report will focus on describing the work in the area of parametric CFD grid generation using novel concepts for defining the interaction between the mesh topology and the geometry in such a way as to separate the mesh topology from the geometric topology while maintaining the link between the mesh topology and the actual geometry.
Risk-based generation dispatch in the power grid for resilience against extreme weather events
NASA Astrophysics Data System (ADS)
Javanbakht, Pirooz
Natural disasters have been considered as one of the main causes of the largest blackouts in North America. When it comes to power grid resiliency against natural hazards, different solutions exist that are mainly categorized based on the time-frame of analysis. At the design stage, robustness and resiliency may be improved through redundant designs and inclusion of advanced measurement, monitoring, control and protection systems. However, since massive destructive energy may be released during the course of a natural disaster (such as a hurricane) causing large-scale and widespread disturbances, design-stage remedies may not be sufficient for ensuring power grid robustness. As a result, to limit the consequent impacts on the operation of the power grid, the system operator may be forced to take immediate remedial actions in real-time. To effectively manage the disturbances caused by severe weather events, weather forecast information should be incorporated into the operational model of the power grid in order to predict imminent contingencies. In this work, a weather-driven generation dispatch model is developed based on stochastic programming to provide a proactive solution for power grid resiliency against imminent large-scale disturbances. Hurricanes and ice storms are studied as example disaster events to provide numerical results. In this approach, the statistics of the natural disaster event are taken into account along with the expected impact on various power grid components in order to determine the availability of the grid. Then, a generation dispatch strategy is devised that helps operate the grid subject to weather-driven operational constraints.
Developing a TI-92 Manual Generator Based on Computer Algebra Systems
ERIC Educational Resources Information Center
Jun, Youngcook
2004-01-01
The electronic medium suitable for mathematics learning and teaching is often designed with a notebook interface provided in a computer algebra system. Such a notebook interface facilitates a workspace for mathematical activities along with an online help system. In this paper, the proposed feature is implemented in the Mathematica's notebook…
Computer algebra and operators
NASA Technical Reports Server (NTRS)
Fateman, Richard; Grossman, Robert
1989-01-01
The symbolic computation of operator expansions is discussed. Some of the capabilities that prove useful when performing computer algebra computations involving operators are considered. These capabilities may be broadly divided into three areas: the algebraic manipulation of expressions from the algebra generated by operators; the algebraic manipulation of the actions of the operators upon other mathematical objects; and the development of appropriate normal forms and simplification algorithms for operators and their actions. Brief descriptions are given of the computer algebra computations that arise when working with various operators and their actions.
The Overgrid Interface for Computational Simulations on Overset Grids
NASA Technical Reports Server (NTRS)
Chan, William M.; Kwak, Dochan (Technical Monitor)
2002-01-01
Computational simulations using overset grids typically involve multiple steps and a variety of software modules. A graphical interface called OVERGRID has been specially designed for such purposes. Data required and created by the different steps include geometry, grids, domain connectivity information and flow solver input parameters. The interface provides a unified environment for the visualization, processing, generation and diagnosis of such data. General modules are available for the manipulation of structured grids and unstructured surface triangulations. Modules more specific for the overset approach include surface curve generators, hyperbolic and algebraic surface grid generators, a hyperbolic volume grid generator, Cartesian box grid generators, and domain connectivity: pre-processing tools. An interface provides automatic selection and viewing of flow solver boundary conditions, and various other flow solver inputs. For problems involving multiple components in relative motion, a module is available to build the component/grid relationships and to prescribe and animate the dynamics of the different components.
Generating grids directly on CAD database surfaces using a parametric evaluator approach
NASA Technical Reports Server (NTRS)
Gatzhe, Timothy D.; Melson, Thomas G.
1995-01-01
A very important, but often overlooked step in grid generation is acquiring a suitable geometry definition of the vehicle to be analyzed. In the past, geometry was usually obtained by generating a number of cross-sections of each component. A number of recent efforts have focussed on non-uniform rational B-spline surfaces (NURBS) to provide as single type of analytic surface to deal with inside the grid generator. This approach has required the development of tools to read other types of surfaces and convert them, either exactly or by approximation, into a NURBS surface. This paper describes a more generic parametric evaluator approach, which does not rely on a particular surface type internal to the grid generation system and is less restrictive in the number of surface types that can be represented exactly. This approach has been implemented in the McDonnell Douglas grid generation system, MACGS, and offers direct access to all types of surfaces from a Unigraphics part file.
Protection against loss of utility grid supply for a dispersed storage and generation unit
Redfern, M.A.; Usta, O. . School of Electronic and Electrical Engineering); Fielding, G. . GEC Alsthom Protection and Control)
1993-07-01
The installation of small or medium sized dispersed storage and generation units operating in parallel with the utility supply presents several technical complications for the protection and control of the system. Amongst these is the need to protect the system from islanding caused by the loss of the utility grid supply and the possible subsequent out-of-synchronism reconnection of that supply. This paper examines the requirements of an islanding, or loss of grid, protection and outlines the principal methods used for this type of relaying. A new protection algorithm is introduced which is based on the rate of change of power as measured at the generator's terminals. The responses of the different measurands are examined for a selection of power system operating conditions to demonstrate the operation of this type of protection. The new protection algorithm is shown to trip for loss of grid, for load fluctuations while the dispersed storage and generation unit is operating independently of the utility supply following a loss of grid, and for an out-of-synchronism reconnection of the utility supply to the dispersed storage and generation unit. It is also shown to remain stable for major load fluctuations while the utility supply remains connected to the dispersed generator system.
Teaching Algebra without Algebra
ERIC Educational Resources Information Center
Kalman, Richard S.
2008-01-01
Algebra is, among other things, a shorthand way to express quantitative reasoning. This article illustrates ways for the classroom teacher to convert algebraic solutions to verbal problems into conversational solutions that can be understood by students in the lower grades. Three reasonably typical verbal problems that either appeared as or…
Global Renewable Energy-Based Electricity Generation and Smart Grid System for Energy Security
Islam, M. A.; Hasanuzzaman, M.; Rahim, N. A.; Nahar, A.; Hosenuzzaman, M.
2014-01-01
Energy is an indispensable factor for the economic growth and development of a country. Energy consumption is rapidly increasing worldwide. To fulfill this energy demand, alternative energy sources and efficient utilization are being explored. Various sources of renewable energy and their efficient utilization are comprehensively reviewed and presented in this paper. Also the trend in research and development for the technological advancement of energy utilization and smart grid system for future energy security is presented. Results show that renewable energy resources are becoming more prevalent as more electricity generation becomes necessary and could provide half of the total energy demands by 2050. To satisfy the future energy demand, the smart grid system can be used as an efficient system for energy security. The smart grid also delivers significant environmental benefits by conservation and renewable generation integration. PMID:25243201
Global renewable energy-based electricity generation and smart grid system for energy security.
Islam, M A; Hasanuzzaman, M; Rahim, N A; Nahar, A; Hosenuzzaman, M
2014-01-01
Energy is an indispensable factor for the economic growth and development of a country. Energy consumption is rapidly increasing worldwide. To fulfill this energy demand, alternative energy sources and efficient utilization are being explored. Various sources of renewable energy and their efficient utilization are comprehensively reviewed and presented in this paper. Also the trend in research and development for the technological advancement of energy utilization and smart grid system for future energy security is presented. Results show that renewable energy resources are becoming more prevalent as more electricity generation becomes necessary and could provide half of the total energy demands by 2050. To satisfy the future energy demand, the smart grid system can be used as an efficient system for energy security. The smart grid also delivers significant environmental benefits by conservation and renewable generation integration. PMID:25243201
Scenario generation for stochastic optimization problems via the sparse grid method
Chen, Michael; Mehrotra, Sanjay; Papp, David
2015-04-19
We study the use of sparse grids in the scenario generation (or discretization) problem in stochastic programming problems where the uncertainty is modeled using a continuous multivariate distribution. We show that, under a regularity assumption on the random function involved, the sequence of optimal objective function values of the sparse grid approximations converges to the true optimal objective function values as the number of scenarios increases. The rate of convergence is also established. We treat separately the special case when the underlying distribution is an affine transform of a product of univariate distributions, and show how the sparse grid methodmore » can be adapted to the distribution by the use of quadrature formulas tailored to the distribution. We numerically compare the performance of the sparse grid method using different quadrature rules with classic quasi-Monte Carlo (QMC) methods, optimal rank-one lattice rules, and Monte Carlo (MC) scenario generation, using a series of utility maximization problems with up to 160 random variables. The results show that the sparse grid method is very efficient, especially if the integrand is sufficiently smooth. In such problems the sparse grid scenario generation method is found to need several orders of magnitude fewer scenarios than MC and QMC scenario generation to achieve the same accuracy. As a result, it is indicated that the method scales well with the dimension of the distribution--especially when the underlying distribution is an affine transform of a product of univariate distributions, in which case the method appears scalable to thousands of random variables.« less
NASA Technical Reports Server (NTRS)
Ferlemann, Paul G.; Gollan, Rowan J.
2010-01-01
Computational design and analysis of three-dimensional hypersonic inlets with shape transition has been a significant challenge due to the complex geometry and grid required for three-dimensional viscous flow calculations. Currently, the design process utilizes an inviscid design tool to produce initial inlet shapes by streamline tracing through an axisymmetric compression field. However, the shape is defined by a large number of points rather than a continuous surface and lacks important features such as blunt leading edges. Therefore, a design system has been developed to parametrically construct true CAD geometry and link the topology of a structured grid to the geometry. The Adaptive Modeling Language (AML) constitutes the underlying framework that is used to build the geometry and grid topology. Parameterization of the CAD geometry allows the inlet shapes produced by the inviscid design tool to be generated, but also allows a great deal of flexibility to modify the shape to account for three-dimensional viscous effects. By linking the grid topology to the parametric geometry, the GridPro grid generation software can be used efficiently to produce a smooth hexahedral multiblock grid. To demonstrate the new capability, a matrix of inlets were designed by varying four geometry parameters in the inviscid design tool. The goals of the initial design study were to explore inviscid design tool geometry variations with a three-dimensional analysis approach, demonstrate a solution rate which would enable the use of high-fidelity viscous three-dimensional CFD in future design efforts, process the results for important performance parameters, and perform a sample optimization.
On the grid generation methods in harmonic mapping on plane and curved surfaces
NASA Technical Reports Server (NTRS)
Sritharan, S. S.; Smith, P. W.
1984-01-01
Harmonic grid generation methods for multiply connected plane regions and regions on curved surfaces are discussed. In particular, using a general formulation on an analytic Riemannian manifold, it is proved that these mappings are globally one-to-one and onto.
ERIC Educational Resources Information Center
Chaudhry, Hina
2013-01-01
This study is a part of the smart grid initiative providing electric vehicle charging infrastructure. It is a refueling structure, an energy generating photovoltaic system and charge point electric vehicle charging station. The system will utilize advanced design and technology allowing electricity to flow from the site's normal electric service…
NASA Astrophysics Data System (ADS)
Chiappini, D.; Donno, A.
2016-06-01
In this paper we present a comparison of three different grids generated with a fractal method and used for fluid dynamic simulations through a kinetic approach. We start from the theoretical element definition and we introduce some optimizations in order to fulfil requirements. The study is performed with analysing results both in terms of friction factor at different Reynolds regimes and streamlines paths.
Geometry Laboratory (GEOLAB) surface modeling and grid generation technology and services
NASA Technical Reports Server (NTRS)
Kerr, Patricia A.; Smith, Robert E.; Posenau, Mary-Anne K.
1995-01-01
The facilities and services of the GEOmetry LABoratory (GEOLAB) at the NASA Langley Research Center are described. Included in this description are the laboratory functions, the surface modeling and grid generation technologies used in the laboratory, and examples of the tasks performed in the laboratory.
NASA Technical Reports Server (NTRS)
Shih, Ming H.; Soni, Bharat K.
1993-01-01
The issue of time efficiency in grid generation is addressed by developing a user friendly graphical interface for interactive/automatic construction of structured grids around complex turbomachinery/axis-symmetric configurations. The accuracy of geometry modeling and its fidelity is accomplished by adapting the nonuniform rational b-spline (NURBS) representation. A customized interactive grid generation code, TIGER, has been developed to facilitate the grid generation process for complicated internal, external, and internal-external turbomachinery fields simulations. The FORMS Library is utilized to build user-friendly graphical interface. The algorithm allows a user to redistribute grid points interactively on curves/surfaces using NURBS formulation with accurate geometric definition. TIGER's features include multiblock, multiduct/shroud, multiblade row, uneven blade count, and patched/overlapping block interfaces. It has been applied to generate grids for various complicated turbomachinery geometries, as well as rocket and missile configurations.
Leibniz algebras associated with representations of filiform Lie algebras
NASA Astrophysics Data System (ADS)
Ayupov, Sh. A.; Camacho, L. M.; Khudoyberdiyev, A. Kh.; Omirov, B. A.
2015-12-01
In this paper we investigate Leibniz algebras whose quotient Lie algebra is a naturally graded filiform Lie algebra nn,1. We introduce a Fock module for the algebra nn,1 and provide classification of Leibniz algebras L whose corresponding Lie algebra L / I is the algebra nn,1 with condition that the ideal I is a Fock nn,1-module, where I is the ideal generated by squares of elements from L. We also consider Leibniz algebras with corresponding Lie algebra nn,1 and such that the action I ×nn,1 → I gives rise to a minimal faithful representation of nn,1. The classification up to isomorphism of such Leibniz algebras is given for the case of n = 4.
Yu, Zhaoyuan; Yuan, Linwang; Luo, Wen; Feng, Linyao; Lv, Guonian
2015-01-01
Passive infrared (PIR) motion detectors, which can support long-term continuous observation, are widely used for human motion analysis. Extracting all possible trajectories from the PIR sensor networks is important. Because the PIR sensor does not log location and individual information, none of the existing methods can generate all possible human motion trajectories that satisfy various spatio-temporal constraints from the sensor activation log data. In this paper, a geometric algebra (GA)-based approach is developed to generate all possible human trajectories from the PIR sensor network data. Firstly, the representation of the geographical network, sensor activation response sequences and the human motion are represented as algebraic elements using GA. The human motion status of each sensor activation are labeled using the GA-based trajectory tracking. Then, a matrix multiplication approach is developed to dynamically generate the human trajectories according to the sensor activation log and the spatio-temporal constraints. The method is tested with the MERL motion database. Experiments show that our method can flexibly extract the major statistical pattern of the human motion. Compared with direct statistical analysis and tracklet graph method, our method can effectively extract all possible trajectories of the human motion, which makes it more accurate. Our method is also likely to provides a new way to filter other passive sensor log data in sensor networks. PMID:26729123
Yu, Zhaoyuan; Yuan, Linwang; Luo, Wen; Feng, Linyao; Lv, Guonian
2015-01-01
Passive infrared (PIR) motion detectors, which can support long-term continuous observation, are widely used for human motion analysis. Extracting all possible trajectories from the PIR sensor networks is important. Because the PIR sensor does not log location and individual information, none of the existing methods can generate all possible human motion trajectories that satisfy various spatio-temporal constraints from the sensor activation log data. In this paper, a geometric algebra (GA)-based approach is developed to generate all possible human trajectories from the PIR sensor network data. Firstly, the representation of the geographical network, sensor activation response sequences and the human motion are represented as algebraic elements using GA. The human motion status of each sensor activation are labeled using the GA-based trajectory tracking. Then, a matrix multiplication approach is developed to dynamically generate the human trajectories according to the sensor activation log and the spatio-temporal constraints. The method is tested with the MERL motion database. Experiments show that our method can flexibly extract the major statistical pattern of the human motion. Compared with direct statistical analysis and tracklet graph method, our method can effectively extract all possible trajectories of the human motion, which makes it more accurate. Our method is also likely to provides a new way to filter other passive sensor log data in sensor networks. PMID:26729123
Performance Analysis of a Permanent-Magnet Induction Generator under Unbalanced Grid Voltages
NASA Astrophysics Data System (ADS)
Tsuda, Toshihiro; Fukami, Tadashi; Kanamaru, Yasunori; Miyamoto, Toshio
This paper presents electrical and magnetic characteristics of a permanent-magnet induction generator (PMIG) under unbalanced grid voltages. The method of symmetrical components and two-dimensional finite element analysis (2D-FEA) are used to calculate these characteristics and the results are confirmed through experiments. Even if the voltage of power grids is unbalanced, the PMIG can operate at high efficiency over a wide range of slip and the built-in permanent-magnet (PM) rotor is little affected by the negative-sequence rotating field.
NASA Astrophysics Data System (ADS)
Eichman, Joshua David
Renewable resources including wind, solar, geothermal, biomass, hydroelectric, wave and tidal, represent an opportunity for environmentally preferred generation of electricity that also increases energy security and independence. California is very proactive in encouraging the implementation of renewable energy in part through legislation like Assembly Bill 32 and the development and execution of Renewable Portfolio Standards (RPS); however renewable technologies are not without challenges. All renewable resources have some resource limitations, be that from location, capacity, cost or availability. Technologies like wind and solar are intermittent in nature but represent one of the most abundant resources for generating renewable electricity. If RPS goals are to be achieved high levels of intermittent renewables must be considered. This work explores the effects of high penetration of renewables on a grid system, with respect to resource availability and identifies the key challenges from the perspective of the grid to introducing these resources. The HiGRID tool was developed for this analysis because no other tool could explore grid operation, while maintaining system reliability, with a diverse set of renewable resources and a wide array of complementary technologies including: energy efficiency, demand response, energy storage technologies and electric transportation. This tool resolves the hourly operation of conventional generation resources (nuclear, coal, geothermal, natural gas and hydro). The resulting behavior from introducing additional renewable resources and the lifetime costs for each technology is analyzed.
User's manual for the HYPGEN hyperbolic grid generator and the HGUI graphical user interface
NASA Technical Reports Server (NTRS)
Chan, William M.; Chiu, Ing-Tsau; Buning, Pieter G.
1993-01-01
The HYPGEN program is used to generate a 3-D volume grid over a user-supplied single-block surface grid. This is accomplished by solving the 3-D hyperbolic grid generation equations consisting of two orthogonality relations and one cell volume constraint. In this user manual, the required input files and parameters and output files are described. Guidelines on how to select the input parameters are given. Illustrated examples are provided showing a variety of topologies and geometries that can be treated. HYPGEN can be used in stand-alone mode as a batch program or it can be called from within a graphical user interface HGUI that runs on Silicon Graphics workstations. This user manual provides a description of the menus, buttons, sliders, and typein fields in HGUI for users to enter the parameters needed to run HYPGEN. Instructions are given on how to configure the interface to allow HYPGEN to run either locally or on a faster remote machine through the use of shell scripts on UNIX operating systems. The volume grid generated is copied back to the local machine for visualization using a built-in hook to PLOT3D.
Grid generation by elliptic partial differential equations for a tri-element Augmentor-Wing airfoil
NASA Technical Reports Server (NTRS)
Sorenson, R. L.
1982-01-01
Two efforts to numerically simulate the flow about the Augmentor-Wing airfoil in the cruise configuration using the GRAPE elliptic partial differential equation grid generator algorithm are discussed. The Augmentor-Wing consists of a main airfoil with a slotted trailing edge for blowing and two smaller airfoils shrouding the blowing jet. The airfoil and the algorithm are described, and the application of GRAPE to an unsteady viscous flow simulation and a transonic full-potential approach is considered. The procedure involves dividing a complicated flow region into an arbitrary number of zones and ensuring continuity of grid lines, their slopes, and their point distributions across the zonal boundaries. The method for distributing the body-surface grid points is discussed.
Three-dimensional unstructured grid generation via incremental insertion and local optimization
NASA Technical Reports Server (NTRS)
Barth, Timothy J.; Wiltberger, N. Lyn; Gandhi, Amar S.
1992-01-01
Algorithms for the generation of 3D unstructured surface and volume grids are discussed. These algorithms are based on incremental insertion and local optimization. The present algorithms are very general and permit local grid optimization based on various measures of grid quality. This is very important; unlike the 2D Delaunay triangulation, the 3D Delaunay triangulation appears not to have a lexicographic characterization of angularity. (The Delaunay triangulation is known to minimize that maximum containment sphere, but unfortunately this is not true lexicographically). Consequently, Delaunay triangulations in three-space can result in poorly shaped tetrahedral elements. Using the present algorithms, 3D meshes can be constructed which optimize a certain angle measure, albeit locally. We also discuss the combinatorial aspects of the algorithm as well as implementational details.
A grid generation method to calculate the flow field in a three-dimensional cascade of blades
NASA Astrophysics Data System (ADS)
Inoue, Kenji
1992-05-01
A method is described for generating boundary fitted grids to calculate the flow field across a three dimensional cascade of blades placed radially in the axially symmetric space between the hub and casing. Successive application of a series of stretching and conformal transformation maps one-period domain of the cascade onto a box in computational space. The grid in physical space is then obtained by inverse transformation of the grid points in computational space, being an H-type grid and having a periodicity which includes the inclination of grid lines at the periodic boundary.
NASA Technical Reports Server (NTRS)
Dulikravich, D. S.
1981-01-01
A fast algorithm was developed for accurately generating boundary-conforming, three-dimensional, consecutively refined computational grids applicable to arbitrary wing-body and axial turbomachinery geometries. The method is based on using an analytic function to generate two-dimensional grids on a number of coaxial axisymmetric surfaces positioned between the centerbody and the outer radial boundary. These grids are of the O-type and are characterized by quasi-orthogonality, geometric periodicity, and an adequate resolution throughout the flow field. Because the built-in nonorthogonal coordinate stretching and shearing cause the grid lines leaving the blade or wing trailing edge to end at downstream infinity, the numerical treatment of the three-dimensional trailing vortex sheets is simplified.
Dynamic analysis of combined photovoltaic source and synchronous generator connected to power grid
NASA Astrophysics Data System (ADS)
Mahabal, Divya
In the world of expanding economy and technology, the energy demand is likely to increase even with the global efforts of saving and increasing energy efficiency. Higher oil prices, effects of greenhouse gases, and concerns over other environmental impacts gave way to Distributed Generation (DG). With adequate awareness and support, DG's can meet these rising energy demands at lower prices compared to conventional methods. Extensive research is taking place in different areas like fuel cells, photovoltaic cells, wind turbines, and gas turbines. DG's when connected to a grid increase the overall efficiency of the power grid. It is believed that three-fifth of the world's electricity would account for renewable energy by middle of 21st century. This thesis presents the dynamic analysis of a grid connected photovoltaic (PV) system and synchronous generator. A grid is considered as an infinite bus. The photovol-taic system and synchronous generator act as small scale distributed energy resources. The output of the photovoltaic system depends on the light intensity, temperature, and irradiance levels of sun. The maximum power point tracking and DC/AC converter are also modeled for the photovoltaic system. The PV system is connected to the grid through DC/AC system. Different combinations of PV and synchronous generator are modeled with the grid to study the dynamics of the proposed system. The dynamics of the test system is analyzed by subjecting the system to several disturbances under various conditions. All modules are individually modeled and con-nected using MATLAB/Simulink software package. Results from the study show that, as the penetration of renewable energy sources like PV increases into the power system, the dynamics of the system becomes faster. When considering cases such as load switching, PV cannot deliver more power as the performance of PV depends on environmental conditions. Synchronous generator in power system can produce the required amount of
NASA Technical Reports Server (NTRS)
Sorenson, R. L.; Steger, J. L.
