Applications of algebraic grid generation
NASA Technical Reports Server (NTRS)
Eiseman, Peter R.; Smith, Robert E.
1990-01-01
Techniques and applications of algebraic grid generation are described. The techniques are univariate interpolations and transfinite assemblies of univariate interpolations. Because algebraic grid generation is computationally efficient, the use of interactive graphics in conjunction with the techniques is advocated. A flexible approach, which works extremely well in an interactive environment, called the control point form of algebraic grid generation is described. The applications discussed are three-dimensional grids constructed about airplane and submarine configurations.
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.
Algebraic grid generation for complex geometries
NASA Technical Reports Server (NTRS)
Shih, T. I.-P.; Bailey, R. T.; Nguyen, H. L.; Roelke, R. J.
1991-01-01
An efficient computer program called GRID2D/3D has been developed to generate single and composite grid systems within geometrically complex two- and three-dimensional (2D and 3D) spatial domains that can deform with time. GRID2D/3D generates single grid systems by using algebraic grid generation methods based on transfinite interpolation. The distribution of grid points within the spatial domain is controlled by stretching functions and 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 2D spatial domains the boundary curves are constructed by using either cubic or tension spline interpolation. For 3D spatial domains the boundary surfaces are constructed by using a new technique, developed in this study, referred to as 3D bidirectional Hermite interpolation.
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.
Interactive algebraic grid-generation technique
NASA Technical Reports Server (NTRS)
Smith, R. E.; Wiese, M. R.
1986-01-01
An algebraic grid generation technique and use of an associated interactive computer program are described. The technique, called the two boundary technique, is based on Hermite cubic interpolation between two fixed, nonintersecting boundaries. The boundaries are referred to as the bottom and top, and they are defined by two ordered sets of points. Left and right side boundaries which intersect the bottom and top boundaries may also be specified by two ordered sets of points. when side boundaries are specified, linear blending functions are used to conform interior interpolation to the side boundaries. Spacing between physical grid coordinates is determined as a function of boundary data and uniformly space 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 presented. The technique works best in an interactive graphics environment where computational displays and user responses are quickly exchanged. An interactive computer program based on the technique and called TBGG (two boundary grid generation) is also described.
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 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.
HOMAR: A computer code for generating homotopic grids using algebraic relations: User's manual
NASA Technical Reports Server (NTRS)
Moitra, Anutosh
1989-01-01
A computer code for fast automatic generation of quasi-three-dimensional grid systems for aerospace configurations is described. The code employs a homotopic method to algebraically generate two-dimensional grids in cross-sectional planes, which are stacked to produce a three-dimensional grid system. Implementation of the algebraic equivalents of the homotopic relations for generating body geometries and grids are explained. Procedures for controlling grid orthogonality and distortion are described. Test cases with description and specification of inputs are presented in detail. The FORTRAN computer program and notes on implementation and use are included.
HOMAR: A computer code for generating homotopic grids using algebraic relations: User's manual
NASA Astrophysics Data System (ADS)
Moitra, Anutosh
1989-07-01
A computer code for fast automatic generation of quasi-three-dimensional grid systems for aerospace configurations is described. The code employs a homotopic method to algebraically generate two-dimensional grids in cross-sectional planes, which are stacked to produce a three-dimensional grid system. Implementation of the algebraic equivalents of the homotopic relations for generating body geometries and grids are explained. Procedures for controlling grid orthogonality and distortion are described. Test cases with description and specification of inputs are presented in detail. The FORTRAN computer program and notes on implementation and use are included.
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.
FASTWO - A 2-D interactive algebraic grid generator
NASA Technical Reports Server (NTRS)
Luh, Raymond Ching-Chung; Lombard, C. K.
1988-01-01
This paper presents a very simple and effective computational procedure, FASTWO, for generating patched composite finite difference grids in 2-D for any geometry. Major components of the interactive graphics based method that is closely akin to and borrows many tools from transfinite interpolation are highlighted. Several grids produced by FASTWO are shown to illustrate its powerful capability. Comments about extending the methodology to 3-D are also given.
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.
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.
Algebraic-hyperbolic grid generation with precise control of intersection of angles
NASA Astrophysics Data System (ADS)
Brakhage, Karl-Heinz; Müller, Siegfried
2000-05-01
A new approach to construct high quality meshes for flow calculations is investigated in the context of algebraic grid generation, where the angle of intersection between two alternate co-ordinate lines can be specified by the user. From an initial grid, new co-ordinate lines in one parameter direction are determined by solving a set of ordinary differential equations (ODE). These trajectories intersect the alternate co-ordinate lines of the initial grid in a prescribed angle. The resulting grid function is proven to be folding-free. The advantages with respect to grid quality achieved by prescribing the angles are gained at the expense that the boundary distribution can only be prescribed on three of four boundaries. In view of a sparse representation of the grid function, the points of intersection are interpolated by a B-spline surface. Thus, the grid can be accessed evaluating the generated parametric representation of the computational domain. Investigations of several test configurations have shown that useful grids with high resolution can be computed from the B-spline representation only depending on a small number of locally chosen parameters. Therefore, only a small amount of computational memory is required for storing these parameters and evaluating the grid function can be efficiently performed at reduced computational costs. This is particularly promising when the mesh has to be frequently changed or updated in time. Copyright
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.
Algebraic Grid Generation for an Afterbody with Finite Span, Tapered Fins.
1986-10-01
of conformal mapping and transfinite interpolation. The method is an extension of previous work for the generation of a 3-D grid about an afterbody...a combination of conformal mapping and transfinite interpolation. The method is an extension of previous work for the generation of a 3-D grid about...intersection - see Fig. 5 zF fin airfoil thickness - see Fig. 5 F ,r normalized coordinates used in transfinite interpolation I - -~r~nw~t#~JtAJ4Ufwig
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.
Parallel unstructured grid generation
NASA Technical Reports Server (NTRS)
Loehner, Rainald; Camberos, Jose; Merriam, Marshal
1991-01-01
A parallel unstructured grid generation algorithm is presented and implemented on the Hypercube. Different processor hierarchies are discussed, and the appropraite hierarchies for mesh generation and mesh smoothing are selected. A domain-splitting algorithm for unstructured grids which tries to minimize the surface-to-volume ratio of each subdomain is described. This splitting algorithm is employed both for grid generation and grid smoothing. Results obtained on the Hypercube demonstrate the effectiveness of the algorithms developed.
Unstructured surface grid generation
NASA Technical Reports Server (NTRS)
Samareh-Abolhassani, Jamshid
1993-01-01
Viewgraphs on unstructured surface grid generation are presented. Topics covered include: requirements for curves, surfaces, solids, and text; surface approximation; triangulation; advancing; projection; mapping; and parametric curves.
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.
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.
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
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.
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.
Shuttle computational grid generation
NASA Technical Reports Server (NTRS)
Ing, Chang
1987-01-01
The well known Karman-Trefftz conformal transformation, consisting of repeated applications of the same basic formula, were found to be quite successful to body, wing, and wing-body cross sections. This grid generation technique is extended to cross sections of more complex forms, and also more automatic. Computer programs were written for the selection of hinge points on cross section with angular shapes, the Karman-Trefftz tranformation of arbitrary shapes, and the special transform of hinge point on the imaginary axis. A feasibility study is performed for the future application of conformal mapping grid generation to complex three dimensional configurations. Examples such as Orbiter vehicle section and a few others were used.
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.
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.
Grid generation strategies for turbomachinery configurations
NASA Technical Reports Server (NTRS)
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.
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
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.
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.
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.
Surface grid generation for multi-block structured grids
NASA Astrophysics Data System (ADS)
Spekreijse, S. P.; Boerstoel, J. W.; Kuyvenhoven, J. L.; van der Marel, M. J.
A new grid generation technique for the computation of a structured grid on a generally curved surface in 3D is discussed. The starting assumption is that the parameterization of the surface exists, i.e. a smooth geometrical shape function exists which maps the parametric space (the unit square) one-to-one on the surface. The grid generation system computes a grid on the surface with as boundary conditions the following data specified along the four edges of the surface: (1) the position of the boundary grid points, (2) the grid line slopes at the boundary grid points, (3) the first grid cell lengths at the boundary grid points. The fourth-order elliptic biharmonic equations are used to compute the two families of grid lines in the parametric space. After that, each grid point in the parametric space is found as the intersection point between two individual grid lines, one from each family. The grid points on the surface are finally found by mapping the grid points in the parametric space on the surface via the geometrical shape function. Results are shown for an O-type 2D Euler grid, a C-type 2D Navier-Stokes grid and on some curved surfaces in 3D space.
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.
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.
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.
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.
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.
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.
Surface grid generation in a parameter space
NASA Astrophysics Data System (ADS)
Samareh-Abolhassani, Jamshid; Stewart, John E.
1994-07-01
A robust and efficient technique is discussed for surface-grid generation on a general curvilinear surface. This technique is based on a nonuniform parameter space and allows for the generation of surface grids on highly skewed and nonuniform spaced background surface-grids. This method has been successfully integrated into the GRIDGEN software system.
Surface Grid Generation in a Parameter Space
NASA Astrophysics Data System (ADS)
Samareh-Abolhassani, Jamshid; Stewart, John E.
1994-07-01
A robust and efficient technique is discussed for surface-grid generation on a general curvilinear surface. This technique is based on a non-uniform parameter space and allows for the generation of surface grids on highly skewed and nonuniform spaced background surface-grids. This method has been successfully integrated into the GRIDGEN software system.