1983-01-01
An algorithm for generating computational grids about arbitrary three-dimensional bodies is developed. The elliptic partial differential equation (PDE) approach developed by Steger and Sorenson and used in the NASA computer program GRAPE is extended from two to three dimensions. Forcing functions which are found automatically by the algorithm give the user the ability to control mesh cell size and skewness at boundary surfaces. This algorithm, as is typical of PDE grid generators, gives smooth grid lines and spacing in the interior of the grid. The method is applied to a rectilinear wind-tunnel case and to two body shapes in spherical coordinates.
NASA Technical Reports Server (NTRS)
Parikh, Paresh; Pirzadeh, Shahyar; Loehner, Rainald
1990-01-01
A set of computer programs for 3-D unstructured grid generation, fluid flow calculations, and flow field visualization was developed. The grid generation program, called VGRID3D, generates grids over complex configurations using the advancing front method. In this method, the point and element generation is accomplished simultaneously, VPLOT3D is an interactive, menudriven pre- and post-processor graphics program for interpolation and display of unstructured grid data. The flow solver, VFLOW3D, is an Euler equation solver based on an explicit, two-step, Taylor-Galerkin algorithm which uses the Flux Corrected Transport (FCT) concept for a wriggle-free solution. Using these programs, increasingly complex 3-D configurations of interest to aerospace community were gridded including a complete Space Transportation System comprised of the space-shuttle orbitor, the solid-rocket boosters, and the external tank. Flow solutions were obtained on various configurations in subsonic, transonic, and supersonic flow regimes.
EAGLEView: A surface and grid generation program and its data management
NASA Technical Reports Server (NTRS)
Remotigue, M. G.; Hart, E. T.; Stokes, M. L.
1992-01-01
An old and proven grid generation code, the EAGLE grid generation package, is given an added dimension of a graphical interface and a real time data base manager. The Numerical Aerodynamic Simulation (NAS) Panel Library is used for the graphical user interface. Through the panels, EAGLEView constructs the EAGLE script command and sends it to EAGLE to be processed. After the object is created, the script is saved in a mini-buffer which can be edited and/or saved and reinterpreted. The graphical objects are set-up in a linked-list and can be selected or queried by pointing and clicking the mouse. The added graphical enhancement to the EAGLE system emphasizes the unique capability to construct field points around complex geometry and visualize the construction every step of the way.
NASA Astrophysics Data System (ADS)
Alfieri, Luisa
2015-12-01
Power quality (PQ) disturbances are becoming an important issue in smart grids (SGs) due to the significant economic consequences that they can generate on sensible loads. However, SGs include several distributed energy resources (DERs) that can be interconnected to the grid with static converters, which lead to a reduction of the PQ levels. Among DERs, wind turbines and photovoltaic systems are expected to be used extensively due to the forecasted reduction in investment costs and other economic incentives. These systems can introduce significant time-varying voltage and current waveform distortions that require advanced spectral analysis methods to be used. This paper provides an application of advanced parametric methods for assessing waveform distortions in SGs with dispersed generation. In particular, the Standard International Electrotechnical Committee (IEC) method, some parametric methods (such as Prony and Estimation of Signal Parameters by Rotational Invariance Technique (ESPRIT)), and some hybrid methods are critically compared on the basis of their accuracy and the computational effort required.
NASA Technical Reports Server (NTRS)
Choo, Yung; Vickerman, Mary; Lee, Ki D.; Thompson, David S.
2000-01-01
There are two distinct icing-related problems for airfoils that can be simulated. One is predicting the effects of ice on the aerodynamic performance of airfoils when ice geometry is known ("icing effects" study). The other is simulating ice accretion under specified icing conditions ("ice accretion" simulation). This paper will address development of two different software packages for two-dimensional geometry preparation and grid generation for both "icing effects" and "ice accretion" studies.
A sparse grid based method for generative dimensionality reduction of high-dimensional data
NASA Astrophysics Data System (ADS)
Bohn, Bastian; Garcke, Jochen; Griebel, Michael
2016-03-01
Generative dimensionality reduction methods play an important role in machine learning applications because they construct an explicit mapping from a low-dimensional space to the high-dimensional data space. We discuss a general framework to describe generative dimensionality reduction methods, where the main focus lies on a regularized principal manifold learning variant. Since most generative dimensionality reduction algorithms exploit the representer theorem for reproducing kernel Hilbert spaces, their computational costs grow at least quadratically in the number n of data. Instead, we introduce a grid-based discretization approach which automatically scales just linearly in n. To circumvent the curse of dimensionality of full tensor product grids, we use the concept of sparse grids. Furthermore, in real-world applications, some embedding directions are usually more important than others and it is reasonable to refine the underlying discretization space only in these directions. To this end, we employ a dimension-adaptive algorithm which is based on the ANOVA (analysis of variance) decomposition of a function. In particular, the reconstruction error is used to measure the quality of an embedding. As an application, the study of large simulation data from an engineering application in the automotive industry (car crash simulation) is performed.
Customized turbulent flow fields generated by means of an active grid
NASA Astrophysics Data System (ADS)
Hoelling, Michael; Reinke, Nico; Peinke, Joachim
2014-11-01
Wind tunnel experiments, which should clarify the interaction of wind energy converters and the ambient turbulent field, should be performed under realistic flow conditions. For the generation of realistic turbulent flow conditions we use an active grid. This grid allows for the generation of flows with high turbulence intensity and even to repeat those turbulent fields to a certain degree. Moreover, flow features are to a certain extent tuneable, e.g. velocity increments distributions or energy density spectrum, realized by individually controllable horizontal and vertical rotating axes, which are equipped with flaps. The rotation patterns of the axes over time are defined in an excitation protocol. The challenge is designing an excitation protocol, which generates a flow flied for a specific application. A general approach is still missing. Our approach allows estimating the flow features to given excitation protocols. The approach is based on the assumption that the flow field behind an active grid consists basically of different turbulent pulses, which belong to the excitation setting. Our approach gives a sequence of those pulses, which we call synthetic velocity time series, which is made on a computer.
Numerical modeling of wind waves generated by tropical cyclones using moving grids
NASA Astrophysics Data System (ADS)
Tolman, Hendrik L.; Alves, Jose-Henrique G. M.
A version of the WAVEWATCH III wave model featuring a continuously moving spatial grid is presented. The new model option/version is intended for research into wind waves generated by tropical cyclones in deep water away from the coast. The main advantage of such an approach is that the cyclones can be modeled with spatial grids that cover much smaller areas than conventional fixed grids, making model runs with high spatial resolution more economically feasible. The model modifications necessary are fairly trivial. Most complications occur due to the Garden Sprinkler effect (GSE) and methods used to mitigate it. The basic testing of the model is performed using idealized wind fields consisting of a Rankine vortex. The model is also applied to hurricane Lili in the Gulf of Mexico in October 2002. The latter application shows that the moving grid approach provides a natural way to deal with hurricane wind fields that have a high-resolution in space, but a low resolution in time. Although the new model version is originally intended for tropical cyclones, it is suitable for high-resolution modeling of waves due to any moving weather pattern.
Techniques for grid manipulation and adaptation. [computational fluid dynamics
NASA Technical Reports Server (NTRS)
Choo, Yung K.; Eisemann, Peter R.; Lee, Ki D.
1992-01-01
Two approaches have been taken to provide systematic grid manipulation for improved grid quality. One is the control point form (CPF) of algebraic grid generation. It provides explicit control of the physical grid shape and grid spacing through the movement of the control points. It works well in the interactive computer graphics environment and hence can be a good candidate for integration with other emerging technologies. The other approach is grid adaptation using a numerical mapping between the physical space and a parametric space. Grid adaptation is achieved by modifying the mapping functions through the effects of grid control sources. The adaptation process can be repeated in a cyclic manner if satisfactory results are not achieved after a single application.
A Vector Control for Grid-connected Wind Power Generation with Doubly Fed Induction Generator
NASA Astrophysics Data System (ADS)
Kai, Takaaki; Tanaka, Yuji; Kaneda, Hirotoshi; Kobayashi, Daichi; Tanaka, Akio
Recently, doubly fed induction generator (DFIG) and synchronous generator are mostly applied for wind power generation due to high efficiently for wind energy capture. An inverter system is required to control wind turbine speed and power factor in those generators. The inverter rating of the synchronous generator equals to generator rating. However, DFIG has the advantage that the inverter rating is about 25% to the generator rating. The paper describes a vector control of DFIG inter-connected to power line. The performance of proposed vector control is examined using power system simulation software PSCAD/EMTDC for the DFIG inter-connected to 6.6kv distribution line. The results show good dynamic responses and high accuracy to the stator active power control and the stator reactive power control.
NASA Astrophysics Data System (ADS)
Andreeva, Tatiana; Durgin, William
2001-11-01
This paper focuses on ultrasonic measurements of a grid-generated turbulent flow using the travel time technique. In the present work an attempt to describe a turbulent flow by means of statistics of ultrasound wave propagation time is undertaken in combination with Kolmogorov (2/3)-power law. There are two objectives in current research work. The first one is to demonstrate an application of the travel-time ultrasonic technique for data acquisition in the grid-generated turbulence produced in a wind tunnel. The second one is to use the experimental data to verify or refute the analytically obtained expression for travel time dispersion as a function of velocity fluctuation metrics. The theoretical analysis and derivations of that formula are based on Kolmogorov theory. The series of experiment was conducted at different values of wind speeds and distances from the grid giving rise to different values of the dimensional turbulence characteristic coefficient K. Theoretical analysis, based on the experimental data reveals strong dependence of the turbulent characteristic K on the mean wind velocity. Tabulated values of the turbulent characteristic coefficient may be used for further understanding of the effect of turbulence on sound propagation.
Smagglce: Surface Modeling and Grid Generation for Iced Airfoils: Phase 1 Results
NASA Technical Reports Server (NTRS)
Vickerman, Mary B.; Choo, Yung K.; Braun, Donald C.; Baez, Marivell; Gnepp, Steven
1999-01-01
SmaggIce (Surface Modeling and Grid Generation for Iced Airfoils) is a software toolkit used in the process of aerodynamic performance prediction of iced airfoils with grid-based Computational Fluid Dynamics (CFD). It includes tools for data probing, boundary smoothing, domain decomposition, and structured grid generation and refinement. SmaggIce provides the underlying computations to perform these functions, a GUI (Graphical User Interface) to control and interact with those functions, and graphical displays of results, it is being developed at NASA Glenn Research Center. This paper discusses the overall design of SmaggIce as well as what has been implemented in Phase 1. Phase 1 results provide two types of software tools: interactive ice shape probing and interactive ice shape control. The ice shape probing tools will provide aircraft icing engineers and scientists with an interactive means to measure the physical characteristics of ice shapes. On the other hand, the ice shape control features of SmaggIce will allow engineers to examine input geometry data, correct or modify any deficiencies in the geometry, and perform controlled systematic smoothing to a level that will make the CFD process manageable.
Modified Perfect Harmonics Cancellation Control of a Grid Interfaced SPV Power Generation
NASA Astrophysics Data System (ADS)
Singh, B.; Shahani, D. T.; Verma, A. K.
2015-03-01
This paper deals with a grid interfaced solar photo voltaic (SPV) power generating system with modified perfect harmonic cancellation (MPHC) control for power quality improvement in terms of mitigation of the current harmonics, power factor correction, control of point of common coupling (PCC) voltage with reactive power compensation and load balancing in a three phase distribution system. The proposed grid interfaced SPV system consists of a SPV array, a dc-dc boost converter and a voltage source converter (VSC) used for the compensation of other connected linear and nonlinear loads at PCC. The reference grid currents are estimated using MPHC method and control signals are derived by using pulse width modulation (PWM) current controller of VSC. The SPV power is fed to the common dc bus of VSC and dc-dc boost converter using maximum power point tracking (MPPT). The dc link voltage of VSC is regulated by using dc voltage proportional integral (PI) controller. The analysis of the proposed SPV power generating system is carried out under dc/ac short circuit and severe SPV-SX and SPV-TX intrusion.
urthy, S.S.; Jha, C.S. ); Rao, P.S.N. )
1990-03-01
Results of an investigation dealing with the behavior of grid connected induction generators (GCIG) driven by typical prime movers such as mini-hydro/wind turbines are presented. Certain practical operational problems of such systems are identified. Analytical techniques are developed to study the behavior of such systems. The system consists of the induction generator (IG) feeding a 11 kV grid through a step up transformer and a transmission line. Terminal capacitors to compensate for the lagging VAR are included in the study. Computer simulation is carried out to predict the system performance at the given input power from the turbine. Effects of variations in grid voltage, frequency, input power and terminal capacitance on the machine and system performance are studied. Analysis of self excitation conditions on disconnection of supply has been carried out. Behavior of a 200 kW hydel system and 55/11 kW 22 kW wind driven system corresponding to actual field conditions are presented and discussed.
On Dunkl angular momenta algebra
NASA Astrophysics Data System (ADS)
Feigin, Misha; Hakobyan, Tigran
2015-11-01
We consider the quantum angular momentum generators, deformed by means of the Dunkl operators. Together with the reflection operators they generate a subalgebra in the rational Cherednik algebra associated with a finite real reflection group. We find all the defining relations of the algebra, which appear to be quadratic, and we show that the algebra is of Poincaré-Birkhoff-Witt (PBW) type. We show that this algebra contains the angular part of the Calogero-Moser Hamiltonian and that together with constants it generates the centre of the algebra. We also consider the gl( N ) version of the subalge-bra of the rational Cherednik algebra and show that it is a non-homogeneous quadratic algebra of PBW type as well. In this case the central generator can be identified with the usual Calogero-Moser Hamiltonian associated with the Coxeter group in the harmonic confinement.
A Laplacian Equation Method for Numerical Generation of Boundary-Fitted 3D Orthogonal Grids
NASA Astrophysics Data System (ADS)
Theodoropoulos, T.; Bergeles, G. C.
1989-06-01
A sethod for generating boundary fitted orthogonal curvilinear grids in 3-dimensional space is described. The mapping between the curvilinear coordinates and the Cartesian coordinates is provided by a set of Laplace equations which, expressed in curvilinear coordinates, involve the components of the metric tensor and are therefore non-linear and coupled. An iterative algorithm is described, which achieves a numerical solution. Grids appropriate for the calculation of flow fields over complex topography or in complex flow passages as those found in turbomachinery, and for other engineering applications can be constructed using the proposed method. Various examples are presented and plotted in perspective, and data for the assessment of the properties of the resulting meshes is provided.
NASA Astrophysics Data System (ADS)
Kai, Takaaki; Tanaka, Yuji; Kaneda, Hirotoshi; Kobayashi, Daichi; Tanaka, Akio
Recently, doubly fed induction generator (DFIG) and synchronous generator are mostly applied for wind power generation, and variable speed control and power factor control are executed for high efficiently for wind energy capture and high quality for power system voltage. In variable speed control, a wind speed or a generator speed is used for maximum power point tracking. However, performances of a wind generation power fluctuation due to wind speed variation have not yet investigated for those controls. The authors discuss power smoothing by those controls for the DFIG inter-connected to 6.6kV distribution line. The performances are verified using power system simulation software PSCAD/EMTDC for actual wind speed data and are examined from an approximate equation of wind generation power fluctuation for wind speed variation.
NASA Technical Reports Server (NTRS)
Shanmugasundaram, Ramakrishnan; Garriz, Javier A.; Samareh, Jamshid A.
1997-01-01
The grid generation used to model rotorcraft configurations for Computational Fluid Dynamics (CFD) analysis is highly complicated and time consuming. The highly complex geometry and irregular shapes encountered in entire rotorcraft configurations are typically modeled using overset grids. Another promising approach is to utilize unstructured grid methods. With either approach the majority of time is spent manually setting up the topology. For less complicated geometries such as isolated rotor blades, less time is obviously required. This paper discusses the capabilities of a tool called Rotor blade Optimized Topology Organizer and Renderer(ROTOR) being developed to quickly generate block structured grids and unstructured tetrahedral grids about isolated blades. The key algorithm uses individual airfoil sections to construct a Non-Uniform Rational B-Spline(NURBS) surface representation of the rotor blade. This continuous surface definition can be queried to define the block topology used in constructing a structured mesh around the rotor blade. Alternatively, the surface definition can be used to define the surface patches and grid cell spacing requirements for generating unstructured surface and volume grids. Presently, the primary output for ROTOR is block structured grids using 0-H and H-H topologies suitable for full-potential solvers. This paper will discuss the present capabilities of the tool and highlight future work.
Lazarov, R; Pasciak, J; Jones, J
2002-02-01
Construction, analysis and numerical testing of efficient solution techniques for solving elliptic PDEs that allow for parallel implementation have been the focus of the research. A number of discretization and solution methods for solving second order elliptic problems that include mortar and penalty approximations and domain decomposition methods for finite elements and finite volumes have been investigated and analyzed. Techniques for parallel domain decomposition algorithms in the framework of PETC and HYPRE have been studied and tested. Hierarchical parallel grid refinement and adaptive solution methods have been implemented and tested on various model problems. A parallel code implementing the mortar method with algebraically constructed multiplier spaces was developed.
NASA Technical Reports Server (NTRS)
Fujii, K.
1983-01-01
A method for generating three dimensional, finite difference grids about complicated geometries by using Poisson equations is developed. The inhomogenous terms are automatically chosen such that orthogonality and spacing restrictions at the body surface are satisfied. Spherical variables are used to avoid the axis singularity, and an alternating-direction-implicit (ADI) solution scheme is used to accelerate the computations. Computed results are presented that show the capability of the method. Since most of the results presented have been used as grids for flow-field computations, this is indicative that the method is a useful tool for generating three-dimensional grids about complicated geometries.
Analytical Grid Generation for accurate representation of clearances in CFD for Screw Machines
NASA Astrophysics Data System (ADS)
Rane, S.; Kovačević, A.; Stošić, N.
2015-08-01
One of the major factors affecting the performance prediction of twin screw compressors by use of computational fluid dynamics (CFD) is the accuracy with which the leakage gaps are captured by the discretization methods. The accuracy of mapping leakage flows can be improved by increasing the number of grid points on the profile. However, this method faces limitations when it comes to the complex deforming domains of a twin screw compressor because the computational time increases tremendously. In order to address this problem, an analytical grid distribution procedure is formulated that can independently refine the region of high importance for leakage flows in the interlobe space. This paper describes the procedure of analytical grid generation with the refined mesh in the interlobe area and presents a test case to show the influence of the mesh refinement in that area on the performance prediction. It is shown that by using this method, the flow domains in the vicinity of the interlobe gap and the blowhole area are refined which improves accuracy of leakage flow predictions.
Experiments on the motion of gas bubbles in turbulence generated by an active grid
NASA Astrophysics Data System (ADS)
Poorte, R. E. G.; Biesheuvel, A.
2002-06-01
The random motion of nearly spherical bubbles in the turbulent flow behind a grid is studied experimentally. In quiescent water these bubbles rise at high Reynolds number. The turbulence is generated by an active grid of the design of Makita (1991), and can have turbulence Reynolds number R[lambda] of up to 200. Minor changes in the geometry of the grid and in its mode of operation improves the isotropy of the turbulence, compared with that reported by Makita (1991) and Mydlarski & Warhaft (1996). The trajectory of each bubble is measured with high spatial and temporal resolution with a specially developed technique that makes use of a position-sensitive detector. Bubble statistics such as the mean rise velocity and the root-mean-square velocity fluctuations are obtained by ensemble averaging over many identical bubbles. The resulting bubble mean rise velocity is significantly reduced (up to 35%) compared with the quiescent conditions. The vertical bubble velocity fluctuations are found to be non-Gaussian, whereas the horizontal displacements are Gaussian for all times. The diffusivity of bubbles is considerably less than that of fluid particles. These findings are qualitatively consistent with results obtained through theoretical analysis and numerical simulations by Spelt & Biesheuvel (1997).
A Framework for Parallel Unstructured Grid Generation for Complex Aerodynamic Simulations
NASA Technical Reports Server (NTRS)
Zagaris, George; Pirzadeh, Shahyar Z.; Chrisochoides, Nikos
2009-01-01
A framework for parallel unstructured grid generation targeting both shared memory multi-processors and distributed memory architectures is presented. The two fundamental building-blocks of the framework consist of: (1) the Advancing-Partition (AP) method used for domain decomposition and (2) the Advancing Front (AF) method used for mesh generation. Starting from the surface mesh of the computational domain, the AP method is applied recursively to generate a set of sub-domains. Next, the sub-domains are meshed in parallel using the AF method. The recursive nature of domain decomposition naturally maps to a divide-and-conquer algorithm which exhibits inherent parallelism. For the parallel implementation, the Master/Worker pattern is employed to dynamically balance the varying workloads of each task on the set of available CPUs. Performance results by this approach are presented and discussed in detail as well as future work and improvements.
Effect of Contraction on Turbulence and Temperature Fluctuations Generated by a Warm Grid
NASA Technical Reports Server (NTRS)
Mills, Robert R., Jr.; Corrsin, Stanley
1959-01-01
Hot-wire anemometer measurements were made of several statistical properties of approximately homogeneous and isotropic fields of turbulence and temperature fluctuations generated by a warm grid in a uniform airstream sent through a 4-to-1 contraction. These measurements were made both in the contraction and in the axisymmetric domain farther downstream. In addition to confirming the well-known turbulence anisotropy induced by strain, the data show effects on the skewnesses of both longitudinal velocity fluctuation (which has zero skewness in isotropic turbulence) and its derivative. The concomitant anisotropy in the temperature field accelerates the decay of temperature fluctuations.
Mathematical model of an off-grid hybrid solar and wind power generating system
NASA Astrophysics Data System (ADS)
Blasone, M.; Dell'Anno, F.; De Luca, R.; Torre, G.
2014-12-01
The dynamics of an off-grid power generating system, coupled to a storage unit and to household appliances, is described by means of an analytic hydrodynamic analog. Following this analogy, by noticing that the effux rate from a leaking bucket is described, in terms of the liquid content, by Torricelli's formula, we denote as "Torricelli's smart consumer" a user being able to calibrate its energy consumption rate with respect to the energy level in the storage unit as if the hydrodynamic model would strictly apply. Simple solutions to the nonlinear dynamic problem associated to this type of smart consumer are found and generalization to other types of smart consumers are sought.
ERIC Educational Resources Information Center
Aydin, Sinan
2014-01-01
Linear algebra is a basic mathematical subject taught in mathematics and science depar-tments of universities. The teaching and learning of this course has always been difficult. This study aims to contribute to the research in linear algebra education, focusing on linear dependence and independence concepts. This was done by introducing…
Bols, Joris; Taelman, L; De Santis, G; Degroote, J; Verhegghe, B; Segers, P; Vierendeels, J
2016-01-01
The trend towards realistic numerical models of (pathologic) patient-specific vascular structures brings along larger computational domains and more complex geometries, increasing both the computation time and the operator time. Hexahedral grids effectively lower the computational run time and the required computational infrastructure, but at high cost in terms of operator time and minimal cell quality, especially when the computational analyses are targeting complex geometries such as aneurysm necks, severe stenoses and bifurcations. Moreover, such grids generally do not allow local refinements. As an attempt to overcome these limitations, a novel approach to hexahedral meshing is proposed in this paper, which combines the automated generation of multi-block structures with a grid-based method. The robustness of the novel approach is tested on common complex geometries, such as tree-like structures (including trifurcations), stenoses, and aneurysms. Additionally, the performance of the generated grid is assessed using two numerical examples. In the first example, a grid sensitivity analysis is performed for blood flow simulated in an abdominal mouse aorta and compared to tetrahedral grids with a prismatic boundary layer. In the second example, the fluid-structure interaction in a model of an aorta with aortic coarctation is simulated and the effect of local grid refinement is analyzed. PMID:26208183
Ultrasonic technique in determination of grid-generated turbulent flow characteristics
NASA Astrophysics Data System (ADS)
Andreeva, Tatiana A.