Surface grid generation in a parameter space
Samareh-Abolhassani, J.; Stewart, J.E. )
1994-07-01
A robust and efficient technique is discussed for surface-grid generation on a general curvilinear surface. This technique is based on a nonuniform parameter space and allows for the generation of surface grids on highly skewed and nonuniform spaced background surface-grids. This method has been successfully integrated into the GRIDGEN software system. 8 refs., 6 figs.
Surface grid generation in a parameter space
NASA Technical Reports Server (NTRS)
Samareh-Abolhassani, Jamshid; Stewart, John E.
1994-01-01
A robust and efficient technique is discussed for surface-grid generation on a general curvilinear surface. This technique is based on a nonuniform parameter space and allows for the generation of surface grids on highly skewed and nonuniform spaced background surface-grids. This method has been successfully integrated into the GRIDGEN software system.
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
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.
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.
Interactive Hyperbolic Grid Generation for Projectile CFD
1992-05-01
J . F . "A Composite Grid Generation Code for General 3D Regions - The EAGLE Code." AIAA Journal, vol. 26, no. 3, p. 271, March 1988. Thompson , J . F ., and...Grid Generation." AGARD FDP Specialists Meeting on "Mesh Generation for Complex Three-Dimensional Configurations." Leon, Norway, May 1989. Thompson
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.
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.
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.
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.
Parallel unstructured grid generation for computational aerosciences
NASA Technical Reports Server (NTRS)
Shephard, Mark S.
1993-01-01
The objective of this research project is to develop efficient parallel automatic grid generation procedures for use in computational aerosciences. This effort is focused on a parallel version of the Finite Octree grid generator. Progress made during the first six months is reported.
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
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.
Grid generation on surfaces in 3 dimensions
NASA Technical Reports Server (NTRS)
Eiseman, Peter R.
1986-01-01
The development of a surface grid generation algorithm was initiated. The basic adaptive movement technique of mean-value-relaxation was extended from the viewpoint of a single coordinate grid over a surface described by a single scalar function to that of a surface more generally defined by vector functions and covered by a collection of smoothly connected grids. Within the multiconnected assemblage, the application of control was examined in several instances.
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.
Performance of algebraic multi-grid solvers based on unsmoothed and smoothed aggregation schemes
NASA Astrophysics Data System (ADS)
Webster, R.
2001-08-01
A comparison is made of the performance of two algebraic multi-grid (AMG0 and AMG1) solvers for the solution of discrete, coupled, elliptic field problems. In AMG0, the basis functions for each coarse grid/level approximation (CGA) are obtained directly by unsmoothed aggregation, an appropriate scaling being applied to each CGA to improve consistency. In AMG1 they are assembled using a smoothed aggregation with a constrained energy optimization method providing the smoothing. Although more costly, smoothed basis functions provide a better (more consistent) CGA. Thus, AMG1 might be viewed as a benchmark for the assessment of the simpler AMG0. Selected test problems for D'Arcy flow in pipe networks, Fick diffusion, plane strain elasticity and Navier-Stokes flow (in a Stokes approximation) are used in making the comparison. They are discretized on the basis of both structured and unstructured finite element meshes. The range of discrete equation sets covers both symmetric positive definite systems and systems that may be non-symmetric and/or indefinite. Both global and local mesh refinements to at least one order of resolving power are examined. Some of these include anisotropic refinements involving elements of large aspect ratio; in some hydrodynamics cases, the anisotropy is extreme, with aspect ratios exceeding two orders. As expected, AMG1 delivers typical multi-grid convergence rates, which for all practical purposes are independent of mesh bandwidth. AMG0 rates are slower. They may also be more discernibly mesh-dependent. However, for the range of mesh bandwidths examined, the overall cost effectiveness of the two solvers is remarkably similar when a full convergence to machine accuracy is demanded. Thus, the shorter solution times for AMG1 do not necessarily compensate for the extra time required for its costly grid generation. This depends on the severity of the problem and the demanded level of convergence. For problems requiring few iterations, where grid
Johnson Space Center CFD grid generation requirements
NASA Technical Reports Server (NTRS)
Martin, Fred
1993-01-01
Topics are presented in viewgraph form and include the following: heavy lift launch vehicles, space shuttles, space transportation system, grid generation, computational fluid dynamics, space station, and flow distribution.
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
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.
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.
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.
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.
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.
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).
Grid generation for 3D turbine configurations
Reymond, J.D.; Haeuser, J.; Xia, Y.
1996-12-31
Grid generation in domains with complex geometries presents the same degree of difficulty for both internal and external flow fields. A high degree of curvature of the flow bounding surfaces results in a mesh generation process, which has to exactly describe the geometry and therefore is not straightforward. However, for internal flow problems, such as an interblade channel of a turbine, the difficulties become particularly accute when the distance between the elements is relatively small (confined domains). It often occurs that the grids generated on the different surfaces of an internal domain are incompatible producing nonsmooth grids in some areas of the flow compartment. This incompatibility problem is particularly present if the distance between opposite surfaces varies considerably along the domain.