The present study utilizes the ultrasonic travel-time technique to diagnose grid-generated turbulence. The statistics of the travel-time variations of ultrasonic wave propagation along a path are used to determine some metrics of the turbulence. The motivation for this work stems from the observation of substantial delta-t variation in ultrasonic measuring devices like flow meters and circulation meters. Typically, averaging can be used to extract mean values from such time series. The corollary is that the fluctuations contain information about the turbulence. Experimental data were obtained for ultrasonic wave propagation downstream of a heated grid in a wind tunnel. Such grid-generated turbulence is well characterized and features a mean flow with superimposed velocity and temperature fluctuations. The ultrasonic path could be perpendicular or oblique to the mean flow direction. Path lengths were of the order of 0.3 m and the transducers were of 100 kHz working frequency. The data acquisition and control system featured a very high-speed analog to digital conversion card that enabled excellent resolution of ultrasonic signals. Experimental data for the travel-time variance were validated using ray acoustic theory along with the Kolmogorov "2/3" law. It is demonstrated that the ultrasonic technique, together with theoretical models, provides a basis for turbulent flow diagnostics. As a result, the structure constant appearing in the Kolmogorov "2/3" law is determined based on the experimental data. The effect of turbulence on acoustic waves, in terms of the travel time, was studied for various mean velocities and for different angular orientations of the acoustic waves with respect to the mean flow. Average travel time in the presence of turbulence was shorter then in the undisturbed media. The effect of the time shift between the travel times in turbulent and undisturbed media is associated with Fermat's principle. The travel time and log-amplitude variance of
Integration of permanent magnet synchronous generator wind turbines into power grid
NASA Astrophysics Data System (ADS)
Abedini, Asghar
The world is seeing an ever-increasing demand for electrical energy. The future growth of electrical power generation needs to be a mix of technologies including fossil fuels, hydro, nuclear, wind, and solar. The federal and state energy agencies have taken several proactive steps to increase the share of renewable energy in the total generated electrical power. In 2005, 11.1% of the total 1060 GW electricity generation capacity was from Renewable Energy Sources (RES) in the US. The power capacity portfolio included 9.2% from hydroelectric, 0.87% from wind, and 0.7% from biomass. Other renewable power capacity included 2.8 GW of geothermal, 0.4 GW of solar thermal, and 0.2 GW of solar PV. Although the share of renewable energy sources is small compared with the total power capacity, they are experiencing a high and steady growth. The US is leading the world in wind energy growth with a 27% increase in 2006 and a projected 26% increase in 2007, according to the American Wind Energy Association (AWEA). The US Department of Energy benchmarked a goal to meet 5% of the nation's energy need by launching the Wind Powering America (WPA) program. Although renewable energy sources have many benefits, their utilization in the electrical grid does not come without cost. The higher penetration of RES has introduced many technical and non-technical challenges, including power quality, reliability, safety and protection, load management, grid interconnections and control, new regulations, and grid operation economics. RES such as wind and PV are also intermittent in nature. The energy from these sources is available as long as there is wind or sunlight. However, these are energies that are abundant in the world and the power generated from these sources is pollution free. Due to high price of foundation of wind farms, employing variable speed wind turbines to maximize the extracted energy from blowing wind is more beneficial. On the other hand, since wind power is intermittent
NASA Technical Reports Server (NTRS)
1998-01-01
Pointwise Inc.'s, Gridgen Software is a system for the generation of 3D (three dimensional) multiple block, structured grids. Gridgen is a visually-oriented, graphics-based interactive code used to decompose a 3D domain into blocks, distribute grid points on curves, initialize and refine grid points on surfaces and initialize volume grid points. Gridgen is available to U.S. citizens and American-owned companies by license.
40 CFR 761.308 - Sample selection by random number generation on any two-dimensional square grid.
Code of Federal Regulations, 2010 CFR
2010-07-01
... 40 Protection of Environment 30 2010-07-01 2010-07-01 false Sample selection by random number generation on any two-dimensional square grid. 761.308 Section 761.308 Protection of Environment... Â§ 761.79(b)(3) § 761.308 Sample selection by random number generation on any two-dimensional...
40 CFR 761.308 - Sample selection by random number generation on any two-dimensional square grid.
Code of Federal Regulations, 2011 CFR
2011-07-01
... 40 Protection of Environment 31 2011-07-01 2011-07-01 false Sample selection by random number generation on any two-dimensional square grid. 761.308 Section 761.308 Protection of Environment... Â§ 761.79(b)(3) § 761.308 Sample selection by random number generation on any two-dimensional...
40 CFR 761.308 - Sample selection by random number generation on any two-dimensional square grid.
Code of Federal Regulations, 2012 CFR
2012-07-01
... 40 Protection of Environment 32 2012-07-01 2012-07-01 false Sample selection by random number generation on any two-dimensional square grid. 761.308 Section 761.308 Protection of Environment... Â§ 761.79(b)(3) § 761.308 Sample selection by random number generation on any two-dimensional...
40 CFR 761.308 - Sample selection by random number generation on any two-dimensional square grid.
Code of Federal Regulations, 2013 CFR
2013-07-01
... 40 Protection of Environment 32 2013-07-01 2013-07-01 false Sample selection by random number generation on any two-dimensional square grid. 761.308 Section 761.308 Protection of Environment... Â§ 761.79(b)(3) § 761.308 Sample selection by random number generation on any two-dimensional...
40 CFR 761.308 - Sample selection by random number generation on any two-dimensional square grid.
Code of Federal Regulations, 2014 CFR
2014-07-01
... 40 Protection of Environment 31 2014-07-01 2014-07-01 false Sample selection by random number generation on any two-dimensional square grid. 761.308 Section 761.308 Protection of Environment... Â§ 761.79(b)(3) § 761.308 Sample selection by random number generation on any two-dimensional...
Ultrasonic Technique in Characterization of the Grid-Generated Turbulent Flow
NASA Astrophysics Data System (ADS)
Andreeva, Tatiana; Durgin, William
2002-11-01
Ultrasonic time-of-flight method using dual transducers is utilized to determine some characteristics of grid-generated turbulent flow produced in a wind tunnel. The ultrasonic flowmeter equation is reconsidered, where the effects of turbulent velocity and sound speed fluctuations are included. The result is an integral equation for the corresponding correlation functions. The influence of temperature inhomogeneous on ultrasonic wave propagation is investigated using a set of experiments with a heated grid. In this paper experimentally measured travel time data are used to solve integral equation analytically in terms of correlation functions of turbulent velocity and sound speed fluctuations, and demonstrate qualitatively and quantitatively effect of turbulence on ultrasound wave propagation. First, the auto-correlation function of the travel time is constructed experimentally and is an integral of the unknown auto-correlation function of turbulent velocity. Such a relationship is known as the 2D Volterra integral equation and can be solved numerically to find the unknown auto-correlation functions of turbulent velocity and sound speed fluctuations. This leads to a new method of finding a spectral density of turbulent velocity from the flowmeter equation.
2013-05-06
AMG2013 is a parallel algebraic multigrid solver for linear systems arising from problems on unstructured grids. It has been derived directly from the Boomer AMG solver in the hypre library, a large linear solvers library that is being developed in the Center for Applied Scientific Computing (CASC) at LLNL. The driver provided in the benchmark can build various test problems. The default problem is a Laplace type problem on an unstructured domain with various jumps and an anisotropy in one part.
GSIMF : a web service based software and database management system for the generation grids.
Wang, N.; Ananthan, B.; Gieraltowski, G.; May, E.; Vaniachine, A.; Tech-X Corp.
2008-01-01
To process the vast amount of data from high energy physics experiments, physicists rely on Computational and Data Grids; yet, the distribution, installation, and updating of a myriad of different versions of different programs over the Grid environment is complicated, time-consuming, and error-prone. Our Grid Software Installation Management Framework (GSIMF) is a set of Grid Services that has been developed for managing versioned and interdependent software applications and file-based databases over the Grid infrastructure. This set of Grid services provide a mechanism to install software packages on distributed Grid computing elements, thus automating the software and database installation management process on behalf of the users. This enables users to remotely install programs and tap into the computing power provided by Grids.
A reflection on grid generation in the 90s: Trends, needs, and influences
Thompson, J.F.
1996-12-31
In a book called Art and Physics: Parallel Visions in Space, Time & Light, I read that Newton made reference to {open_quotes}the glory of geometry{close_quotes}. This book goes on to point out that the development of perspective was a milestone in the history of art, suddenly opening the 2D canvas to the 3D world. In fact, Renaissance parents urged their children to become professional perspectivists because the skill was in such demand. Grid generation has analogously moved computational simulation from squares and circles into the real world. And, although I didn`t suggest the field to my kids, there has been some demand for a few such folks. But our measure of real success is actually in reducing that demand.
NASA Technical Reports Server (NTRS)
Choo, Yung K.; Slater, John W.; Vickerman, Mary B.; VanZante, Judith F.; Wadel, Mary F. (Technical Monitor)
2002-01-01
Issues associated with analysis of 'icing effects' on airfoil and wing performances are discussed, along with accomplishments and efforts to overcome difficulties with ice. Because of infinite variations of ice shapes and their high degree of complexity, computational 'icing effects' studies using available software tools must address many difficulties in geometry acquisition and modeling, grid generation, and flow simulation. The value of each technology component needs to be weighed from the perspective of the entire analysis process, from geometry to flow simulation. Even though CFD codes are yet to be validated for flows over iced airfoils and wings, numerical simulation, when considered together with wind tunnel tests, can provide valuable insights into 'icing effects' and advance our understanding of the relationship between ice characteristics and their effects on performance degradation.
Materials Innovation for Next-Generation T&D Grid Components. Workshop Summary Report
Taylor, Emmanuel; Kramer, Caroline; Marchionini, Brian; Sabouni, Ridah; Cheung, Kerry; Lee, Dominic F
2015-10-01
The Materials Innovations for Next-Generation T&D Grid Components Workshop was co-sponsored by the U.S. Department of Energy (DOE) Office of Electricity Delivery and Energy Reliability and the Oak Ridge National Laboratory (ORNL) and held on August 26 27, 2015, at the ORNL campus in Oak Ridge, Tennessee. The workshop was planned and executed under the direction of workshop co-chair Dr. Kerry Cheung (DOE) and co-chair Dr. Dominic Lee (ORNL). The information contained herein is based on the results of the workshop, which was attended by nearly 50 experts from government, industry, and academia. The research needs and pathways described in this report reflect the expert opinions of workshop participants, but they are not intended to represent the views of the entire electric power community.
Cartographic Production for the FLaSH Map Study: Generation of Rugosity Grids, 2008
Robbins, Lisa L.; Knorr, Paul O.; Hansen, Mark
2010-01-01
Project Summary This series of raster data is a U.S. Geological Survey (USGS) Data Series release from the Florida Shelf Habitat Project (FLaSH). This disc contains two raster images in Environmental Systems Research Institute, Inc. (ESRI) raster grid format, jpeg image format, and Geo-referenced Tagged Image File Format (GeoTIFF). Data is also provided in non-image ASCII format. Rugosity grids at two resolutions (250 m and 1000 m) were generated for West Florida shelf waters to 250 m using a custom algorithm that follows the methods of Valentine and others (2004). The Methods portion of this document describes the specific steps used to generate the raster images. Rugosity, also referred to as roughness, ruggedness, or the surface-area ratio (Riley and others, 1999; Wilson and others, 2007), is a visual and quantitative measurement of terrain complexity, a common variable in ecological habitat studies. The rugosity of an area can affect biota by influencing habitat, providing shelter from elements, determining the quantity and type of living space, influencing the type and quantity of flora, affecting predator-prey relationships by providing cover and concealment, and, as an expression of vertical relief, can influence local environmental conditions such as temperature and moisture. In the marine environment rugosity can furthermore influence current flow rate and direction, increase the residence time of water in an area through eddying and current deflection, influence local water conditions such as chemistry, turbidity, and temperature, and influence the rate and nature of sedimentary deposition. State-of-the-art computer-mapping techniques and data-processing tools were used to develop shelf-wide raster and vector data layers. Florida Shelf Habitat (FLaSH) Mapping Project (http://coastal.er.usgs.gov/flash) endeavors to locate available data, identify data gaps, synthesize existing information, and expand our understanding of geologic processes in our dynamic
NASA Astrophysics Data System (ADS)
Szabó, S.; Bódis, K.; Huld, T.; Moner-Girona, M.
2011-07-01
Three rural electrification options are analysed showing the cost optimal conditions for a sustainable energy development applying renewable energy sources in Africa. A spatial electricity cost model has been designed to point out whether diesel generators, photovoltaic systems or extension of the grid are the least-cost option in off-grid areas. The resulting mapping application offers support to decide in which regions the communities could be electrified either within the grid or in an isolated mini-grid. Donor programs and National Rural Electrification Agencies (or equivalent governmental departments) could use this type of delineation for their program boundaries and then could use the local optimization tools adapted to the prevailing parameters. The views expressed in this paper are those of the authors and do not necessarily represent European Commission and UNEP policy.
Marquette, Ian
2013-07-15
We introduce the most general quartic Poisson algebra generated by a second and a fourth order integral of motion of a 2D superintegrable classical system. We obtain the corresponding quartic (associative) algebra for the quantum analog, extend Daskaloyannis construction obtained in context of quadratic algebras, and also obtain the realizations as deformed oscillator algebras for this quartic algebra. We obtain the Casimir operator and discuss how these realizations allow to obtain the finite-dimensional unitary irreducible representations of quartic algebras and obtain algebraically the degenerate energy spectrum of superintegrable systems. We apply the construction and the formula obtained for the structure function on a superintegrable system related to type I Laguerre exceptional orthogonal polynomials introduced recently.
2012-03-16
GENI Project: The CRA team is developing control technology to help grid operators more actively manage power flows and integrate renewables by optimally turning on and off entire power lines in coordination with traditional control of generation and load resources. The control technology being developed would provide grid operators with tools to help manage transmission congestion by identifying the facilities whose on/off status must change to lower generation costs, increase utilization of renewable resources and improve system reliability. The technology is based on fast optimization algorithms for the near to real-time change in the on/off status of transmission facilities and their software implementation.
Software for Refining or Coarsening Computational Grids
NASA Technical Reports Server (NTRS)
Daines, Russell; Woods, Jody
2002-01-01
A computer program performs calculations for refinement or coarsening of computational grids of the type called "structured" (signifying that they are geometrically regular and/or are specified by relatively simple algebraic expressions). This program is designed to facilitate analysis of the numerical effects of changing structured grids utilized in computational fluid dynamics (CFD) software. Unlike prior grid-refinement and -coarsening programs, this program is not limited to doubling or halving: the user can specify any refinement or coarsening ratio, which can have a noninteger value. In addition to this ratio, the program accepts, as input, a grid file and the associated restart file, which is basically a file containing the most recent iteration of flow-field variables computed on the grid. The program then refines or coarsens the grid as specified, while maintaining the geometry and the stretching characteristics of the original grid. The program can interpolate from the input restart file to create a restart file for the refined or coarsened grid. The program provides a graphical user interface that facilitates the entry of input data for the grid-generation and restart-interpolation routines.
Software for Refining or Coarsening Computational Grids
NASA Technical Reports Server (NTRS)
Daines, Russell; Woods, Jody
2003-01-01
A computer program performs calculations for refinement or coarsening of computational grids of the type called structured (signifying that they are geometrically regular and/or are specified by relatively simple algebraic expressions). This program is designed to facilitate analysis of the numerical effects of changing structured grids utilized in computational fluid dynamics (CFD) software. Unlike prior grid-refinement and -coarsening programs, this program is not limited to doubling or halving: the user can specify any refinement or coarsening ratio, which can have a noninteger value. In addition to this ratio, the program accepts, as input, a grid file and the associated restart file, which is basically a file containing the most recent iteration of flow-field variables computed on the grid. The program then refines or coarsens the grid as specified, while maintaining the geometry and the stretching characteristics of the original grid. The program can interpolate from the input restart file to create a restart file for the refined or coarsened grid. The program provides a graphical user interface that facilitates the entry of input data for the grid-generation and restart-interpolation routines.
Optimal Dispatch of Unreliable Electric Grid-Connected Diesel Generator-Battery Power Systems
NASA Astrophysics Data System (ADS)
Xu, D.; Kang, L.
2015-06-01
Diesel generator (DG)-battery power systems are often adopted by telecom operators, especially in semi-urban and rural areas of developing countries. Unreliable electric grids (UEG), which have frequent and lengthy outages, are peculiar to these regions. DG-UEG-battery power system is an important kind of hybrid power system. System dispatch is one of the key factors to hybrid power system integration. In this paper, the system dispatch of a DG-UEG-lead acid battery power system is studied with the UEG of relatively ample electricity in Central African Republic (CAR) and UEG of poor electricity in Congo Republic (CR). The mathematical models of the power system and the UEG are studied for completing the system operation simulation program. The net present cost (NPC) of the power system is the main evaluation index. The state of charge (SOC) set points and battery bank charging current are the optimization variables. For the UEG in CAR, the optimal dispatch solution is SOC start and stop points 0.4 and 0.5 that belong to the Micro-Cycling strategy and charging current 0.1 C. For the UEG in CR, the optimal dispatch solution is of 0.1 and 0.8 that belongs to the Cycle-Charging strategy and 0.1 C. Charging current 0.1 C is suitable for both grid scenarios compared to 0.2 C. It makes the dispatch strategy design easier in commercial practices that there are a few very good candidate dispatch solutions with system NPC values close to that of the optimal solution for both UEG scenarios in CAR and CR.
ERIC Educational Resources Information Center
Schaufele, Christopher; Zumoff, Nancy
Earth Algebra is an entry level college algebra course that incorporates the spirit of the National Council of Teachers of Mathematics (NCTM) Curriculum and Evaluation Standards for School Mathematics at the college level. The context of the course places mathematics at the center of one of the major current concerns of the world. Through…
ERIC Educational Resources Information Center
Cavanagh, Sean
2009-01-01
As educators and policymakers search for ways to prepare students for the rigors of algebra, teachers in the Helena, Montana, school system are starting early by attempting to nurture students' algebraic-reasoning ability, as well as their basic number skills, in early elementary school, rather than waiting until middle or early high school.…
Empirical Analysis of the Variability of Wind Generation in India: Implications for Grid Integration
Phadke, Amol; Abhyankar, NIkit; Rao, Poorvi
2014-06-17
We analyze variability in load and wind generation in India to assess its implications for grid integration of large scale wind projects using actual wind generation and load data from two states in India, Karnataka and Tamil Nadu. We compare the largest variations in load and net load (load ?wind, i.e., load after integrating wind) that the generation fleet has to meet. In Tamil Nadu, where wind capacity is about 53percent of the peak demand, we find that the additional variation added due to wind over the current variation in load is modest; if wind penetration reaches 15percent and 30percent by energy, the additional hourly variation is less than 0.5percent and 4.5percent of the peak demand respectively for 99percent of the time. For wind penetration of 15percent by energy, Tamil Nadu system is found to be capable of meeting the additional ramping requirement for 98.8percent of the time. Potential higher uncertainty in net load compared to load is found to have limited impact on ramping capability requirements of the system if coal plants can me ramped down to 50percent of their capacity. Load and wind aggregation in Tamil Nadu and Karnataka is found to lower the variation by at least 20percent indicating the benefits geographic diversification. These findings suggest modest additional flexible capacity requirements and costs for absorbing variation in wind power and indicate that the potential capacity support (if wind does not generate enough during peak periods) may be the issue that has more bearing on the economics of integrating wind
GRIDGEN Version 1.0: a computer program for generating unstructured finite-volume grids
Lien, Jyh-Ming; Liu, Gaisheng; Langevin, Christian D.
2015-01-01
GRIDGEN is a computer program for creating layered quadtree grids for use with numerical models, such as the MODFLOW–USG program for simulation of groundwater flow. The program begins by reading a three-dimensional base grid, which can have variable row and column widths and spatially variable cell top and bottom elevations. From this base grid, GRIDGEN will continuously divide into four any cell intersecting user-provided refinement features (points, lines, and polygons) until the desired level of refinement is reached. GRIDGEN will then smooth, or balance, the grid so that no two adjacent cells, including overlying and underlying cells, differ by more than a user-specified level tolerance. Once these gridding processes are completed, GRIDGEN saves a tree structure file so that the layered quadtree grid can be quickly reconstructed as needed. Once a tree structure file has been created, GRIDGEN can then be used to (1) export the layered quadtree grid as a shapefile, (2) export grid connectivity and cell information as ASCII text files for use with MODFLOW–USG or other numerical models, and (3) intersect the grid with shapefiles of points, lines, or polygons, and save intersection output as ASCII text files and shapefiles. The GRIDGEN program is demonstrated by creating a layered quadtree grid for the Biscayne aquifer in Miami-Dade County, Florida, using hydrologic features to control where refinement is added.
OTAHAL,THOMAS J.; GALLIS,MICHAIL A.; BARTEL,TIMOTHY J.
2000-06-27
This paper presents an investigation of a technique for using two-dimensional bodies composed of simple polygons with a body decoupled uniform Cmtesian grid in the Direct Simulation Monte Carlo method (DSMC). The method employs an automated grid pre-processing scheme beginning form a CAD geometry definition file, and is based on polygon triangulation using a trapezoid algorithm. A particle-body intersection time comparison is presented between the Icarus DSMC code using a body-fitted structured grid and using a structured body-decoupled Cartesian grid with both linear and logarithmic search techniques. A comparison of neutral flow over a cylinder is presented using the structured body fitted grid and the Cartesian body de-coupled grid.
Grid Sensitivity and Aerodynamic Optimization of Generic Airfoils
NASA Technical Reports Server (NTRS)
Sadrehaghighi, Ideen; Smith, Robert E.; Tiwari, Surendra N.
1995-01-01
An algorithm is developed to obtain the grid sensitivity with respect to design parameters for aerodynamic optimization. The procedure is advocating a novel (geometrical) parameterization using spline functions such as NURBS (Non-Uniform Rational B- Splines) for defining the airfoil geometry. An interactive algebraic grid generation technique is employed to generate C-type grids around airfoils. The grid sensitivity of the domain with respect to geometric design parameters has been obtained by direct differentiation of the grid equations. A hybrid approach is proposed for more geometrically complex configurations such as a wing or fuselage. The aerodynamic sensitivity coefficients are obtained by direct differentiation of the compressible two-dimensional thin-layer Navier-Stokes equations. An optimization package has been introduced into the algorithm in order to optimize the airfoil surface. Results demonstrate a substantially improved design due to maximized lift/drag ratio of the airfoil.
Manonmani, N.; Subbiah, V.; Sivakumar, L.
2015-01-01
The key objective of wind turbine development is to ensure that output power is continuously increased. It is authenticated that wind turbines (WTs) supply the necessary reactive power to the grid at the time of fault and after fault to aid the flowing grid voltage. At this juncture, this paper introduces a novel heuristic based controller module employing differential evolution and neural network architecture to improve the low-voltage ride-through rate of grid-connected wind turbines, which are connected along with doubly fed induction generators (DFIGs). The traditional crowbar-based systems were basically applied to secure the rotor-side converter during the occurrence of grid faults. This traditional controller is found not to satisfy the desired requirement, since DFIG during the connection of crowbar acts like a squirrel cage module and absorbs the reactive power from the grid. This limitation is taken care of in this paper by introducing heuristic controllers that remove the usage of crowbar and ensure that wind turbines supply necessary reactive power to the grid during faults. The controller is designed in this paper to enhance the DFIG converter during the grid fault and this controller takes care of the ride-through fault without employing any other hardware modules. The paper introduces a double wavelet neural network controller which is appropriately tuned employing differential evolution. To validate the proposed controller module, a case study of wind farm with 1.5 MW wind turbines connected to a 25 kV distribution system exporting power to a 120 kV grid through a 30 km 25 kV feeder is carried out by simulation. PMID:26516636
Manonmani, N; Subbiah, V; Sivakumar, L
2015-01-01
The key objective of wind turbine development is to ensure that output power is continuously increased. It is authenticated that wind turbines (WTs) supply the necessary reactive power to the grid at the time of fault and after fault to aid the flowing grid voltage. At this juncture, this paper introduces a novel heuristic based controller module employing differential evolution and neural network architecture to improve the low-voltage ride-through rate of grid-connected wind turbines, which are connected along with doubly fed induction generators (DFIGs). The traditional crowbar-based systems were basically applied to secure the rotor-side converter during the occurrence of grid faults. This traditional controller is found not to satisfy the desired requirement, since DFIG during the connection of crowbar acts like a squirrel cage module and absorbs the reactive power from the grid. This limitation is taken care of in this paper by introducing heuristic controllers that remove the usage of crowbar and ensure that wind turbines supply necessary reactive power to the grid during faults. The controller is designed in this paper to enhance the DFIG converter during the grid fault and this controller takes care of the ride-through fault without employing any other hardware modules. The paper introduces a double wavelet neural network controller which is appropriately tuned employing differential evolution. To validate the proposed controller module, a case study of wind farm with 1.5 MW wind turbines connected to a 25 kV distribution system exporting power to a 120 kV grid through a 30 km 25 kV feeder is carried out by simulation. PMID:26516636
Hecke-Clifford Algebras and Spin Hecke Algebras IV: Odd Double Affine Type
NASA Astrophysics Data System (ADS)
Khongsap, Ta; Wang, Weiqiang
2009-01-01
We introduce an odd double affine Hecke algebra (DaHa) generated by a classical Weyl group W and two skew-polynomial subalgebras of anticommuting generators. This algebra is shown to be Morita equivalent to another new DaHa which are generated by W and two polynomial-Clifford subalgebras. There is yet a third algebra containing a spin Weyl group algebra which is Morita (super)equivalent to the above two algebras. We establish the PBW properties and construct Verma-type representations via Dunkl operators for these algebras.
a Hadoop-Based Algorithm of Generating dem Grid from Point Cloud Data
NASA Astrophysics Data System (ADS)
Jian, X.; Xiao, X.; Chengfang, H.; Zhizhong, Z.; Zhaohui, W.; Dengzhong, Z.
2015-04-01
Airborne LiDAR technology has proven to be the most powerful tools to obtain high-density, high-accuracy and significantly detailed surface information of terrain and surface objects within a short time, and from which the Digital Elevation Model of high quality can be extracted. Point cloud data generated from the pre-processed data should be classified by segmentation algorithms, so as to differ the terrain points from disorganized points, then followed by a procedure of interpolating the selected points to turn points into DEM data. The whole procedure takes a long time and huge computing resource due to high-density, that is concentrated on by a number of researches. Hadoop is a distributed system infrastructure developed by the Apache Foundation, which contains a highly fault-tolerant distributed file system (HDFS) with high transmission rate and a parallel programming model (Map/Reduce). Such a framework is appropriate for DEM generation algorithms to improve efficiency. Point cloud data of Dongting Lake acquired by Riegl LMS-Q680i laser scanner was utilized as the original data to generate DEM by a Hadoop-based algorithms implemented in Linux, then followed by another traditional procedure programmed by C++ as the comparative experiment. Then the algorithm's efficiency, coding complexity, and performance-cost ratio were discussed for the comparison. The results demonstrate that the algorithm's speed depends on size of point set and density of DEM grid, and the non-Hadoop implementation can achieve a high performance when memory is big enough, but the multiple Hadoop implementation can achieve a higher performance-cost ratio, while point set is of vast quantities on the other hand.
The weak Hopf algebras related to generalized Kac-Moody algebra
Wu Zhixiang
2006-06-15
We define a kind of quantized enveloping algebra of a generalized Kac-Moody algebra G by adding a generator J satisfying J{sup m}=J{sup m-1} for some integer m. We denote this algebra by wU{sub q}{sup {tau}}(G). This algebra is a weak Hopf algebra if and only if m=2. In general, it is a bialgebra, and contains a Hopf subalgebra. This Hopf subalgebra is isomorphic to the usually quantum envelope algebra U{sub q}(G) of a generalized Kac-Moody algebra G.
Robinett, Rush D., III; Kukolich, Keith; Wilson, David Gerald; Schenkman, Benjamin L.
2010-06-01
This paper discusses the modeling, analysis, and testing in a real-time simulation environment of the Lanai power grid system for the integration and control of PhotoVoltaic (PV) distributed generation. The Lanai Island in Hawaii is part of the Hawaii Clean Energy Initiative (HCEI) to transition to 30% renewable green energy penetration by 2030. In Lanai the primary loads come from two Castle and Cook Resorts, in addition to residential needs. The total peak load profile is 12470 V, 5.5 MW. Currently there are several diesel generators that meet these loading requirements. As part of the HCEI, Lanai has initially installed 1.2 MW of PV generation. The goal of this study has been to evaluate the impact of the PV with respect to the conventional carbon-based diesel generation in real time simulation. For intermittent PV distributed generation, the overall stability and transient responses are investigated. A simple Lanai 'like' model has been developed in the Matlab/Simulink environment (see Fig. 1) and to accommodate real-time simulation of the hybrid power grid system the Opal-RT Technologies RT-Lab environment is used. The diesel generators have been modelled using the SimPowerSystems toolbox swing equations and a custom Simulink module has been developed for the High level PV generation. All of the loads have been characterized primarily as distribution lines with series resistive load banks with one VAR load bank. Three-phase faults are implemented for each bus. Both conventional and advanced control architectures will be used to evaluate the integration of the PV onto the current power grid system. The baseline numerical results include the stable performance of the power grid during varying cloud cover (PV generation ramping up/down) scenarios. The importance of assessing the real-time scenario is included.
NASA Technical Reports Server (NTRS)
Middlecoff, J. F.; Thomas, P. D.
1979-01-01
The generation of computational grids suitable for obtaining accurate numerical solutions to the three-dimensional Navier-Stokes equations is the subject of intensive research. For a wide class of nozzle configurations, a three-dimensional grid can be constructed by a sequence of two-dimensional grids in successive cross-sectional planes. The present paper is concerned with numerical generation of two-dimensional grids. An effective method of interior grid control is presented based on a modified elliptic system containing free parameters. For a simply connected region, the free parameters are computed from the Dirichlet boundary values. The resulting interior grid point distribution is controlled entirely by a priori selection of the grid point distribution along the boundaries of the section.
Bischof, C.H.; Mauer, A.; Jones, W.T.
1995-12-31
Automatic differentiation (AD) is a methodology for developing reliable sensitivity-enhanced versions of arbitrary computer programs with little human effort. It can vastly accelerate the use of advanced simulation codes in multidisciplinary design optimization, since the time for generating and verifying derivative codes is greatly reduced. In this paper, we report on the application of the recently developed ADIC automatic differentiation tool for ANSI C programs to the CSCMDO multiblock three-dimensional volume grid generator. The ADIC-generated code can easily be interfaced with Fortran derivative codes generated with the ADIFOR AD tool FORTRAN 77 programs, thus providing efficient sensitivity-enhancement techniques for multilanguage, multidiscipline problems.
The fluid dynamic approach to equidistribution methods for grid generation and adaptation
Delzanno, Gian Luca; Finn, John M
2009-01-01
The equidistribution methods based on L{sub p} Monge-Kantorovich optimization [Finn and Delzanno, submitted to SISC, 2009] and on the deformation [Moser, 1965; Dacorogna and Moser, 1990, Liao and Anderson, 1992] method are analyzed primarily in the context of grid generation. It is shown that the first class of methods can be obtained from a fluid dynamic formulation based on time-dependent equations for the mass density and the momentum density, arising from a variational principle. In this context, deformation methods arise from a fluid formulation by making a specific assumption on the time evolution of the density (but with some degree of freedom for the momentum density). In general, deformation methods do not arise from a variational principle. However, it is possible to prescribe an optimal deformation method, related to L{sub 1} Monge-Kantorovich optimization, by making a further assumption on the momentum density. Some applications of the L{sub p} fluid dynamic formulation to imaging are also explored.
Invertible linear transformations and the Lie algebras
NASA Astrophysics Data System (ADS)
Zhang, Yufeng; Tam, Honwah; Guo, Fukui
2008-07-01
With the help of invertible linear transformations and the known Lie algebras, a way to generate new Lie algebras is given. These Lie algebras obtained have a common feature, i.e. integrable couplings of solitary hierarchies could be obtained by using them, specially, the Hamiltonian structures of them could be worked out. Some ways to construct the loop algebras of the Lie algebras are presented. It follows that some various loop algebras are given. In addition, a few new Lie algebras are explicitly constructed in terms of the classification of Lie algebras proposed by Ma Wen-Xiu, which are bases for obtaining new Lie algebras by using invertible linear transformations. Finally, some solutions of a (2 + 1)-dimensional partial-differential equation hierarchy are obtained, whose Hamiltonian form-expressions are manifested by using the quadratic-form identity.
Verburgt, Lukas M
2016-01-01
This paper provides a detailed account of the period of the complex history of British algebra and geometry between the publication of George Peacock's Treatise on Algebra in 1830 and William Rowan Hamilton's paper on quaternions of 1843. During these years, Duncan Farquharson Gregory and William Walton published several contributions on 'algebraical geometry' and 'geometrical algebra' in the Cambridge Mathematical Journal. These contributions enabled them not only to generalize Peacock's symbolical algebra on the basis of geometrical considerations, but also to initiate the attempts to question the status of Euclidean space as the arbiter of valid geometrical interpretations. At the same time, Gregory and Walton were bound by the limits of symbolical algebra that they themselves made explicit; their work was not and could not be the 'abstract algebra' and 'abstract geometry' of figures such as Hamilton and Cayley. The central argument of the paper is that an understanding of the contributions to 'algebraical geometry' and 'geometrical algebra' of the second generation of 'scientific' symbolical algebraists is essential for a satisfactory explanation of the radical transition from symbolical to abstract algebra that took place in British mathematics in the 1830s-1840s. PMID:26806075
A multiblock grid generation technique applied to a jet engine configuration
NASA Technical Reports Server (NTRS)
Stewart, Mark E. M.
1992-01-01
Techniques are presented for quickly finding a multiblock grid for a 2D geometrically complex domain from geometrical boundary data. An automated technique for determining a block decomposition of the domain is explained. Techniques for representing this domain decomposition and transforming it are also presented. Further, a linear optimization method may be used to solve the equations which determine grid dimensions within the block decomposition. These algorithms automate many stages in the domain decomposition and grid formation process and limit the need for human intervention and inputs. They are demonstrated for the meridional or throughflow geometry of a bladed jet engine configuration.
Three-dimensional grid generation method based on a variational principle
NASA Astrophysics Data System (ADS)
Jacquotte, O.-P.; Cabello, J.
This paper reviews the main stages of construction of a variational method to optimize and adapt two- and three-dimensional grids. A measure of the cell deformation can be built on the basis of geometric axioms. The grid is optimized with respect to a global measure of the mesh quality obtained by summation of the elementary contributions. A convexity property is also prescribed that ensures the optimization problem is correctly stated, and that the solver is efficient. Mechanical and geometric interpretations of the method are given. In particular, a volume control term can be used to adapt grids according to a given criterion. Several examples of optimized and adapted grids are presented, to show the method's possibilities.
Surface Modeling and Grid Generation for Iced Airfoils (SmaggIce)
NASA Technical Reports Server (NTRS)
Hammond, Brandy M.
2004-01-01
Many of the troubles associated with problem solving are alleviated when there is a model that can be used to represent the problem. Through the Advanced Graphics and Visualization (G-VIS) Laboratory and other facilities located within the Research Analysis Center, the Computer Services Division (CSD) is able to develop and maintain programs and software that allow for the modeling of various situations. For example, the Icing Research Branch is devoted to investigating the effect of ice that forms on the wings and other airfoils of airplanes while in flight. While running tests that physically generate ice and wind on airfoils within the laboratories and wind tunnels on site are done, it would be beneficial if most of the preliminary work could be done outside of the lab. Therefore, individuals from within CSD have collaborated with Icing Research in order to create SmaggIce. This software allows users to create ice patterns on clean airfoils or open files containing a variety of icing situations, manipulate and measure these forms, generate, divide, and merge grids around these elements for more explicit analysis, and specify and rediscretize subcurves. With the projected completion date of Summer 2005, the majority of the focus of the Smagglce team is user-functionality and error handling. My primary responsibility is to test the Graphical User Interface (GUI) in SmaggIce in order to ensure the usability and verify the expected results of the events (buttons, menus, etc.) within the program. However, there is no standardized, systematic way in which to test all the possible combinations or permutations of events, not to mention unsolicited events such as errors. Moreover, scripting tests, if not done properly and with a view towards inevitable revision, can result in more apparent errors within the software and in effect become useless whenever the developers of the program make a slight change in the way a specific process is executed. My task therefore
Micro-grid for on-site wind-and-hydrogen powered generation
NASA Astrophysics Data System (ADS)
Suskis, P.; Andreiciks, A.; Steiks, I.; Krievs, O.; Kleperis, J.
2014-02-01
The authors propose a micro-grid for autonomous wind-and-hydrogen power generation thus replacing such traditional fossil-fuelled equipment as domestic diesel generators, gas micro-turbines, etc. In the proposed microgrid the excess of electrical energy from a wind turbine is spent on electrolytic production of hydrogen which is then stored under low-pressure in absorbing composite material. The electrolyser has a non-traditional feeding unit and electrode coatings. The proposed DC/DC conversion topologies for different micro-grid nodes are shown to be well-designed. The prototypes elaborated for the converters and hydrogen storage media were tested and have demonstrated a good performance. Rakstā piedāvātā mikrotīkla izpēte ir veikta ar mērķi izstrādāt autonomu, uz vēja un ūdeņraža enerģiju balstītu elektroapgādes sistēmu, kas varētu aizvietot tradicionālās fosilā kurināmā sistēmas, piemēram, mājsaimniecību dīzeļa ģeneratorus, gāzes mikroturbīnas u.c. Mikrotīkla elektroapgādes sistēmā vēja agregāta saražotā elektroenerģija tiek pārveidota atbilstoši standarta maiņsprieguma elektroapgādes parametriem un piegādāta slodzei. Pārpalikusī enerģija tiek pārveidota un uzkrāta ūdeņraža formā, izmantojot elektrolīzes iekārtu un kompozītmateriālu uzkrājēju. Ja pieejamā vēja enerģija nenosedz slodzes enerģijas patēriņu, elektroenerģijas padeves funkciju ar atbilstoša energoelektronikas pārveidotāja palīdzību pārņem ūdeņraža degvielas elements. Ja, savukārt, slodzei nav nepieciešama enerģija, no vēja saražoto enerģiju izmanto elektrolīzes iekārta un tā tiek uzkrāta ūdeņraža formā, atbilstoši uzkrājēja ietilpībai. Piedāvātajā mikrotīklā ir izmantota elektrolīzes iekārta ar netradicionāliem elektrodu pārklājumiem un barošanas bloku, kā arī zemspiediena kompozītmateriālu ūdeņraža uzkrājējs. Galvenie mikrotīkla elektriskās enerģijas pārveidošanas mezgli ir
2013-05-06
AMG2013 is a parallel algebraic multigrid solver for linear systems arising from problems on unstructured grids. It has been derived directly from the Boomer AMG solver in the hypre library, a large linear solvers library that is being developed in the Center for Applied Scientific Computing (CASC) at LLNL. The driver provided in the benchmark can build various test problems. The default problem is a Laplace type problem on an unstructured domain with various jumpsmore » and an anisotropy in one part.« less
NASA Technical Reports Server (NTRS)
Olynick, David P.; Hassan, H. A.; Moss, James N.
1988-01-01
A grid generation and adaptation procedure based on the method of transfinite interpolation is incorporated into the Direct Simulation Monte Carlo Method of Bird. In addition, time is advanced based on a local criterion. The resulting procedure is used to calculate steady flows past wedges and cones. Five chemical species are considered. In general, the modifications result in a reduced computational effort. Moreover, preliminary results suggest that the simulation method is time step dependent if requirements on cell sizes are not met.
NASA Astrophysics Data System (ADS)
Iga, Shin-ichi
2015-09-01
A generation method for smooth, seamless, and structured triangular grids on a sphere with flexibility in resolution distribution is proposed. This method is applicable to many fields that deal with a sphere on which the required resolution is not uniform. The grids were generated using the spring dynamics method, and adjustments were made using analytical functions. The mesh topology determined its resolution distribution, derived from a combination of conformal mapping factors: polar stereographic projection (PSP), Lambert conformal conic projection (LCCP), and Mercator projection (MP). Their combination generated, for example, a tropically fine grid that had a nearly constant high-resolution belt around the equator, with a gradual decrease in resolution distribution outside of the belt. This grid can be applied to boundary-less simulations of tropical meteorology. The other example involves a regionally fine grid with a nearly constant high-resolution circular region and a gradually decreasing resolution distribution outside of the region. This is applicable to regional atmospheric simulations without grid nesting. The proposed grids are compatible with computer architecture because they possess a structured form. Each triangle of the proposed grids was highly regular, implying a high local isotropy in resolution. Finally, the proposed grids were examined by advection and shallow water simulations.
Manipulation of a grid-generated mixing with an active honeycomb dielectric barrier plasma discharge
NASA Astrophysics Data System (ADS)
Benard, N.; Mizuno, A.; Moreau, E.
2015-12-01
This study defines and characterizes an active system for turbulent and scalar mixing enhancement. This system is made of an active grid composed of 121 holes where the gas flows. A high voltage is applied between printed electrodes and embedded ground electrodes in order to produce a non-thermal surface discharge at the hole exits. The goal is to modify the flow downstream of the active grid. First, electrical and optical characterizations of the actuator are proposed. Second, it is shown that the discharge strongly modifies the flow distribution of the multi-jet exhaust, and the flow change depends on the high voltage applied to the active plasma grid. A minimization of the potential core by 40% is reported when discharge frequency corresponds to jet column mode instability.
MSTB 2 x 6-Inch Low Speed Tunnel Turbulence Generator Grid/Honeycomb PIV Measurements and Analysis
NASA Technical Reports Server (NTRS)
Blackshire, James L.
1997-01-01
An assessment of the turbulence levels present in the Measurement Science and Technology (MSTB) branch's 2 x 6-inch low speed wind tunnel was made using Particle Image Velocimetry (PIV), and a turbulence generator consisting of a grid/honeycomb structure. Approximately 3000 digital PIV images were captured and analyzed covering an approximate 2 x 6-inch area along the centerline of the tunnel just beyond the turbulence generator system. Custom software for analysis and acquisition was developed for semi-automated digital PIV image acquisition and analysis. Comparisons between previously obtained LTA and LV turbulence measurements taken in the tunnel are presented.
Terasaka, K; Yoshimura, S; Kato, Y; Furuta, K; Aramaki, M; Morisaki, T; Tanaka, M Y
2014-11-01
High-impedance Wire Grid (HIWG) detector has been developed to study spatiotemporal behavior of a hot electron clump generated in an electron cyclotron resonance (ECR) plasma. By measuring the floating potentials of the wire electrodes, and generating structure matrix made of geometrical means of the floating potentials, the HIWG detector reconstructs the spatial distribution of high-temperature electron clump at an arbitrary instant of time. Time slices of the spike event in floating potential revealed the growth and decay process of a hot spot occurs in an ECR plasma. PMID:25430112
Terasaka, K. Kato, Y.; Tanaka, M. Y.; Yoshimura, S.; Morisaki, T.; Furuta, K.; Aramaki, M.
2014-11-15
High-impedance Wire Grid (HIWG) detector has been developed to study spatiotemporal behavior of a hot electron clump generated in an electron cyclotron resonance (ECR) plasma. By measuring the floating potentials of the wire electrodes, and generating structure matrix made of geometrical means of the floating potentials, the HIWG detector reconstructs the spatial distribution of high-temperature electron clump at an arbitrary instant of time. Time slices of the spike event in floating potential revealed the growth and decay process of a hot spot occurs in an ECR plasma.
Dynamics of local grid manipulations for internal flow problems
NASA Technical Reports Server (NTRS)
Eiseman, Peter R.; Snyder, Aaron; Choo, Yung K.
1991-01-01
The control point method of algebraic grid generation is briefly reviewed. The review proceeds from the general statement of the method in 2-D unencumbered by detailed mathematical formulation. The method is supported by an introspective discussion which provides the basis for confidence in the approach. The more complex 3-D formulation is then presented as a natural generalization. Application of the method is carried out through 2-D examples which demonstrate the technique.
NREL Controllable Grid Interface for Testing MW-Scale Wind Turbine Generators (Poster)
McDade, M.; Gevorgian, V.; Wallen, R.; Erdman, W.
2013-04-01
In order to understand the behavior of wind turbines experiencing grid disturbances, it is necessary to perform a series of tests and accurate transient simulation studies. The latest edition of the IEC 61400-21 standard describes methods for such tests that include low voltage ride-through (LVRT), active power set-point control, ramp rate limitations, and reactive power capability tests. The IEC methods are being widely adopted on both national and international levels by wind turbine manufacturers, certification authorities, and utilities. On-site testing of wind turbines might be expensive and time consuming since it requires both test equipment transportation and personnel presence in sometimes remote locations for significant periods of time because such tests need to be conducted at certain wind speed and grid conditions. Changes in turbine control software or design modifications may require redoing of all tests. Significant cost and test-time reduction can be achieved if these tests are conducted in controlled laboratory environments that replicate grid disturbances and simulation of wind turbine interactions with power systems. Such testing capability does not exist in the United States today. An initiative by NREL to design and construct a 7-MVA grid simulator to operate with the existing 2.5 MW and new upcoming 5-MW dynamometer facilities will fulfill this role and bring many potential benefits to the U.S. wind industry with the ultimate goal of reducing wind energy integration costs.
Effect of electron extraction from a grid plasma cathode on the generation of emission plasma
NASA Astrophysics Data System (ADS)
Devyatkov, V. N.; Koval, N. N.
2014-11-01
The paper describes the operating mode of a plasma electron source based on a low- pressure arc discharge with grid stabilization of the plasma emission boundary which provides a considerable (up to twofold) increase in discharge and beam currents at an Ar pressure in the vacuum chamber p = 0.02-0.05 Pa, accelerating voltages of up to U = 10 kV, and longitudinal magnetic field of up to Bz = 0.1 T. The discharge and beam currents are increased on electron extraction from the emission plasma through meshes of a fine metal grid due to the energy of a high-voltage power supply which ensures electron emission and acceleration. The electron emission from the plasma cathode and arrival of ions from the acceleration gap in the discharge changes the discharge plasma parameters near the emission grid, thus changing the potential of the emission grid electrode with respect to the discharge cathode. The load is not typical and changes the voltage polarity of the electrode gap connected to the discharge power supply, which is to be taken into account in its calculation and design. The effect of electron emission from the plasma cathode on the discharge system can not only change the discharge and beam current pulse shapes but can also lead to a breakdown of the acceleration gap and failure of semiconductor elements in the discharge power supply unit.
NASA Astrophysics Data System (ADS)
Kato, Takeyoshi; Sugimoto, Hiroyuki; Suzuoki, Yasuo
We established a procedure for estimating regional electricity demand and regional potential capacity of distributed generators (DGs) by using a grid square statistics data set. A photovoltaic power system (PV system) for residential use and a co-generation system (CGS) for both residential and commercial use were taken into account. As an example, the result regarding Aichi prefecture was presented in this paper. The statistical data of the number of households by family-type and the number of employees by business category for about 4000 grid-square with 1km × 1km area was used to estimate the floor space or the electricity demand distribution. The rooftop area available for installing PV systems was also estimated with the grid-square statistics data set. Considering the relation between a capacity of existing CGS and a scale-index of building where CGS is installed, the potential capacity of CGS was estimated for three business categories, i.e. hotel, hospital, store. In some regions, the potential capacity of PV systems was estimated to be about 10,000kW/km2, which corresponds to the density of the existing area with intensive installation of PV systems. Finally, we discussed the ratio of regional potential capacity of DGs to regional maximum electricity demand for deducing the appropriate capacity of DGs in the model of future electricity distribution system.
Optimization Of A Computational Grid
NASA Technical Reports Server (NTRS)
Pearce, Daniel G.
1993-01-01
In improved method of generation of computational grid, grid-generation process decoupled from definition of geometry. Not necessary to redefine boundary. Instead, continuous boundaries in physical domain specified, and then grid points in computational domain mapped onto continuous boundaries.
NASA Astrophysics Data System (ADS)
Jaithwa, Ishan
Deployment of smart grid technologies is accelerating. Smart grid enables bidirectional flows of energy and energy-related communications. The future electricity grid will look very different from today's power system. Large variable renewable energy sources will provide a greater portion of electricity, small DERs and energy storage systems will become more common, and utilities will operate many different kinds of energy efficiency. All of these changes will add complexity to the grid and require operators to be able to respond to fast dynamic changes to maintain system stability and security. This thesis investigates advanced control technology for grid integration of renewable energy sources and STATCOM systems by verifying them on real time hardware experiments using two different systems: d SPACE and OPAL RT. Three controls: conventional, direct vector control and the intelligent Neural network control were first simulated using Matlab to check the stability and safety of the system and were then implemented on real time hardware using the d SPACE and OPAL RT systems. The thesis then shows how dynamic-programming (DP) methods employed to train the neural networks are better than any other controllers where, an optimal control strategy is developed to ensure effective power delivery and to improve system stability. Through real time hardware implementation it is proved that the neural vector control approach produces the fastest response time, low overshoot, and, the best performance compared to the conventional standard vector control method and DCC vector control technique. Finally the entrepreneurial approach taken to drive the technologies from the lab to market via ORANGE ELECTRIC is discussed in brief.
Leibniz algebras associated with some finite-dimensional representation of Diamond Lie algebra
NASA Astrophysics Data System (ADS)
Camacho, Luisa M.; Ladra, Manuel; Karimjanov, Iqboljon A.; Omirov, Bakhrom A.
2016-03-01
In this paper we classify Leibniz algebras whose associated Lie algebra is four-dimensional Diamond Lie algebra 𝕯 and the ideal generated by squares of elements is represented by one of the finite-dimensional indecomposable D-modules Un 1, Un 2 or Wn 1 or Wn 2.
GENIE(++): A Multi-Block Structured Grid System
NASA Technical Reports Server (NTRS)
Williams, Tonya; Nadenthiran, Naren; Thornburg, Hugh; Soni, Bharat K.
1996-01-01
The computer code GENIE++ is a continuously evolving grid system containing a multitude of proven geometry/grid techniques. The generation process in GENIE++ is based on an earlier version. The process uses several techniques either separately or in combination to quickly and economically generate sculptured geometry descriptions and grids for arbitrary geometries. The computational mesh is formed by using an appropriate algebraic method. Grid clustering is accomplished with either exponential or hyperbolic tangent routines which allow the user to specify a desired point distribution. Grid smoothing can be accomplished by using an elliptic solver with proper forcing functions. B-spline and Non-Uniform Rational B-splines (NURBS) algorithms are used for surface definition and redistribution. The built in sculptured geometry definition with desired distribution of points, automatic Bezier curve/surface generation for interior boundaries/surfaces, and surface redistribution is based on NURBS. Weighted Lagrance/Hermite transfinite interpolation methods, interactive geometry/grid manipulation modules, and on-line graphical visualization of the generation process are salient features of this system which result in a significant time savings for a given geometry/grid application.
NASA Technical Reports Server (NTRS)
Crook, Andrew J.; Delaney, Robert A.
1991-01-01
A procedure is studied for generating three-dimensional grids for advanced turbofan engine fan section geometries. The procedure constructs a discrete mesh about engine sections containing the fan stage, an arbitrary number of axisymmetric radial flow splitters, a booster stage, and a bifurcated core/bypass flow duct with guide vanes. The mesh is an h-type grid system, the points being distributed with a transfinite interpolation scheme with axial and radial spacing being user specified. Elliptic smoothing of the grid in the meridional plane is a post-process option. The grid generation scheme is consistent with aerodynamic analyses utilizing the average-passage equation system developed by Dr. John Adamczyk of NASA Lewis. This flow solution scheme requires a series of blade specific grids each having a common axisymmetric mesh, but varying in the circumferential direction according to the geometry of the specific blade row.
Turbomachinery flow calculation on unstructured grids using finite element method
NASA Astrophysics Data System (ADS)
Koschel, W.; Vornberger, A.
An explicit finite-element scheme based on a two-step Taylor-Galerkin algorithm allows the solution of the Euler and Navier-Stokes equations on unstructured grids. Mesh generation methods for unstructured grids are described which lead to efficient flow calculations. Turbulent flow is calculated by using an algebraic turbulence model. To test the numerical accuracy, a laminar and turbulent flow over a flat plate and the supersonic flow in a corner has been calculated. For validation the method is applied to the simulation of the inviscid flow through a transonic turbine cascade and the viscous flow through a subsonic turbine cascade.
NASA Technical Reports Server (NTRS)
Moore, Reagan W.; Jagatheesan, Arun; Rajasekar, Arcot; Wan, Michael; Schroeder, Wayne
2004-01-01
The "Grid" is an emerging infrastructure for coordinating access across autonomous organizations to distributed, heterogeneous computation and data resources. Data grids are being built around the world as the next generation data handling systems for sharing, publishing, and preserving data residing on storage systems located in multiple administrative domains. A data grid provides logical namespaces for users, digital entities and storage resources to create persistent identifiers for controlling access, enabling discovery, and managing wide area latencies. This paper introduces data grids and describes data grid use cases. The relevance of data grids to digital libraries and persistent archives is demonstrated, and research issues in data grids and grid dataflow management systems are discussed.
Grid quality improvement by a grid adaptation technique
NASA Technical Reports Server (NTRS)
Lee, K. D.; Henderson, T. L.; Choo, Y. K.
1991-01-01
A grid adaptation technique is presented which improves grid quality. The method begins with an assessment of grid quality by defining an appropriate grid quality measure. Then, undesirable grid properties are eliminated by a grid-quality-adaptive grid generation procedure. The same concept has been used for geometry-adaptive and solution-adaptive grid generation. The difference lies in the definition of the grid control sources; here, they are extracted from the distribution of a particular grid property. Several examples are presented to demonstrate the versatility and effectiveness of the method.
NASA Astrophysics Data System (ADS)
Cardenas, Jesus Alvaro
An energy and environmental crisis will emerge throughout the world if we continue with our current practices of generation and distribution of electricity. A possible solution to this problem is based on the Smart grid concept, which is heavily influenced by Information and Communication Technology (ICT). Although the electricity industry is mostly regulated, there are global models used as roadmaps for Smart Grids' implementation focusing on technologies and the basic generation-distribution-transmission model. This project aims to further enhance a business model for a future global deployment. It takes into consideration the many factors interacting in this energy provision process, based on the diffusion of technologies and literature surveys on the available documents in the Internet as well as peer-reviewed publications. Tariffs and regulations, distributed energy generation, integration of service providers, consumers becoming producers, self-healing devices, and many other elements are shifting this industry into a major change towards liberalization and deregulation of this sector, which has been heavily protected by the government due to the importance of electricity for consumers. We propose an Energy Management Business Model composed by four basic elements: Supply Chain, Information and Communication Technology (ICT), Stakeholders Response, and the resulting Green Efficient Energy (GEE). We support the developed model based on the literature survey, we support it with the diffusion analysis of these elements, and support the overall model with two surveys: one for peers and professionals, and other for experts in the field, based on the Smart Grid Carnegie Melon Maturity Model (CMU SEI SGMM). The contribution of this model is a simple path to follow for entities that want to achieve environmental friendly energy with the involvement of technology and all stakeholders.
NASA Technical Reports Server (NTRS)
Rizk, Y. M.; Steger, J. L.; Chaussee, D. S.
1985-01-01
The present paper describes a numerical mesh generation technique to be used with an implicit finite difference method for simulating visous supersonic flow about low-aspect-ratio wing body configurations using a single grid strategy. The computational domain is segmented into multiple regions, with borders located in supersonic areas to avoid the otherwise costly interfacing procedure between adjacent segments. The numerical procedure is applied to calculate the turbulent flow around the shuttle orbiter and a canard projectile at supersonic free stream Mach number.
Singh, Ruchi; Vyakaranam, Bharat GNVSR
2012-02-14
This document is one of a series of reports estimating the benefits of deploying technologies similar to those implemented on the Smart Grid Investment Grant (SGIG) projects. Four technical reports cover the various types of technologies deployed in the SGIG projects, distribution automation, demand response, energy storage, and renewables integration. A fifth report in the series examines the benefits of deploying these technologies on a national level. This technical report examines the impacts of addition of renewable resources- solar and wind in the distribution system as deployed in the SGIG projects.
NASA Astrophysics Data System (ADS)
Murthy, S. S.; Singh, Bhim; Sandeep, Vuddanti
2016-06-01
This paper deals with the design and development of a novel single-phase two winding self-excited squirrel cage induction generator (SEIG) for off-grid renewable energy based power generation. The principles underlying the design process and experience with SPEED design tool are described to design a 5 kW, 50 Hz, 230 V, 4 pole single phase AC generator. All possible configurations to reduce harmonic components of induced e.m.f. are attempted for desired performance and to get an optimum design keeping in view the manufacturing constraints. The development of a prototype based on this design has been completed with the help of an industry. Typical test results on the prototype are presented to demonstrate its performance. Computed results are obtained with a design based computational procedure for performance analysis and a critical comparison is made with test results.
Twisted Quantum Toroidal Algebras
NASA Astrophysics Data System (ADS)
Jing, Naihuan; Liu, Rongjia
2014-09-01
We construct a principally graded quantum loop algebra for the Kac-Moody algebra. As a special case a twisted analog of the quantum toroidal algebra is obtained together with the quantum Serre relations.
Supersymmetry algebra cohomology. I. Definition and general structure
NASA Astrophysics Data System (ADS)
Brandt, Friedemann
2010-12-01
This paper concerns standard supersymmetry algebras in diverse dimensions, involving bosonic translational generators and fermionic supersymmetry generators. A cohomology related to these supersymmetry algebras, termed supersymmetry algebra cohomology, and corresponding "primitive elements" are defined by means of a BRST (Becchi-Rouet-Stora-Tyutin)-type coboundary operator. A method to systematically compute this cohomology is outlined and illustrated by simple examples.
Analysis and Validation of Grid dem Generation Based on Gaussian Markov Random Field
NASA Astrophysics Data System (ADS)
Aguilar, F. J.; Aguilar, M. A.; Blanco, J. L.; Nemmaoui, A.; García Lorca, A. M.
2016-06-01
Digital Elevation Models (DEMs) are considered as one of the most relevant geospatial data to carry out land-cover and land-use classification. This work deals with the application of a mathematical framework based on a Gaussian Markov Random Field (GMRF) to interpolate grid DEMs from scattered elevation data. The performance of the GMRF interpolation model was tested on a set of LiDAR data (0.87 points/m2) provided by the Spanish Government (PNOA Programme) over a complex working area mainly covered by greenhouses in Almería, Spain. The original LiDAR data was decimated by randomly removing different fractions of the original points (from 10% to up to 99% of points removed). In every case, the remaining points (scattered observed points) were used to obtain a 1 m grid spacing GMRF-interpolated Digital Surface Model (DSM) whose accuracy was assessed by means of the set of previously extracted checkpoints. The GMRF accuracy results were compared with those provided by the widely known Triangulation with Linear Interpolation (TLI). Finally, the GMRF method was applied to a real-world case consisting of filling the LiDAR-derived DSM gaps after manually filtering out non-ground points to obtain a Digital Terrain Model (DTM). Regarding accuracy, both GMRF and TLI produced visually pleasing and similar results in terms of vertical accuracy. As an added bonus, the GMRF mathematical framework makes possible to both retrieve the estimated uncertainty for every interpolated elevation point (the DEM uncertainty) and include break lines or terrain discontinuities between adjacent cells to produce higher quality DTMs.
Forecasting Wind and Solar Generation: Improving System Operations, Greening the Grid
Tian; Tian; Chernyakhovskiy, Ilya
2016-01-01
This document discusses improving system operations with forecasting and solar generation. By integrating variable renewable energy (VRE) forecasts into system operations, power system operators can anticipate up- and down-ramps in VRE generation in order to cost-effectively balance load and generation in intra-day and day-ahead scheduling. This leads to reduced fuel costs, improved system reliability, and maximum use of renewable resources.
Automorphisms and Derivations of the Insertion-Elimination Algebra and Related Graded Lie Algebras
NASA Astrophysics Data System (ADS)
Ondrus, Matthew; Wiesner, Emilie
2016-07-01
This paper addresses several structural aspects of the insertion-elimination algebra {mathfrak{g}}, a Lie algebra that can be realized in terms of tree-inserting and tree-eliminating operations on the set of rooted trees. In particular, we determine the finite-dimensional subalgebras of {mathfrak{g}}, the automorphism group of {mathfrak{g}}, the derivation Lie algebra of {mathfrak{g}}, and a generating set. Several results are stated in terms of Lie algebras admitting a triangular decomposition and can be used to reproduce results for the generalized Virasoro algebras.
Incorporation of wind generation to the Mexican power grid: Steady state analysis
Tovar, J.H.; Guardado, J.L.; Cisneros, F.; Cadenas, R.; Lopez, S.
1997-09-01
This paper describes a steady state analysis related with the incorporation of large amounts of eolic generation into the Mexican power system. An equivalent node is used to represent individual eolic generators in the wind farm. Possible overloads, losses, voltage and reactive profiles and estimated severe contingencies are analyzed. Finally, the conclusions of this study are presented.
NASA Technical Reports Server (NTRS)
Chan, William M.; Rogers, Stuart E.; Nash, Steven M.; Buning, Pieter G.; Meakin, Robert
2005-01-01
Chimera Grid Tools (CGT) is a software package for performing computational fluid dynamics (CFD) analysis utilizing the Chimera-overset-grid method. For modeling flows with viscosity about geometrically complex bodies in relative motion, the Chimera-overset-grid method is among the most computationally cost-effective methods for obtaining accurate aerodynamic results. CGT contains a large collection of tools for generating overset grids, preparing inputs for computer programs that solve equations of flow on the grids, and post-processing of flow-solution data. The tools in CGT include grid editing tools, surface-grid-generation tools, volume-grid-generation tools, utility scripts, configuration scripts, and tools for post-processing (including generation of animated images of flows and calculating forces and moments exerted on affected bodies). One of the tools, denoted OVERGRID, is a graphical user interface (GUI) that serves to visualize the grids and flow solutions and provides central access to many other tools. The GUI facilitates the generation of grids for a new flow-field configuration. Scripts that follow the grid generation process can then be constructed to mostly automate grid generation for similar configurations. CGT is designed for use in conjunction with a computer-aided-design program that provides the geometry description of the bodies, and a flow-solver program.
Algebraic vs physical N = 6 3-algebras
Cantarini, Nicoletta; Kac, Victor G.
2014-01-15
In our previous paper, we classified linearly compact algebraic simple N = 6 3-algebras. In the present paper, we classify their “physical” counterparts, which actually appear in the N = 6 supersymmetric 3-dimensional Chern-Simons theories.
NASA Technical Reports Server (NTRS)
Dulikravich, D. S.
1982-01-01
A fast computer program, GRID3C, was developed to generate multilevel three dimensional, C type, periodic, boundary conforming grids for the calculation of realistic turbomachinery and propeller flow fields. The technique is based on two analytic functions that conformally map a cascade of semi-infinite slits to a cascade of doubly infinite strips on different Riemann sheets. Up to four consecutively refined three dimensional grids are automatically generated and permanently stored on four different computer tapes. Grid nonorthogonality is introduced by a separate coordinate shearing and stretching performed in each of three coordinate directions. The grids are easily clustered closer to the blade surface, the trailing and leading edges and the hub or shroud regions by changing appropriate input parameters. Hub and duct (or outer free boundary) have different axisymmetric shapes. A vortex sheet of arbitrary thickness emanating smoothly from the blade trailing edge is generated automatically by GRID3C. Blade cross sectional shape, chord length, twist angle, sweep angle, and dihedral angle can vary in an arbitrary smooth fashion in the spanwise direction.
Makarov, Yuri V.; Huang, Zhenyu; Etingov, Pavel V.; Ma, Jian; Guttromson, Ross T.; Subbarao, Krishnappa; Chakrabarti, Bhujanga B.
2010-01-01
unique features make this work a significant step forward toward the objective of incorporating of wind, solar, load, and other uncertainties into power system operations. Currently, uncertainties associated with wind and load forecasts, as well as uncertainties associated with random generator outages and unexpected disconnection of supply lines, are not taken into account in power grid operation. Thus, operators have little means to weigh the likelihood and magnitude of upcoming events of power imbalance. In this project, funded by the U.S. Department of Energy (DOE), a framework has been developed for incorporating uncertainties associated with wind and load forecast errors, unpredicted ramps, and forced generation disconnections into the energy management system (EMS) as well as generation dispatch and commitment applications. A new approach to evaluate the uncertainty ranges for the required generation performance envelope including balancing capacity, ramping capability, and ramp duration has been proposed. The approach includes three stages: forecast and actual data acquisition, statistical analysis of retrospective information, and prediction of future grid balancing requirements for specified time horizons and confidence levels. Assessment of the capacity and ramping requirements is performed using a specially developed probabilistic algorithm based on a histogram analysis, incorporating all sources of uncertainties of both continuous (wind and load forecast errors) and discrete (forced generator outages and start-up failures) nature. A new method called the “flying brick” technique has been developed to evaluate the look-ahead required generation performance envelope for the worst case scenario within a user-specified confidence level. A self-validation algorithm has been developed to validate the accuracy of the confidence intervals.
Abdelli, Radia; Rekioua, Djamila; Rekioua, Toufik; Tounzi, Abdelmounaïm
2013-07-01
This paper presents a modulated hysteresis direct torque control (MHDTC) applied to an induction generator (IG) used in wind energy conversion systems (WECs) connected to the electrical grid through a back-to-back converter. The principle of this strategy consists in superposing to the torque reference a triangular signal, as in the PWM strategy, with the desired switching frequency. This new modulated reference is compared to the estimated torque by using a hysteresis controller as in the classical direct torque control (DTC). The aim of this new approach is to lead to a constant frequency and low THD in grid current with a unit power factor and a minimum voltage variation despite the wind variation. To highlight the effectiveness of the proposed method, a comparison was made with classical DTC and field oriented control method (FOC). The obtained simulation results, with a variable wind profile, show an adequate dynamic of the conversion system using the proposed method compared to the classical approaches. PMID:23615169
Grid-connected in-stream hydroelectric generation based on the doubly fed induction machine
NASA Astrophysics Data System (ADS)
Lenberg, Timothy J.
Within the United States, there is a growing demand for new environmentally friendly power generation. This has led to a surge in wind turbine development. Unfortunately, wind is not a stable prime mover, but water is. Why not apply the advances made for wind to in-stream hydroelectric generation? One important advancement is the creation of the Doubly Fed Induction Machine (DFIM). This thesis covers the application of a gearless DFIM topology for hydrokinetic generation. After providing background, this thesis presents many of the options available for the mechanical portion of the design. A mechanical turbine is then specified. Next, a method is presented for designing a DFIM including the actual design for this application. In Chapter 4, a simulation model of the system is presented, complete with a control system that maximizes power generation based on water speed. This section then goes on to present simulation results demonstrating proper operation.
A simple mathematical description of an off-grid hybrid solar-wind power generating system
NASA Astrophysics Data System (ADS)
Blasone, M.; Dell'Anno, F.; De Luca, R.; Torre, G.
2013-05-01
We give a detailed description of the energy balance equation for a stand-alone hybrid solar-wind power generating system. The dimensions of the power generator and the energy capacity of a buffer battery (used as an energy storage system) are chosen to suit a known consumer's profile. Future applications of the mathematical model developed and analogies with a similar hydrodynamic problem are discussed.
The evolution of grid-generated turbulence under conditions of stable thermal stratification
NASA Astrophysics Data System (ADS)
Yoon, Kyunghwan; Warhaft, Z.
1990-06-01
The effects of a stable negatively buoyant linear temperature profile on the evolution of grid-induced turbulence is investigated experimentally in the 0.91 x 0.91 x 9.14-m test section of a low-speed open-circuit wind tunnel at mean velocity 2.8-4.2 m/sec. The derivation of the governing equations is outlined; the test setup and instrumentation are described; and the results are presented in extensive tables and graphs and discussed in detail. Four main flow regimes are identified on the basis of the turbulence Richardson number Ri(u): (1) dynamically passive flow at Ri(u) less than 0.1, (2) buoyancy-force-induced decay of heat flux and vertical velocity variance at Ri(u) between 0.1 and about 1, (3) complete collapse of the heat flux at Ri(u) between 1 and 2, and (4) continuing low heat flux at Ri(u) greater than 2, except for the most stable case studied (mesh Froude number 84.8), where a significant net countergradient heat flux is observed.
Description of a solder pulse generator for the single step formation of ball grid arrays
Schmale, D.T.; Frear, D.R.; Yost, F.G.; Essien, M.
1997-02-01
The traditional geometry for surface mount devices is the peripheral array where the leads are on the edges of the device. As the technology drives towards high input/output (I/O) count (increasing number of leads) and smaller packages with finer pitch (less distance between peripheral leads), limitations on peripheral surface mount devices arise. The leads on these fine pitch devices are fragile and can be easily bent. It becomes increasingly difficult to deliver solder past to leads spaced as little as 0.012 inch apart. Too much solder mass can result in bridging between leads while too little solder can contribute to the loss of mechanical and electrical continuity. A solution is to shift the leads from the periphery of the device to the area under the device. This scheme is called areal array packaging and is exemplified by the ball grid array (BGA) package. A system has been designed and constructed to deposit an entire array of several hundred uniform solder droplets onto a printed circuit board in a fraction of a second. The solder droplets wet to the interconnect lands on a pc board and forms a basis for later application of a BGA device. The system consists of a piezoelectric solder pulse unit, heater controls, an inert gas chamber and an analog power supply/pulse unit.
Chowdhury, B.H.; Muknahallipatna, S.; Cupal, J.J.; Hamann, J.C.; Dinwoodie, T.; Shugar, D.
1997-12-31
The University of Wyoming (UW) campus is serving as the site for a 50 kilowatt solar photovoltaic (PV) system. Three sub-systems were sited and built on the UW campus in 1996. The first sub-system, a 10 kW roof-integrated system of PV roof tiles is located on the roof of the Engineering building. The second sub-system--a 5 kW rack-mounted, ballasted PV system is on a walkway roof of the Engineering building. The third sub-system is a 35 kW shade structure system and located adjacent to the parking lot of the university`s football stadium. The three sub-systems differ in their design strategy since each is being used for research and education at the university. Each sub-system, being located at some distance away from one another, supplies a different part of the campus grid. Efforts continue at setting up a central monitoring system which will receive data remotely from all locations. A part of this monitoring system is complete. While the initial monitoring data shows satisfactory performance, a number of reliability problems with PV modules and inverters have delayed full functionality of the system.
Grid and aerodynamic sensitivity analyses of airplane components
NASA Technical Reports Server (NTRS)
Sadrehaghighi, Ideen; Smith, Robert E.; Tiwari, Surendra N.
1993-01-01
An algorithm is developed to obtain the grid sensitivity with respect to design parameters for aerodynamic optimization. The procedure is advocating a novel (geometrical) parameterization using spline functions such as NURBS (Non-Uniform Rational B-Splines) for defining the wing-section geometry. An interactive algebraic grid generation technique, known as Two-Boundary Grid Generation (TBGG) is employed to generate C-type grids around wing-sections. The grid sensitivity of the domain with respect to geometric design parameters has been obtained by direct differentiation of the grid equations. A hybrid approach is proposed for more geometrically complex configurations such as a wing or fuselage. The aerodynamic sensitivity coefficients are obtained by direct differentiation of the compressible two-dimensional thin-layer Navier-Stokes equations. An optimization package has been introduced into the algorithm in order to optimize the wing-section surface. Results demonstrate a substantially improved design due to maximized lift/drag ratio of the wing-section.
NASA Astrophysics Data System (ADS)
Camera, Corrado; Bruggeman, Adriana; Hadjinicolaou, Panos; Pashiardis, Stelios; Lange, Manfred
2014-05-01
High-resolution gridded daily datasets are essential for natural resource management and the analysis of climate changes and their effects. This study aimed to create gridded datasets of daily precipitation and daily minimum and maximum temperature, for the future (2020-2050). The horizontal resolution of the developed datasets is 1 x 1 km2, covering the area under control of the Republic of Cyprus (5.760 km2). The study is divided into two parts. The first consists of the evaluation of the performance of different interpolation techniques for daily rainfall and temperature data (1980-2010) for the creation of the gridded datasets. Rainfall data recorded at 145 stations and temperature data from 34 stations were used. For precipitation, inverse distance weighting (IDW) performs best for local events, while a combination of step-wise geographically weighted regression and IDW proves to be the best method for large scale events. For minimum and maximum temperature, a combination of step-wise linear multiple regression and thin plate splines is recognized as the best method. Six Regional Climate Models (RCMs) for the A1B SRES emission scenario from the EU ENSEMBLE project database were selected as sources for future climate projections. The RCMs were evaluated for their capacity to simulate Cyprus climatology for the period 1980-2010. Data for the period 2020-2050 from the three best performing RCMs were downscaled, using the change factors approach, at the location of observational stations. Daily time series were created with a stochastic rainfall and temperature generator. The RainSim V3 software (Burton et al., 2008) was used to generate spatial-temporal coherent rainfall fields. The temperature generator was developed in R and modeled temperature as a weakly stationary process with the daily mean and standard deviation conditioned on the wet and dry state of the day (Richardson, 1981). Finally gridded datasets depicting projected future climate conditions were
Hoff, T.; Wenger, H.
1994-07-01
A common practice of electric utilities experiencing transmission and distribution (T and D) system overloads is to expand the substation, add lines, or upgrade equipment, all of which are capital intensive options. In 1988, it was hypothesized that strategically sited photovoltaics (PV) could benefit parts of T and D systems near or at overloaded conditions. An evaluation methodology was developed and applied to a test case (Kerman Substation near Fresno, California). Analytical results suggested that the value of PV to the T and D system could substantially exceed its energy and generation capacity value. The importance of this finding indicated the need for empirical validation. This led to the construction of a 0.5 MW PV demonstration plant by Pacific Gas and Electric Company (PG and E) at Kerman, California as part of the PVUSA (PV for Utility Scale Applications) project. PVUSA is a national public-private partnership that is assessing and demonstrating the viability of utility-scale photovoltaic electric generation systems. The Kerman PV plant, commissioned for commercial operation in June, 1993, is reported to be the first grid-support PV demonstration plant in the world. This Interim Report focuses on validating the technical aspects of grid-support PV. It provides interim validation results for four of the eight identified value components that stack up to make the ``value bar``, and compares them to 1992 Case Study estimates. Results are based on improved technical evaluation methodologies, measured plant performance under a variety of conditions, and long-term plant performance estimated using a validated computer simulation program. This report is not intended to be exhaustive in scope. It does, however, provide a thorough progress update of the validation project. Complete documentation of test procedures, data, and evaluation methods will be presented in the Final Report.
ERIC Educational Resources Information Center
National Council of Teachers of Mathematics, Inc., Reston, VA.
This is a reprint of the historical capsules dealing with algebra from the 31st Yearbook of NCTM,"Historical Topics for the Mathematics Classroom." Included are such themes as the change from a geometric to an algebraic solution of problems, the development of algebraic symbolism, the algebraic contributions of different countries, the origin and…
Automated volumetric grid generation for finite element modeling of human hand joints
Hollerbach, K.; Underhill, K.; Rainsberger, R.
1995-02-01
We are developing techniques for finite element analysis of human joints. These techniques need to provide high quality results rapidly in order to be useful to a physician. The research presented here increases model quality and decreases user input time by automating the volumetric mesh generation step.
NASA Astrophysics Data System (ADS)
Azoumah, Y.; Yamegueu, D.; Py, X.
2012-02-01
Access to energy is known as a key issue for poverty reduction. The electrification rate of sub Saharan countries is one of the lowest among the developing countries. However this part of the world has natural energy resources that could help raising its access to energy, then its economic development. An original "flexy energy" concept of hybrid solar pv/diesel/biofuel power plant, without battery storage, is developed in order to not only make access to energy possible for rural and peri-urban populations in Africa (by reducing the electricity generation cost) but also to make the electricity production sustainable in these areas. Some experimental results conducted on this concept prototype show that the sizing of a pv/diesel hybrid system by taking into account the solar radiation and the load/demand profile of a typical area may lead the diesel generator to operate near its optimal point (70-90 % of its nominal power). Results also show that for a reliability of a PV/diesel hybrid system, the rated power of the diesel generator should be equal to the peak load. By the way, it has been verified through this study that the functioning of a pv/Diesel hybrid system is efficient for higher load and higher solar radiation.
Figueroa-O'Farrill, Jose Miguel
2009-11-15
We phrase deformations of n-Leibniz algebras in terms of the cohomology theory of the associated Leibniz algebra. We do the same for n-Lie algebras and for the metric versions of n-Leibniz and n-Lie algebras. We place particular emphasis on the case of n=3 and explore the deformations of 3-algebras of relevance to three-dimensional superconformal Chern-Simons theories with matter.
NASA Astrophysics Data System (ADS)
Finley, Christopher
Power generation using wind turbines increases the electrical system balancing, regulation and ramp rate requirements due to the minute to minute variability in wind speed and the difficulty in accurately forecasting wind speeds. The addition of thermal energy storage, such as ice storage, to a building's space cooling equipment increases the operational flexibility of the equipment by allowing the owner to choose when the chiller is run. The ability of the building owner to increase the power demand from the chiller (e.g. make ice) or to decrease the power demand (e.g. melt ice) to provide electrical system ancillary services was evaluated.
Grid Generator for Two, Three-dimensional Finite Element Subsurface Flow Models
1993-04-28
GRIDMAKER serves as a preprocessor for finite element models in solving two- and three-dimensional subsurface flow and pollutant transport problems. It is designed to generate three-point triangular or four-point quadrilateral elements for two-dimensional domains and eight-point hexahedron elements for three-dimensional domains. A two-dimensional domain of an aquifer with a variable depth layer is treated as a special case for depth-integrated two-dimensional, finite element subsurface flow models. The program accommodates the need for aquifers with heterogeneousmore » systems by identifying the type of material in each element.« less
Quantum cluster algebras and quantum nilpotent algebras
Goodearl, Kenneth R.; Yakimov, Milen T.
2014-01-01
A major direction in the theory of cluster algebras is to construct (quantum) cluster algebra structures on the (quantized) coordinate rings of various families of varieties arising in Lie theory. We prove that all algebras in a very large axiomatically defined class of noncommutative algebras possess canonical quantum cluster algebra structures. Furthermore, they coincide with the corresponding upper quantum cluster algebras. We also establish analogs of these results for a large class of Poisson nilpotent algebras. Many important families of coordinate rings are subsumed in the class we are covering, which leads to a broad range of applications of the general results to the above-mentioned types of problems. As a consequence, we prove the Berenstein–Zelevinsky conjecture [Berenstein A, Zelevinsky A (2005) Adv Math 195:405–455] for the quantized coordinate rings of double Bruhat cells and construct quantum cluster algebra structures on all quantum unipotent groups, extending the theorem of Geiß et al. [Geiß C, et al. (2013) Selecta Math 19:337–397] for the case of symmetric Kac–Moody groups. Moreover, we prove that the upper cluster algebras of Berenstein et al. [Berenstein A, et al. (2005) Duke Math J 126:1–52] associated with double Bruhat cells coincide with the corresponding cluster algebras. PMID:24982197
NASA Astrophysics Data System (ADS)
Buscheck, T. A.; Bielicki, J. M.; Randolph, J.; Chen, M.; Hao, Y.; Sun, Y.
2013-12-01
Abstract We present an approach to use CO2 to (1) generate dispatchable renewable power that can quickly respond to grid fluctuations and be cost-competitive with natural gas, (2) stabilize the grid by efficiently storing large quantities of energy, (3) enable seasonal storage of solar thermal energy for grid integration, (4) produce brine for power-plant cooling, all which (5) increase CO2 value, rendering CO2 capture to be commerically viable, while (6) sequestering huge quantities of CO2. These attributes reduce carbon intensity of electric power, and enable cost-competitive, dispatchable power from major sources of renewable energy: wind, solar, and geothermal. Conventional geothermal power systems circulate brine as the working fluid to extract heat, but the parasitic power load for this circulation can consume a large portion of gross power output. Recently, CO2 has been considered as a working fluid because its advantageous properties reduce this parasitic loss. We expand on this idea by using multiple working fluids: brine, CO2, and N2. N2 can be separated from air at lower cost than captured CO2, it is not corrosive, and it will not react with the formation. N2 also can improve the economics of energy production and enable energy storage, while reducing operational risk. Extracting heat from geothermal reservoirs often requires submersible pumps to lift brine, but these pumps consume much of the generated electricity. In contrast, our approach drives fluid circulation by injecting supplemental, compressible fluids (CO2, and N2) with high coefficients of thermal expansion. These fluids augment reservoir pressure, produce artesian flow at the producers, and reduce the parasitic load. Pressure augmentation is improved by the thermosiphon effect that results from injecting cold/dense CO2 and N2. These fluids are heated to reservoir temperature, greatly expand, and increase the artesian flow of brine and supplemental fluid at the producers. Rather than using
Upper bound for the length of commutative algebras
Markova, Ol'ga V
2009-12-31
By the length of a finite system of generators for a finite-dimensional associative algebra over an arbitrary field one means the least positive integer k such that the words of length not exceeding k span this algebra (as a vector space). The maximum length for the systems of generators of an algebra is referred to as the length of the algebra. In the present paper, an upper bound for the length of a commutative algebra in terms of a function of two invariants of the algebra, the dimension and the maximal degree of the minimal polynomial for the elements of the algebra, is obtained. As a corollary, a formula for the length of the algebra of diagonal matrices over an arbitrary field is obtained. Bibliography: 8 titles.
You, Shutang; Hadley, Stanton W.; Shankar, Mallikarjun; Liu, Yilu
2016-01-12
This paper studies the generation and transmission expansion co-optimization problem with a high wind power penetration rate in the US Eastern Interconnection (EI) power grid. In this paper, the generation and transmission expansion problem for the EI system is modeled as a mixed-integer programming (MIP) problem. Our paper also analyzed a time series generation method to capture the variation and correlation of both load and wind power across regions. The obtained series can be easily introduced into the expansion planning problem and then solved through existing MIP solvers. Simulation results show that the proposed planning model and series generation methodmore » can improve the expansion result significantly through modeling more detailed information of wind and load variation among regions in the US EI system. Moreover, the improved expansion plan that combines generation and transmission will aid system planners and policy makers to maximize the social welfare in large-scale power grids.« less
Albuquerque, Fabio L.; Moraes, Adelio J.; Guimaraes, Geraldo C.; Sanhueza, Sergio M.R.; Vaz, Alexandre R.
2010-07-15
In the case of photovoltaic (PV) systems acting as distributed generation (DG) systems, the DC energy that is produced is fed to the grid through the power-conditioning unit (inverter). The majority of contemporary inverters used in DG systems are current source inverters (CSI) operating at unity power factor. If, however, we assume that voltage source inverters (VSI) can replace CSIs, we can generate reactive power proportionally to the remaining unused capacity at any given time. According to the theory of instantaneous power, the inverter reactive power can be regulated by changing the amplitude of its output voltage. In addition, the inverter active power can be adjusted by modifying the phase angle of its output voltage. Based on such theory, both the active power supply and the reactive power compensation (RPC) can be carried out simultaneously. When the insolation is weak or the PV modules are inoperative at night, the RPC feature of a PV system can still be used to improve the inverter utilisation factor. Some MATLAB simulation results are included here to show the feasibility of the method. (author)
Makarov, Yuri V.; Huang, Zhenyu; Etingov, Pavel V.; Ma, Jian; Guttromson, Ross T.; Subbarao, Krishnappa; Chakrabarti, Bhujanga B.
2010-09-01
features make this work a significant step forward toward the objective of incorporating of wind, solar, load, and other uncertainties into power system operations. In this report, a new methodology to predict the uncertainty ranges for the required balancing capacity, ramping capability and ramp duration is presented. Uncertainties created by system load forecast errors, wind and solar forecast errors, generation forced outages are taken into account. The uncertainty ranges are evaluated for different confidence levels of having the actual generation requirements within the corresponding limits. The methodology helps to identify system balancing reserve requirement based on a desired system performance levels, identify system “breaking points”, where the generation system becomes unable to follow the generation requirement curve with the user-specified probability level, and determine the time remaining to these potential events. The approach includes three stages: statistical and actual data acquisition, statistical analysis of retrospective information, and prediction of future grid balancing requirements for specified time horizons and confidence intervals. Assessment of the capacity and ramping requirements is performed using a specially developed probabilistic algorithm based on a histogram analysis incorporating all sources of uncertainty and parameters of a continuous (wind forecast and load forecast errors) and discrete (forced generator outages and failures to start up) nature. Preliminary simulations using California Independent System Operator (California ISO) real life data have shown the effectiveness of the proposed approach. A tool developed based on the new methodology described in this report will be integrated with the California ISO systems. Contractual work is currently in place to integrate the tool with the AREVA EMS system.
Banach Algebras Associated to Lax Pairs
NASA Astrophysics Data System (ADS)
Glazebrook, James F.
2015-04-01
Lax pairs featuring in the theory of integrable systems are known to be constructed from a commutative algebra of formal pseudodifferential operators known as the Burchnall- Chaundy algebra. Such pairs induce the well known KP flows on a restricted infinite-dimensional Grassmannian. The latter can be exhibited as a Banach homogeneous space constructed from a Banach *-algebra. It is shown that this commutative algebra of operators generating Lax pairs can be associated with a commutative C*-subalgebra in the C*-norm completion of the *-algebra. In relationship to the Bose-Fermi correspondence and the theory of vertex operators, this C*-algebra has an association with the CAR algebra of operators as represented on Fermionic Fock space by the Gelfand-Naimark-Segal construction. Instrumental is the Plücker embedding of the restricted Grassmannian into the projective space of the associated Hilbert space. The related Baker and tau-functions provide a connection between these two C*-algebras, following which their respective state spaces and Jordan-Lie-Banach algebras structures can be compared.
Carson, James P.; Kuprat, Andrew P.; Jiao, Xiangmin; Dyedov, Volodymyr; del Pin, Facundo; Guccione, Julius M.; Ratcliffe, Mark B.; Einstein, Daniel R.
2010-04-01
Spatial discretization of complex imaging-derived fluid-solid geometries, such as the cardiac environment, is a critical but often overlooked challenge in biomechanical computations. This is particularly true in problems with Lagrangian interfaces, where, the fluid and solid phases must match geometrically. For simplicity and better accuracy, it is also highly desirable for the two phases to share the same surface mesh at the interface between them. We outline a method for solving this problem, and illustrate the approach with a 3D fluid-solid mesh of the mouse heart. An MRI perfusion-fixed dataset of a mouse heart with 50μm isotropic resolution was semi-automatically segmented using a customized multimaterial connected-threshold approach that divided the volume into non-overlapping regions of blood, tissue and background. Subsequently, a multimaterial marching cubes algorithm was applied to the segmented data to produce two detailed, compatible isosurfaces, one for blood and one for tissue. Both isosurfaces were simultaneously smoothed with a multimaterial smoothing algorithm that exactly conserves the volume for each phase. Using these two isosurfaces, we developed and applied novel automated meshing algorithms to generate anisotropic hybrid meshes on arbitrary biological geometries with the number of layers and the desired element anisotropy for each phase as the only input parameters. Since our meshes adapt to the local feature sizes and include boundary layer prisms, they are more efficient and accurate than non-adaptive, isotropic meshes, and the fluid-structure interaction computations will tend to have relative error equilibrated over the whole mesh.
Deforming the Maxwell-Sim algebra
Gibbons, G. W.; Gomis, Joaquim; Pope, C. N.
2010-09-15
The Maxwell algebra is a noncentral extension of the Poincare algebra, in which the momentum generators no longer commute, but satisfy [P{sub {mu}},P{sub {nu}}]=Z{sub {mu}{nu}}. The charges Z{sub {mu}{nu}} commute with the momenta, and transform tensorially under the action of the angular momentum generators. If one constructs an action for a massive particle, invariant under these symmetries, one finds that it satisfies the equations of motion of a charged particle interacting with a constant electromagnetic field via the Lorentz force. In this paper, we explore the analogous constructions where one starts instead with the ISim subalgebra of Poincare, this being the symmetry algebra of very special relativity. It admits an analogous noncentral extension, and we find that a particle action invariant under this Maxwell-Sim algebra again describes a particle subject to the ordinary Lorentz force. One can also deform the ISim algebra to DISim{sub b}, where b is a nontrivial dimensionless parameter. We find that the motion described by an action invariant under the corresponding Maxwell-DISim algebra is that of a particle interacting via a Finslerian modification of the Lorentz force. In an appendix is it shown that the DISim{sub b} algebra is isomorphic to the extended Schroedinger algebra with its standard deformation parameter z, when b=(1/1-z).
Regularized CT reconstruction on unstructured grid
NASA Astrophysics Data System (ADS)
Chen, Yun; Lu, Yao; Ma, Xiangyuan; Xu, Yuesheng
2016-04-01
Computed tomography (CT) is an ill-posed problem. Reconstruction on unstructured grid reduces the computational cost and alleviates the ill-posedness by decreasing the dimension of the solution space. However, there was no systematic study on edge-preserving regularization methods for CT reconstruction on unstructured grid. In this work, we propose a novel regularization method for CT reconstruction on unstructured grid, such as triangular or tetrahedral meshes generated from the initial images reconstructed via analysis reconstruction method (e.g., filtered back-projection). The proposed regularization method is modeled as a three-term optimization problem, containing a weighted least square fidelity term motivated by the simultaneous algebraic reconstruction technique (SART). The related cost function contains two non-differentiable terms, which bring difficulty to the development of the fast solver. A fixed-point proximity algorithm with SART is developed for solving the related optimization problem, and accelerating the convergence. Finally, we compare the regularized CT reconstruction method to SART with different regularization methods. Numerical experiments demonstrated that the proposed regularization method on unstructured grid is effective to suppress noise and preserve edge features.
Moving frames and prolongation algebras
NASA Technical Reports Server (NTRS)
Estabrook, F. B.
1982-01-01
Differential ideals generated by sets of 2-forms which can be written with constant coefficients in a canonical basis of 1-forms are considered. By setting up a Cartan-Ehresmann connection, in a fiber bundle over a base space in which the 2-forms live, one finds an incomplete Lie algebra of vector fields in the fields in the fibers. Conversely, given this algebra (a prolongation algebra), one can derive the differential ideal. The two constructs are thus dual, and analysis of either derives properties of both. Such systems arise in the classical differential geometry of moving frames. Examples of this are discussed, together with examples arising more recently: the Korteweg-de Vries and Harrison-Ernst systems.
Ternary generalization of Heisenberg's algebra
NASA Astrophysics Data System (ADS)
Kerner, Richard
2015-06-01
A concise study of ternary and cubic algebras with Z3 grading is presented. We discuss some underlying ideas leading to the conclusion that the discrete symmetry group of permutations of three objects, S3, and its abelian subgroup Z3 may play an important role in quantum physics. We show then how most of important algebras with Z2 grading can be generalized with ternary composition laws combined with a Z3 grading. We investigate in particular a ternary, Z3-graded generalization of the Heisenberg algebra. It turns out that introducing a non-trivial cubic root of unity, , one can define two types of creation operators instead of one, accompanying the usual annihilation operator. The two creation operators are non-hermitian, but they are mutually conjugate. Together, the three operators form a ternary algebra, and some of their cubic combinations generate the usual Heisenberg algebra. An analogue of Hamiltonian operator is constructed by analogy with the usual harmonic oscillator, and some properties of its eigenfunctions are briefly discussed.
Apelfröjd, Senad; Eriksson, Sandra
2014-01-01
Results from experiments on a tap transformer based grid connection system for a variable speed vertical axis wind turbine are presented. The tap transformer based system topology consists of a passive diode rectifier, DC-link, IGBT inverter, LCL-filter, and tap transformer. Full range variable speed operation is enabled by using the different step-up ratios of a tap transformer. Simulations using MATLAB/Simulink have been performed in order to study the behavior of the system. A full experimental set up of the system has been used in the laboratory study, where a clone of the on-site generator was driven by an induction motor and the system was connected to a resistive load to better evaluate the performance. Furthermore, the system is run and evaluated for realistic wind speeds and variable speed operation. For a more complete picture of the system performance, a case study using real site Weibull parameters is done, comparing different tap selection options. The results show high system efficiency at nominal power and an increase in overall power output for full tap operation in comparison with the base case, a standard transformer. In addition, the loss distribution at different wind speeds is shown, which highlights the dominant losses at low and high wind speeds. Finally, means for further increasing the overall system efficiency are proposed. PMID:25258733
2014-01-01
Results from experiments on a tap transformer based grid connection system for a variable speed vertical axis wind turbine are presented. The tap transformer based system topology consists of a passive diode rectifier, DC-link, IGBT inverter, LCL-filter, and tap transformer. Full range variable speed operation is enabled by using the different step-up ratios of a tap transformer. Simulations using MATLAB/Simulink have been performed in order to study the behavior of the system. A full experimental set up of the system has been used in the laboratory study, where a clone of the on-site generator was driven by an induction motor and the system was connected to a resistive load to better evaluate the performance. Furthermore, the system is run and evaluated for realistic wind speeds and variable speed operation. For a more complete picture of the system performance, a case study using real site Weibull parameters is done, comparing different tap selection options. The results show high system efficiency at nominal power and an increase in overall power output for full tap operation in comparison with the base case, a standard transformer. In addition, the loss distribution at different wind speeds is shown, which highlights the dominant losses at low and high wind speeds. Finally, means for further increasing the overall system efficiency are proposed. PMID:25258733
Complex Kumjian-Pask algebras of 2-graphs
NASA Astrophysics Data System (ADS)
Yusnitha, Isnie; Rosjanuardi, Rizky
2016-02-01
Let Λ be a row-finitek-graph without sources and R be any field. The Kumjian-Pask algebras KPR(Λ) is an algebraic analog of k-graph algebrasC*(Λ). When the field R is the complex field ℂ, there is a special relationship between the complex Kumjian-Pask algebras KP𝕔(Λ) and k-graph algebrasC*(Λ). We examine this relationship particularly to the case 2-graph 𝔽θ+, 2-graph on single vertex generated by m blue edges and n red edges with θ respect to some commutation relations, by analyzing the associated C*-algebras of 𝔽θ+ . As the presence of cycles on 2-graph 𝔽θ+, we can imply that 2-graph algebras C*(𝔽F+ ) is infinite-dimensional. Hence, the complex Kumjian-Pask algebras KP𝕔 (𝔽θ+ ) is also infinite dimensional.
Learning Algebra in a Computer Algebra Environment
ERIC Educational Resources Information Center
Drijvers, Paul
2004-01-01
This article summarises a doctoral thesis entitled "Learning algebra in a computer algebra environment, design research on the understanding of the concept of parameter" (Drijvers, 2003). It describes the research questions, the theoretical framework, the methodology and the results of the study. The focus of the study is on the understanding of…
Realizations of Galilei algebras
NASA Astrophysics Data System (ADS)
Nesterenko, Maryna; Pošta, Severin; Vaneeva, Olena
2016-03-01
All inequivalent realizations of the Galilei algebras of dimensions not greater than five are constructed using the algebraic approach proposed by Shirokov. The varieties of the deformed Galilei algebras are discussed and families of one-parametric deformations are presented in explicit form. It is also shown that a number of well-known and physically interesting equations and systems are invariant with respect to the considered Galilei algebras or their deformations.
Unstructured Grids on NURBS Surfaces
NASA Technical Reports Server (NTRS)
Samareh-Abolhassani, Jamshid
1993-01-01
A simple and efficient computational method is presented for unstructured surface grid generation. This method is built upon an advancing front technique combined with grid projection. The projection technique is based on a Newton-Raphson method. This combined approach has been successfully implemented for structured and unstructured grids. In this paper, the implementation for unstructured grid is discussed.
NASA Technical Reports Server (NTRS)
Iachello, Franco
1995-01-01
An algebraic formulation of quantum mechanics is presented. In this formulation, operators of interest are expanded onto elements of an algebra, G. For bound state problems in nu dimensions the algebra G is taken to be U(nu + 1). Applications to the structure of molecules are presented.
Orientation in operator algebras
Alfsen, Erik M.; Shultz, Frederic W.
1998-01-01
A concept of orientation is relevant for the passage from Jordan structure to associative structure in operator algebras. The research reported in this paper bridges the approach of Connes for von Neumann algebras and ourselves for C*-algebras in a general theory of orientation that is of geometric nature and is related to dynamics. PMID:9618457
Developing Thinking in Algebra
ERIC Educational Resources Information Center
Mason, John; Graham, Alan; Johnson-Wilder, Sue
2005-01-01
This book is for people with an interest in algebra whether as a learner, or as a teacher, or perhaps as both. It is concerned with the "big ideas" of algebra and what it is to understand the process of thinking algebraically. The book has been structured according to a number of pedagogic principles that are exposed and discussed along the way,…
Connecting Arithmetic to Algebra
ERIC Educational Resources Information Center
Darley, Joy W.; Leapard, Barbara B.
2010-01-01
Algebraic thinking is a top priority in mathematics classrooms today. Because elementary school teachers lay the groundwork to develop students' capacity to think algebraically, it is crucial for teachers to have a conceptual understanding of the connections between arithmetic and algebra and be confident in communicating these connections. Many…
Applied Algebra Curriculum Modules.
ERIC Educational Resources Information Center
Texas State Technical Coll., Marshall.
This collection of 11 applied algebra curriculum modules can be used independently as supplemental modules for an existing algebra curriculum. They represent diverse curriculum styles that should stimulate the teacher's creativity to adapt them to other algebra concepts. The selected topics have been determined to be those most needed by students…
Profiles of Algebraic Competence
ERIC Educational Resources Information Center
Humberstone, J.; Reeve, R.A.
2008-01-01
The algebraic competence of 72 12-year-old female students was examined to identify profiles of understanding reflecting different algebraic knowledge states. Beginning algebraic competence (mapping abilities: word-to-symbol and vice versa, classifying, and solving equations) was assessed. One week later, the nature of assistance required to map…
Ternary Virasoro - Witt algebra.
Zachos, C.; Curtright, T.; Fairlie, D.; High Energy Physics; Univ. of Miami; Univ. of Durham
2008-01-01
A 3-bracket variant of the Virasoro-Witt algebra is constructed through the use of su(1,1) enveloping algebra techniques. The Leibniz rules for 3-brackets acting on other 3-brackets in the algebra are discussed and verified in various situations.
Structure of classical affine and classical affine fractional W-algebras
Suh, Uhi Rinn
2015-01-15
We introduce a classical BRST complex (See Definition 3.2.) and show that one can construct a classical affine W-algebra via the complex. This definition clarifies that classical affine W-algebras can be considered as quasi-classical limits of quantum affine W-algebras. We also give a definition of a classical affine fractional W-algebra as a Poisson vertex algebra. As in the classical affine case, a classical affine fractional W-algebra has two compatible λ-brackets and is isomorphic to an algebra of differential polynomials as a differential algebra. When a classical affine fractional W-algebra is associated to a minimal nilpotent, we describe explicit forms of free generators and compute λ-brackets between them. Provided some assumptions on a classical affine fractional W-algebra, we find an infinite sequence of integrable systems related to the algebra, using the generalized Drinfel’d and Sokolov reduction.
GRIDS: Grid-Scale Rampable Intermittent Dispatchable Storage
2010-09-01
GRIDS Project: The 12 projects that comprise ARPA-E’s GRIDS Project, short for “Grid-Scale Rampable Intermittent Dispatchable Storage,” are developing storage technologies that can store renewable energy for use at any location on the grid at an investment cost less than $100 per kilowatt hour. Flexible, large-scale storage would create a stronger and more robust electric grid by enabling renewables to contribute to reliable power generation.
Arc Length Based Grid Distribution For Surface and Volume Grids
NASA Technical Reports Server (NTRS)
Mastin, C. Wayne
1996-01-01
Techniques are presented for distributing grid points on parametric surfaces and in volumes according to a specified distribution of arc length. Interpolation techniques are introduced which permit a given distribution of grid points on the edges of a three-dimensional grid block to be propagated through the surface and volume grids. Examples demonstrate how these methods can be used to improve the quality of grids generated by transfinite interpolation.
Shifted genus expanded W ∞ algebra and shifted Hurwitz numbers
NASA Astrophysics Data System (ADS)
Zheng, Quan
2016-05-01
We construct the shifted genus expanded W ∞ algebra, which is isomorphic to the central subalgebra A ∞ of infinite symmetric group algebra and to the shifted Schur symmetrical function algebra Λ* defined by Okounkov and Olshanskii. As an application, we get some differential equations for the generating functions of the shifted Hurwitz numbers; thus, we can express the generating functions in terms of the shifted genus expanded cut-and-join operators.
Constraint algebra in bigravity
Soloviev, V. O.
2015-07-15
The number of degrees of freedom in bigravity theory is found for a potential of general form and also for the potential proposed by de Rham, Gabadadze, and Tolley (dRGT). This aim is pursued via constructing a Hamiltonian formalismand studying the Poisson algebra of constraints. A general potential leads to a theory featuring four first-class constraints generated by general covariance. The vanishing of the respective Hessian is a crucial property of the dRGT potential, and this leads to the appearance of two additional second-class constraints and, hence, to the exclusion of a superfluous degree of freedom—that is, the Boulware—Deser ghost. The use of a method that permits avoiding an explicit expression for the dRGT potential is a distinctive feature of the present study.
A new Rayleigh quotient minimization algorithm based on algebraic multigrid.
Lehoucq, Richard B.; Hetmaniuk, Ulrich L.
2005-01-01
Mandel and McCormick [2] introduced the RQMG method, which approximately minimizes the Rayleigh quotient over a sequence of grids. In this talk, we will present an algebraic extension. We replace the geometric mesh information with the algebraic information defined by an AMG preconditioner. At each level, we improve the smoother to accelerate the convergence. With a series of numerical experiments, we assess the efficiency of this new algorithm to compute several eigenpairs.
Algorithmic Questions for Linear Algebraic Groups. Ii
NASA Astrophysics Data System (ADS)
Sarkisjan, R. A.
1982-04-01
It is proved that, given a linear algebraic group defined over an algebraic number field and satisfying certain conditions, there exists an algorithm which determines whether or not two double cosets of a special type coincide in its adele group, and which enumerates all such double cosets. This result is applied to the isomorphism problem for finitely generated nilpotent groups, and also to other problems.Bibliography: 18 titles.
Single axioms for Boolean algebra.
McCune, W.
2000-06-30
Explicit single axioms are presented for Boolean algebra in terms of (1) the Sheffer stroke; (2) disjunction and negation; (3) disjunction, conjunction, and negation; and (4) disjunction, conjunction, negation, 0, and 1. It was previously known that single axioms exist for these systems, but the procedures to generate them are exponential, producing huge equations. Automated deduction techniques were applied to find axioms of lengths 105, 131, 111, and 127, respectively, each with six variables.
Near-Body Grid Adaption for Overset Grids
NASA Technical Reports Server (NTRS)
Buning, Pieter G.; Pulliam, Thomas H.
2016-01-01
A solution adaption capability for curvilinear near-body grids has been implemented in the OVERFLOW overset grid computational fluid dynamics code. The approach follows closely that used for the Cartesian off-body grids, but inserts refined grids in the computational space of original near-body grids. Refined curvilinear grids are generated using parametric cubic interpolation, with one-sided biasing based on curvature and stretching ratio of the original grid. Sensor functions, grid marking, and solution interpolation tasks are implemented in the same fashion as for off-body grids. A goal-oriented procedure, based on largest error first, is included for controlling growth rate and maximum size of the adapted grid system. The adaption process is almost entirely parallelized using MPI, resulting in a capability suitable for viscous, moving body simulations. Two- and three-dimensional examples are presented.
Connecting Algebra and Chemistry.
ERIC Educational Resources Information Center
O'Connor, Sean
2003-01-01
Correlates high school chemistry curriculum with high school algebra curriculum and makes the case for an integrated approach to mathematics and science instruction. Focuses on process integration. (DDR)
Reno, Matthew J.; Riehm, Andrew Charles; Hoekstra, Robert John; Munoz-Ramirez, Karina; Stamp, Jason Edwin; Phillips, Laurence R.; Adams, Brian M.; Russo, Thomas V.; Oldfield, Ron A.; McLendon, William Clarence, III; Nelson, Jeffrey Scott; Hansen, Clifford W.; Richardson, Bryan T.; Stein, Joshua S.; Schoenwald, David Alan; Wolfenbarger, Paul R.
2011-02-01
Design and operation of the electric power grid (EPG) relies heavily on computational models. High-fidelity, full-order models are used to study transient phenomena on only a small part of the network. Reduced-order dynamic and power flow models are used when analysis involving thousands of nodes are required due to the computational demands when simulating large numbers of nodes. The level of complexity of the future EPG will dramatically increase due to large-scale deployment of variable renewable generation, active load and distributed generation resources, adaptive protection and control systems, and price-responsive demand. High-fidelity modeling of this future grid will require significant advances in coupled, multi-scale tools and their use on high performance computing (HPC) platforms. This LDRD report demonstrates SNL's capability to apply HPC resources to these 3 tasks: (1) High-fidelity, large-scale modeling of power system dynamics; (2) Statistical assessment of grid security via Monte-Carlo simulations of cyber attacks; and (3) Development of models to predict variability of solar resources at locations where little or no ground-based measurements are available.
NASA Astrophysics Data System (ADS)
Zhou, Yi; Nagata, Kouji; Sakai, Yasuhiko; Ito, Yasumasa; Hayase, Toshiyuki
2016-04-01
Direct numerical simulations are performed to investigate the helical properties of single-square-grid-generated turbulence. The streamwise evolution of the probability density functions of the relative helicity density h reveals the existence of a transition from a quasi-two-dimensional state to a three-dimensional state. The correlations between the helicity and the enstrophy level as well as the dissipation level are examined. When conditioned on a high level of dissipation or enstrophy, in the energy decay region the velocity and vorticity vectors in both instantaneous and fluctuating fields become more aligned. However, this correlation does not hold in the production region. We also study the second-order structure function and reveal that a well-defined 2/3 power-law can be found at a location quite close to the grid, where the turbulent flow is still in the transition state.
NASA Astrophysics Data System (ADS)
Onda, Hiroshi; Ozawa, Seiichi
A macro-action is a typical series of useful actions that brings high expected rewards to an agent. Murata et al. have proposed an Actor-Critic model which can generate macro-actions automatically based on the information on state values and visiting frequency of states. However, their model has not assumed that generated macro-actions are utilized for leaning different tasks. In this paper, we extend the Murata's model such that generated macro-actions can help an agent learn an optimal policy quickly in multi-task Grid-World (MTGW) maze problems. The proposed model is applied to two MTGW problems, each of which consists of six different maze tasks. From the experimental results, it is concluded that the proposed model could speed up learning if macro-actions are generated in the so-called correlated regions.
ERIC Educational Resources Information Center
Merlin, Ethan M.
2013-01-01
This article describes how the author has developed tasks for students that address the missed "essence of the matter" of algebraic transformations. Specifically, he has found that having students practice "perceiving" algebraic structure--by naming the "glue" in the expressions, drawing expressions using…
ERIC Educational Resources Information Center
Levy, Alissa Beth
2012-01-01
The California Department of Education (CDE) has long asserted that success Algebra I by Grade 8 is the goal for all California public school students. In fact, the state's accountability system penalizes schools that do not require all of their students to take the Algebra I end-of-course examination by Grade 8 (CDE, 2009). In this…
NASA Technical Reports Server (NTRS)
Lawson, C. L.; Krogh, F. T.; Gold, S. S.; Kincaid, D. R.; Sullivan, J.; Williams, E.; Hanson, R. J.; Haskell, K.; Dongarra, J.; Moler, C. B.
1982-01-01
The Basic Linear Algebra Subprograms (BLAS) library is a collection of 38 FORTRAN-callable routines for performing basic operations of numerical linear algebra. BLAS library is portable and efficient source of basic operations for designers of programs involving linear algebriac computations. BLAS library is supplied in portable FORTRAN and Assembler code versions for IBM 370, UNIVAC 1100 and CDC 6000 series computers.
ERIC Educational Resources Information Center
Cavanagh, Sean
2008-01-01
A popular humorist and avowed mathphobe once declared that in real life, there's no such thing as algebra. Kathie Wilson knows better. Most of the students in her 8th grade class will be thrust into algebra, the definitive course that heralds the beginning of high school mathematics, next school year. The problem: Many of them are about three…
Algebraic independence properties related to certain infinite products
NASA Astrophysics Data System (ADS)
Tanaka, Taka-aki
2011-09-01
In this paper we establish algebraic independence of the values of a certain infinite product as well as its all successive derivatives at algebraic points other than its zeroes, using the fact that the logarithmic derivative of an infinite product gives a partial fraction expansion. Such an infinite product is generated by a linear recurrence. The method used for proving the algebraic independence is based on the theory of Mahler functions of several variables.
ERIC Educational Resources Information Center
Hewitt, Dave
2012-01-01
This study looks at a mixed ability group of 21 Year 5 primary students (aged 9-10 years old) who had previously never had formal instruction using letters to stand for unknowns or variables in a mathematics context; nor had they been introduced to formal algebraic notation. Three lessons were taught using the computer software "Grid Algebra"…
Unstructured grid research and use at NASA Lewis Research Center
NASA Technical Reports Server (NTRS)
Potapczuk, Mark G.
1993-01-01
Computational fluid dynamics applications of grid research at LRC include inlets, nozzles, and ducts; turbomachinery; propellers - ducted and unducted; and aircraft icing. Some issues related to internal flow grid generation are resolution requirements on several boundaries, shock resolution vs. grid periodicity, grid spacing at blade/shroud gap, grid generation in turbine blade passages, and grid generation for inlet/nozzle geometries. Aircraft icing grid generation issues include (1) small structures relative to airfoil chord must be resolved; (2) excessive number of grid points in far-field using structured grid; and (3) grid must be recreated as ice shape grows.
The Algebra of Lexical Semantics
NASA Astrophysics Data System (ADS)
Kornai, András
The current generative theory of the lexicon relies primarily on tools from formal language theory and mathematical logic. Here we describe how a different formal apparatus, taken from algebra and automata theory, resolves many of the known problems with the generative lexicon. We develop a finite state theory of word meaning based on machines in the sense of Eilenberg [11], a formalism capable of describing discrepancies between syntactic type (lexical category) and semantic type (number of arguments). This mechanism is compared both to the standard linguistic approaches and to the formalisms developed in AI/KR.
NASA Technical Reports Server (NTRS)
Slater, John W.; Liou, Meng-Sing; Hindman, Richard G.
1994-01-01
An approach is presented for the generation of two-dimensional, structured, dynamic grids. The grid motion may be due to the motion of the boundaries of the computational domain or to the adaptation of the grid to the transient, physical solution. A time-dependent grid is computed through the time integration of the grid speeds which are computed from a system of grid speed equations. The grid speed equations are derived from the time-differentiation of the grid equations so as to ensure that the dynamic grid maintains the desired qualities of the static grid. The grid equations are the Euler-Lagrange equations derived from a variational statement for the grid. The dynamic grid method is demonstrated for a model problem involving boundary motion, an inviscid flow in a converging-diverging nozzle during startup, and a viscous flow over a flat plate with an impinging shock wave. It is shown that the approach is more accurate for transient flows than an approach in which the grid speeds are computed using a finite difference with respect to time of the grid. However, the approach requires significantly more computational effort.
NASA Astrophysics Data System (ADS)
Dar, Zamiyad
The prices in the electricity market change every five minutes. The prices in peak demand hours can be four or five times more than the prices in normal off peak hours. Renewable energy such as wind power has zero marginal cost and a large percentage of wind energy in a power grid can reduce the price significantly. The variability of wind power prevents it from being constantly available in peak hours. The price differentials between off-peak and on-peak hours due to wind power variations provide an opportunity for a storage device owner to buy energy at a low price and sell it in high price hours. In a large and complex power grid, there are many locations for installation of a storage device. Storage device owners prefer to install their device at locations that allow them to maximize profit. Market participants do not possess much information about the system operator's dispatch, power grid, competing generators and transmission system. The publicly available data from the system operator usually consists of Locational Marginal Prices (LMP), load, reserve prices and regulation prices. In this thesis, we develop a method to find the optimum location of a storage device without using the grid, transmission or generator data. We formulate and solve an optimization problem to find the most profitable location for a storage device using only the publicly available market pricing data such as LMPs, and reserve prices. We consider constraints arising due to storage device operation limitations in our objective function. We use binary optimization and branch and bound method to optimize the operation of a storage device at a given location to earn maximum profit. We use two different versions of our method and optimize the profitability of a storage unit at each location in a 36 bus model of north eastern United States and south eastern Canada for four representative days representing four seasons in a year. Finally, we compare our results from the two versions of our
Semigroups and computer algebra in algebraic structures
NASA Astrophysics Data System (ADS)
Bijev, G.
2012-11-01
Some concepts in semigroup theory can be interpreted in several algebraic structures. A generalization fA,B,fA,B(X) = A(X')B of the complement operator (') on Boolean matrices is made, where A and B denote any rectangular Boolean matrices. While (') is an isomorphism between Boolean semilattices, the generalized complement operator is homomorphism in the general case. The map fA,B and its general inverse (fA,B)+ have quite similar properties to those in the linear algebra and are useful for solving linear equations in Boolean matrix algebras. For binary relations on a finite set, necessary and sufficient conditions for the equation αξβ = γ to have a solution ξ are proved. A generalization of Green's equivalence relations in semigroups for rectangular matrices is proposed. Relationships between them and the Moore-Penrose inverses are investigated. It is shown how any generalized Green's H-class could be constructed by given its corresponding linear subspaces and converted into a group isomorphic to a linear group. Some information about using computer algebra methods concerning this paper is given.
Lie algebra extensions of current algebras on S3
NASA Astrophysics Data System (ADS)
Kori, Tosiaki; Imai, Yuto
2015-06-01
An affine Kac-Moody algebra is a central extension of the Lie algebra of smooth mappings from S1 to the complexification of a Lie algebra. In this paper, we shall introduce a central extension of the Lie algebra of smooth mappings from S3 to the quaternization of a Lie algebra and investigate its root space decomposition. We think this extension of current algebra might give a mathematical tool for four-dimensional conformal field theory as Kac-Moody algebras give it for two-dimensional conformal field theory.
Grid and design variables sensitivity analyses for NACA four-digit wing-sections
NASA Technical Reports Server (NTRS)
Sadrehaghighi, Ideen; Smith, Robert E.; Tiwari, Surendra N.
1993-01-01
Two distinct parameterization procedures are developed for investigating the grid sensitivity with respect to design parameters of a wing-section example. The first procedure is based on traditional (physical) relations defining NACA four-digit wing-sections. The second is advocating a novel (geometrical) parameterization using spline functions such as NURBS (Non-Uniform Rational B-Splines) for defining the wing-section geometry. An interactive algebraic grid generation technique, known as Hermite Cubic Interpolation, is employed to generate C-type grids around wing-sections. The grid sensitivity of the domain with respect to design and grid parameters has been obtained by direct differentiation of the grid equations. A hybrid approach is proposed for more geometrically complex configurations. A comparison of the sensitivity coefficients with those obtained using a finite-difference approach has been made to verify the feasibility of the approach. The aerodynamic sensitivity coefficients are obtained using the compressible two-dimensional thin-layer Navier-Stokes equations.
Twisted conformal algebra related to κ -Minkowski space
NASA Astrophysics Data System (ADS)
Meljanac, Stjepan; Pachoł, Anna; Pikutić, Danijel
2015-11-01
Twisted deformations of the conformal symmetry in the Hopf algebraic framework are constructed. The first one is obtained by a Jordanian twist built up from dilatation and momenta generators. The second is the lightlike κ -deformation of the Poincaré algebra extended to the conformal algebra, obtained by a twist corresponding to the extended Jordanian r -matrix. The κ -Minkowski spacetime is covariant quantum space under both of these deformations. The extension of the conformal algebra by the noncommutative coordinates is presented in two cases. The differential realizations for κ -Minkowski coordinates, as well as their left-right dual counterparts, are also included.
Polynomial Extensions of the Weyl C*-Algebra
NASA Astrophysics Data System (ADS)
Accardi, Luigi; Dhahri, Ameur
2015-09-01
We introduce higher order (polynomial) extensions of the unique (up to isomorphisms) nontrivial central extension of the Heisenberg algebra, which can be concretely realized as sub-Lie algebras of the polynomial algebra generated by the creation and annihilation operators in the Schrödinger representation. The simplest nontrivial of these extensions (the quadratic one) is isomorphic to the Galilei algebra, widely studied in quantum physics. By exponentiation of this representation we construct the corresponding polynomial analogue of the Weyl C*-algebra and compute the polynomial Weyl relations. From this we deduce the explicit form of the composition law of the associated nonlinear extensions of the 1-dimensional Heisenberg group. The above results are used to calculate a simple explicit form of the vacuum characteristic functions of the nonlinear field operators of the Galilei algebra, as well as of their moments. The corresponding measures turn out to be an interpolation family between Gaussian and Meixner, in particular Gamma.
C-Graded vertex algebras and conformal flow
Laber, Rob; Mason, Geoffrey
2014-01-15
We consider C-graded vertex algebras, which are vertex algebras V with a C-grading such that V is an admissible V-module generated by “lowest weight vectors.” We show that such vertex algebras have a “good” representation theory in the sense that there is a Zhu algebra A(V) and a bijection between simple admissible V-modules and simple A(V)-modules. We also consider pseudo vertex operator algebras (PVOAs), which are C-graded vertex algebras with a conformal vector such that the homogeneous subspaces of V are generalized eigenspaces for L(0); essentially, these are VOAs that lack any semisimplicity or integrality assumptions on L(0). As a motivating example, we show that deformation of the conformal structure (conformal flow) of a strongly regular VOA (e.g., a lattice theory, or Wess-Zumino-Witten model) is a path in a space whose points are PVOAs.
Coreflections in Algebraic Quantum Logic
NASA Astrophysics Data System (ADS)
Jacobs, Bart; Mandemaker, Jorik
2012-07-01
Various generalizations of Boolean algebras are being studied in algebraic quantum logic, including orthomodular lattices, orthomodular po-sets, orthoalgebras and effect algebras. This paper contains a systematic study of the structure in and between categories of such algebras. It does so via a combination of totalization (of partially defined operations) and transfer of structure via coreflections.
Four Lie algebras associated with R6 and their applications
NASA Astrophysics Data System (ADS)
Zhang, Yufeng; Tam, Honwah
2010-09-01
The first part in the paper reads that a three-dimensional Lie algebra is first introduced, whose corresponding loop algebra is constructed, for which isospectral problems are established. By employing zero curvature equations, a modified Kaup-Newell (mKN) soliton hierarchy of evolution equations is obtained. The corresponding hereditary operator and Hamiltonian structure are worked out, respectively. Then two types of enlarging semisimple Lie algebras isomorphic to the linear space R6 are followed to construct, one of them is a complex Lie algebra. Their corresponding loop algebras are also given so that two types of new isospectral problems are introduced to generate two kinds of integrable couplings of the above mKN hierarchy. The hereditary operators, Hamiltonian structures of the hierarchies are produced again, respectively. The exact computing formulas of the constant γ appearing in the trace identity and the variational identity are derived under the semisimple algebras. The second part of this paper is devoted to constructing two kinds of Lie algebras by using product of complex vectors, which are also isomorphic to the linear space R6. Then we make use of the corresponding loop algebras to produce two integrable hierarchies along with bi-Hamiltonian structures. From various aspects, we give some ways for constructing Lie algebras which have extensive applications in generating integrable Hamiltonian systems.
Developing Algebraic Thinking.
ERIC Educational Resources Information Center
Alejandre, Suzanne
2002-01-01
Presents a teaching experience that resulted in students getting to a point of full understanding of the kinesthetic activity and the algebra behind it. Includes a lesson plan for a traffic jam activity. (KHR)
Algebraic integrability: a survey.
Vanhaecke, Pol
2008-03-28
We give a concise introduction to the notion of algebraic integrability. Our exposition is based on examples and phenomena, rather than on detailed proofs of abstract theorems. We mainly focus on algebraic integrability in the sense of Adler-van Moerbeke, where the fibres of the momentum map are affine parts of Abelian varieties; as it turns out, most examples from classical mechanics are of this form. Two criteria are given for such systems (Kowalevski-Painlevé and Lyapunov) and each is illustrated in one example. We show in the case of a relatively simple example how one proves algebraic integrability, starting from the differential equations for the integrable vector field. For Hamiltonian systems that are algebraically integrable in the generalized sense, two examples are given, which illustrate the non-compact analogues of Abelian varieties which typically appear in such systems. PMID:17588863
Algebraic Semantics for Narrative
ERIC Educational Resources Information Center
Kahn, E.
1974-01-01
This paper uses discussion of Edmund Spenser's "The Faerie Queene" to present a theoretical framework for explaining the semantics of narrative discourse. The algebraic theory of finite automata is used. (CK)
Post, R.F.
1960-08-01
An electronic grid is designed employing magnetic forces for controlling the passage of charged particles. The grid is particularly applicable to use in gas-filled tubes such as ignitrons. thyratrons, etc., since the magnetic grid action is impartial to the polarity of the charged particles and, accordingly. the sheath effects encountered with electrostatic grids are not present. The grid comprises a conductor having sections spaced apart and extending in substantially opposite directions in the same plane, the ends of the conductor being adapted for connection to a current source.
Aprepro - Algebraic Preprocessor
2005-08-01
Aprepro is an algebraic preprocessor that reads a file containing both general text and algebraic, string, or conditional expressions. It interprets the expressions and outputs them to the output file along witht the general text. Aprepro contains several mathematical functions, string functions, and flow control constructs. In addition, functions are included that, with some additional files, implement a units conversion system and a material database lookup system.
Geometric Algebra for Physicists
NASA Astrophysics Data System (ADS)
Doran, Chris; Lasenby, Anthony
2007-11-01
Preface; Notation; 1. Introduction; 2. Geometric algebra in two and three dimensions; 3. Classical mechanics; 4. Foundations of geometric algebra; 5. Relativity and spacetime; 6. Geometric calculus; 7. Classical electrodynamics; 8. Quantum theory and spinors; 9. Multiparticle states and quantum entanglement; 10. Geometry; 11. Further topics in calculus and group theory; 12. Lagrangian and Hamiltonian techniques; 13. Symmetry and gauge theory; 14. Gravitation; Bibliography; Index.
Covariant deformed oscillator algebras
NASA Technical Reports Server (NTRS)
Quesne, Christiane
1995-01-01
The general form and associativity conditions of deformed oscillator algebras are reviewed. It is shown how the latter can be fulfilled in terms of a solution of the Yang-Baxter equation when this solution has three distinct eigenvalues and satisfies a Birman-Wenzl-Murakami condition. As an example, an SU(sub q)(n) x SU(sub q)(m)-covariant q-bosonic algebra is discussed in some detail.
A process algebra model of QED
NASA Astrophysics Data System (ADS)
Sulis, William
2016-03-01
The process algebra approach to quantum mechanics posits a finite, discrete, determinate ontology of primitive events which are generated by processes (in the sense of Whitehead). In this ontology, primitive events serve as elements of an emergent space-time and of emergent fundamental particles and fields. Each process generates a set of primitive elements, using only local information, causally propagated as a discrete wave, forming a causal space termed a causal tapestry. Each causal tapestry forms a discrete and finite sampling of an emergent causal manifold (space-time) M and emergent wave function. Interactions between processes are described by a process algebra which possesses 8 commutative operations (sums and products) together with a non-commutative concatenation operator (transitions). The process algebra possesses a representation via nondeterministic combinatorial games. The process algebra connects to quantum mechanics through the set valued process and configuration space covering maps, which associate each causal tapestry with sets of wave functions over M. Probabilities emerge from interactions between processes. The process algebra model has been shown to reproduce many features of the theory of non-relativistic scalar particles to a high degree of accuracy, without paradox or divergences. This paper extends the approach to a semi-classical form of quantum electrodynamics.
NASA Astrophysics Data System (ADS)
Hiley, B. J.
In this chapter, we examine in detail the non-commutative symplectic algebra underlying quantum dynamics. By using this algebra, we show that it contains both the Weyl-von Neumann and the Moyal quantum algebras. The latter contains the Wigner distribution as the kernel of the density matrix. The underlying non-commutative geometry can be projected into either of two Abelian spaces, so-called `shadow phase spaces'. One of these is the phase space of Bohmian mechanics, showing that it is a fragment of the basic underlying algebra. The algebraic approach is much richer, giving rise to two fundamental dynamical time development equations which reduce to the Liouville equation and the Hamilton-Jacobi equation in the classical limit. They also include the Schrödinger equation and its wave-function, showing that these features are a partial aspect of the more general non-commutative structure. We discuss briefly the properties of this more general mathematical background from which the non-commutative symplectic algebra emerges.
DG Poisson algebra and its universal enveloping algebra
NASA Astrophysics Data System (ADS)
Lü, JiaFeng; Wang, XingTing; Zhuang, GuangBin
2016-05-01
In this paper, we introduce the notions of differential graded (DG) Poisson algebra and DG Poisson module. Let $A$ be any DG Poisson algebra. We construct the universal enveloping algebra of $A$ explicitly, which is denoted by $A^{ue}$. We show that $A^{ue}$ has a natural DG algebra structure and it satisfies certain universal property. As a consequence of the universal property, it is proved that the category of DG Poisson modules over $A$ is isomorphic to the category of DG modules over $A^{ue}$. Furthermore, we prove that the notion of universal enveloping algebra $A^{ue}$ is well-behaved under opposite algebra and tensor product of DG Poisson algebras. Practical examples of DG Poisson algebras are given throughout the paper including those arising from differential geometry and homological algebra.
The Taylor spectrum and transversality for a Heisenberg algebra of operators
Dosi, Anar A
2010-05-11
A problem on noncommutative holomorphic functional calculus is considered for a Banach module over a finite-dimensional nilpotent Lie algebra. As the main result, the transversality property of algebras of noncommutative holomorphic functions with respect to the Taylor spectrum is established for a family of bounded linear operators generating a Heisenberg algebra. Bibliography: 25 titles.
On unstructured grids and solvers
NASA Technical Reports Server (NTRS)
Barth, T. J.
1990-01-01
The fundamentals and the state-of-the-art technology for unstructured grids and solvers are highlighted. Algorithms and techniques pertinent to mesh generation are discussed. It is shown that grid generation and grid manipulation schemes rely on fast multidimensional searching. Flow solution techniques for the Euler equations, which can be derived from the integral form of the equations are discussed. Sample calculations are also provided.
Algebraic multigrid preconditioner for the cardiac bidomain model.
Plank, Gernot; Liebmann, Manfred; Weber dos Santos, Rodrigo; Vigmond, Edward J; Haase, Gundolf
2007-04-01
The bidomain equations are considered to be one of the most complete descriptions of the electrical activity in cardiac tissue, but large scale simulations, as resulting from discretization of an entire heart, remain a computational challenge due to the elliptic portion of the problem, the part associated with solving the extracellular potential. In such cases, the use of iterative solvers and parallel computing environments are mandatory to make parameter studies feasible. The preconditioned conjugate gradient (PCG) method is a standard choice for this problem. Although robust, its efficiency greatly depends on the choice of preconditioner. On structured grids, it has been demonstrated that a geometric multigrid preconditioner performs significantly better than an incomplete LU (ILU) preconditioner. However, unstructured grids are often preferred to better represent organ boundaries and allow for coarser discretization in the bath far from cardiac surfaces. Under these circumstances, algebraic multigrid (AMG) methods are advantageous since they compute coarser levels directly from the system matrix itself, thus avoiding the complexity of explicitly generating coarser, geometric grids. In this paper, the performance of an AMG preconditioner (BoomerAMG) is compared with that of the standard ILU preconditioner and a direct solver. BoomerAMG is used in two different ways, as a preconditioner and as a standalone solver. Two 3-D simulation examples modeling the induction of arrhythmias in rabbit ventricles were used to measure performance in both sequential and parallel simulations. It is shown that the AMG preconditioner is very well suited for the solution of the bidomain equation, being clearly superior to ILU preconditioning in all regards, with speedups by factors in the range 5.9-7.7. PMID:17405366
Constructive Learning in Undergraduate Linear Algebra
ERIC Educational Resources Information Center
Chandler, Farrah Jackson; Taylor, Dewey T.
2008-01-01
In this article we describe a project that we used in our undergraduate linear algebra courses to help our students successfully master fundamental concepts and definitions and generate interest in the course. We describe our philosophy and discuss the projects overall success.
Octonions and subalgebras of the exceptional algebras
NASA Astrophysics Data System (ADS)
Buccella, F.; Della Selva, A.; Sciarrino, A.
1989-03-01
The vector space of the generators of E8 is realized in terms of 3×3 traceless matrices, two independent sets of octonions imaginary units, and the two G2 acting on them. In this way one gets an appropriate framework to describe in a simple way how exceptional algebras and their fundamental representations transform under their subalgebras.
NASA Astrophysics Data System (ADS)
Stegall, S. T.; Zhang, H. M.; Shi, L.
2014-12-01
Presently there exist data gaps in global surface temperature products such as NOAATemp and other international datasets. Studies have indicated that these data gaps may have an impact on derived global temperature trends in these datasets, particularly in the recent decade or so. This is an important area for improving the NOAATemp dataset. While gaps in in situ data coverage are expected to continue in the foreseeable future, satellite data are available over these regions, and some studies have shown the potential usefulness of satellite data to mitigate the impact of these gaps in in situdata. Thus it is important to systematically evaluate the potential utility of satellite data in gap filling, such as using the NOAA NCDC's 2-m air temperature dataset retrieved from NOAA POES satellite's HIRS measurements. Comparisons of monthly gridded HIRS T2m to NOAATemp will be presented. Similarities and differences in spatial patterns, global averages, and trends between the two data sets will be shown and discussed, including zonal, meridional, and global averages and other statistics. High-quality USCRN station data and HIRS will also be compared, and RMSE and biases will be analyzed and presented.
Compatible Relaxation and Coarsening in Algebraic Multigrid
Brannick, J J; Falgout, R D
2009-09-22
We introduce a coarsening algorithm for algebraic multigrid (AMG) based on the concept of compatible relaxation (CR). The algorithm is significantly different from standard methods, most notably because it does not rely on any notion of strength of connection. We study its behavior on a number of model problems, and evaluate the performance of an AMG algorithm that incorporates the coarsening approach. Lastly, we introduce a variant of CR that provides a sharper metric of coarse-grid quality and demonstrate its potential with two simple examples.
Spatial Operator Algebra for multibody system dynamics
NASA Technical Reports Server (NTRS)
Rodriguez, G.; Jain, A.; Kreutz-Delgado, K.
1992-01-01
The Spatial Operator Algebra framework for the dynamics of general multibody systems is described. The use of a spatial operator-based methodology permits the formulation of the dynamical equations of motion of multibody systems in a concise and systematic way. The dynamical equations of progressively more complex grid multibody systems are developed in an evolutionary manner beginning with a serial chain system, followed by a tree topology system and finally, systems with arbitrary closed loops. Operator factorizations and identities are used to develop novel recursive algorithms for the forward dynamics of systems with closed loops. Extensions required to deal with flexible elements are also discussed.
White, Vicky
2003-05-21
By now almost everyone has heard of 'The Grid', or 'Grid Computing' as it should more properly be described. There are frequent articles in both the popular and scientific press talking about 'The Grid' or about some specific Grid project. Run II Experiments, US-CMS, BTeV, the Sloane Digital Sky Survey and the Lattice QCD folks are all incorporating aspects of Grid Computing in their plans, and the Fermilab Computing Division is supporting and encouraging these efforts. Why are we doing this and what does it have to do with running a physics experiment or getting scientific results? I will explore some of these questions and try to give an overview, not so much of the technical aspects of Grid Computing, rather of what the phenomenon means for our field.
NASA Astrophysics Data System (ADS)
Chung, S. H.; Lee-Taylor, J.; Asher, W.; Hodzic, A.; Madronich, S.; Aumont, B.; Pankow, J. F.; Barsanti, K. C.
2012-12-01
A major weakness in current air quality and climate models is the ability to simulate secondary organic aerosol (SOA) levels and physiochemical properties accurately. A new approach to model SOA formation is the carbon number (nc) polarity grid (CNPG) framework. The CNPG framework makes use of a nc vs. polarity grid for representing relevant organic compounds and their time-dependent concentrations. The nc vs polarity grid is well suited for modeling SOA because nc together with some suitable measure of total molecular polarity provides the minimum yet sufficient formation for estimating the parameters required to calculate partitioning coefficients. Furthermore, CNPG allows consideration of the effects of variation in the activity coefficients of the partitioning compounds, variation in the mean molecular weight of the absorbing organic phase, water uptake, and the possibility of phase separation in the organic aerosol phase. In this work, we use the GECKO-A (Generator of Explicit Chemistry and Kinetics of Organics in the Atmosphere) chemistry mechanism to produce the chemical structures of SOA precursor oxidization products and their time-dependent concentrations. The SIMPOL group contribution method is used to calculate the enthalpy of vaporization ΔHvap for each product. The total molecular polarity is then calculated as ΔHvap,diff, the difference between each compound's ΔHvap and that of its carbon-number equivalent straight-chain hydrocarbon. The gas- and particle-phase concentrations of each compound are mapped onto the nc vs polarity grid as a function of time to evaluate the time evolution of SOA-relevant oxidation products and to help guide lumping strategies for reducing complexity. In addition to using ΔHvap,diff, use of other measures of polarity will also be explored. Initial SOA precursor studies include toluene (C7) + n-heptadecane (C17) and α-pinene, under atmospherically relevant conditions. Results will be discussed in the context of the
Algebraic properties of basic isohedral marked tilings
NASA Astrophysics Data System (ADS)
Greco, Gabriele H.
2006-05-01
In 1977 Grünbaum and Shephard described all possible 93 types of isohedral marked tilings of the plane; 46 of them are called basic, since their induced tile group is trivial. The aim of this paper is to give an algebraic description of all basic tilings. A purely algebraic characterization of the adjacency symmetries of tiles of the 46 basic tilings is presented. Moreover, 46 related abstract definitions of two-dimensional crystallographic groups supplement and extend those of the well-known book Generators and Relations for Discrete Groups by Coxeter and Moser.
Some remarks on representations of Yang-Mills algebras
NASA Astrophysics Data System (ADS)
Herscovich, Estanislao
2015-01-01
In this article, we present some new properties of representations of Yang-Mills algebras. We first show that any free Lie algebra with m generators is a quotient of the Yang-Mills algebra 𝔶𝔪(n) on n generators, for n ≥ 2m. We derive from this that any semisimple Lie algebra and even any affine Kac-Moody algebra is a quotient of 𝔶𝔪(n) for n ≥ 4. Combining this with previous results on representations of Yang-Mills algebras given in [Herscovich and Solotar, Ann. Math. 173(2), 1043-1080 (2011)], one may obtain solutions to the Yang-Mills equations by differential operators acting on sections of twisted vector bundles on the affine space of dimension n ≥ 4 associated to representations of any semisimple Lie algebra. We also show that this quotient property does not hold for n = 3, since any morphism of Lie algebras from 𝔶𝔪(3) to 𝔰𝔩(2, k) has in fact solvable image.
Permutation centralizer algebras and multimatrix invariants
NASA Astrophysics Data System (ADS)
Mattioli, Paolo; Ramgoolam, Sanjaye
2016-03-01
We introduce a class of permutation centralizer algebras which underly the combinatorics of multimatrix gauge-invariant observables. One family of such noncommutative algebras is parametrized by two integers. Its Wedderburn-Artin decomposition explains the counting of restricted Schur operators, which were introduced in the physics literature to describe open strings attached to giant gravitons and were subsequently used to diagonalize the Gaussian inner product for gauge invariants of two-matrix models. The structure of the algebra, notably its dimension, its center and its maximally commuting subalgebra, is related to Littlewood-Richardson numbers for composing Young diagrams. It gives a precise characterization of the minimal set of charges needed to distinguish arbitrary matrix gauge invariants, which are related to enhanced symmetries in gauge theory. The algebra also gives a star product for matrix invariants. The center of the algebra allows efficient computation of a sector of multimatrix correlators. These generate the counting of a certain class of bicoloured ribbon graphs with arbitrary genus.
The kinematic algebras from the scattering equations
NASA Astrophysics Data System (ADS)
Monteiro, Ricardo; O'Connell, Donal
2014-03-01
We study kinematic algebras associated to the recently proposed scattering equations, which arise in the description of the scattering of massless particles. In particular, we describe the role that these algebras play in the BCJ duality between colour and kinematics in gauge theory, and its relation to gravity. We find that the scattering equations are a consistency condition for a self-dual-type vertex which is associated to each solution of those equations. We also identify an extension of the anti-self-dual vertex, such that the two vertices are not conjugate in general. Both vertices correspond to the structure constants of Lie algebras. We give a prescription for the use of the generators of these Lie algebras in trivalent graphs that leads to a natural set of BCJ numerators. In particular, we write BCJ numerators for each contribution to the amplitude associated to a solution of the scattering equations. This leads to a decomposition of the determinant of a certain kinematic matrix, which appears naturally in the amplitudes, in terms of trivalent graphs. We also present the kinematic analogues of colour traces, according to these algebras, and the associated decomposition of that determinant.
NASA Technical Reports Server (NTRS)
Swinbank, Richard; Purser, James
2006-01-01
Recent years have seen a resurgence of interest in a variety of non-standard computational grids for global numerical prediction. The motivation has been to reduce problems associated with the converging meridians and the polar singularities of conventional regular latitude-longitude grids. A further impetus has come from the adoption of massively parallel computers, for which it is necessary to distribute work equitably across the processors; this is more practicable for some non-standard grids. Desirable attributes of a grid for high-order spatial finite differencing are: (i) geometrical regularity; (ii) a homogeneous and approximately isotropic spatial resolution; (iii) a low proportion of the grid points where the numerical procedures require special customization (such as near coordinate singularities or grid edges). One family of grid arrangements which, to our knowledge, has never before been applied to numerical weather prediction, but which appears to offer several technical advantages, are what we shall refer to as "Fibonacci grids". They can be thought of as mathematically ideal generalizations of the patterns occurring naturally in the spiral arrangements of seeds and fruit found in sunflower heads and pineapples (to give two of the many botanical examples). These grids possess virtually uniform and highly isotropic resolution, with an equal area for each grid point. There are only two compact singular regions on a sphere that require customized numerics. We demonstrate the practicality of these grids in shallow water simulations, and discuss the prospects for efficiently using these frameworks in three-dimensional semi-implicit and semi-Lagrangian weather prediction or climate models.