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.
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.
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.
Unstructured Cartesian/prismatic grid generation for complex geometries
NASA Technical Reports Server (NTRS)
Karman, Steve L., Jr.
1995-01-01
The generation of a hybrid grid system for discretizing complex three dimensional (3D) geometries is described. The primary grid system is an unstructured Cartesian grid automatically generated using recursive cell subdivision. This grid system is sufficient for computing Euler solutions about extremely complex 3D geometries. A secondary grid system, using triangular-prismatic elements, may be added for resolving the boundary layer region of viscous flows near surfaces of solid bodies. This paper describes the grid generation processes used to generate each grid type. Several example grids are shown, demonstrating the ability of the method to discretize complex geometries, with very little pre-processing required by the user.
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.
Numerical Grid Generation and Potential Airfoil Analysis and Design
1988-01-01
contents include a discussion of grid generation concepts and schemes in the literature , iter- ative methods for numerical grid generation and two...to multicomponent rN airfoils, arbitrary multiple bodies and cascade grid generation for the first time. We present representative results as a... literature , iter- ative methods for numerical grid generation and two differential grid gen- eration schemes: (1) an elliptic, and (2) a parabolic scheme. A
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.
Numerical interactive grid generation for 3-D flow calculations
NASA Astrophysics Data System (ADS)
Jacobs, J. M. J. W.; Kassies, A.; Boerstoel, J. W.; Buijsen, F.; Kuijvenhoven, J. L.
1988-08-01
A method for the generation of three-dimensional block-structured grids is described. The grid generation process is decomposed into two major stages: block decomposition of the flow domain and construction of a grid in each block. Examples of grids are shown together with flow solver results. Improvements and future extensions of the present concepts are discussed.
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.
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.
Interactive Grid Generation on Small Computers
1990-01-31
boundary which can generally be given as a continuum which then involves an infinite number of points, it has been called a transfinite interpolation to...to 31 Jan 90 4. TITL AND SUBTITLE S. FUNDING NUMBERS INTERACTIVE GRID GENERATION ON SMALL COIIPUTERS F49620-89-C-0096 65502F 3005/Al 0 AUTH RLS) Peter...R. Eiseman AD-A221 234 7. PERFORMING ORGANIZATION NAME(S) AND AOORESS(ES) S. PERFORMING ORGANIZATION Program Development Corporation REPORT NUMBER
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.
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.
Cartesian-cell based grid generation and adaptive mesh refinement
NASA Technical Reports Server (NTRS)
Coirier, William J.; Powell, Kenneth G.
1993-01-01
Viewgraphs on Cartesian-cell based grid generation and adaptive mesh refinement are presented. Topics covered include: grid generation; cell cutting; data structures; flow solver formulation; adaptive mesh refinement; and viscous flow.
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.
Multiple block grid generation in the interactive environment
NASA Astrophysics Data System (ADS)
Steinbrenner, John P.; Chawner, John R.; Fouts, Chris L.
1990-06-01
Concepts employed in grid generation codes to speed up the process of obtaining a CFD solution are reviewed, including the use of multiple blocks and interactive graphics. The GRIDGEN interactive, multiple block grid generation codes, are presented as an example of grid generation software that employs these techniques. The features of a hypothetical ideal interactive multiple block grid generation code are identified through a brief discussion of existing technology.
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.
Grid generation software engineering at Los Alamos
Clark, G.L.; Ankeny, L.A.
1988-01-01
We have collected and re-engineered a small library of computer codes for general-purpose grid generation in one-, two-, and three-dimensional domains. The design intent was to produce easy-to-use general purpose codes that are portable to as many different hardware and software environments as practical, that are consistent in programming style and user interface, and that cover a gamut of applications. The paper describes some of the features of the codes, emphasizing the perspective of the potential user or programmer, rather than that of the researcher interested in mathematical techniques. 7 refs., 3 figs.
Software systems used for unstructured grid generation at NASA Langley
NASA Technical Reports Server (NTRS)
Bockelie, Michael J.
1993-01-01
These viewgraphs provide an overview of grid generation system for 3D configurations (Euler Grids) and grid generators of viscous and inviscid flow, solution adaptive for steady and unsteady flow. The five systems presented are VGRID, FELISA, TETRA, NGP, and TGRID.
Evaluation of grid generation technologies from an applied perspective
NASA Technical Reports Server (NTRS)
Hufford, Gary S.; Harrand, Vincent J.; Patel, Bhavin C.; Mitchell, Curtis R.
1995-01-01
An analysis of the grid generation process from the point of view of an applied CFD engineer is given. Issues addressed include geometric modeling, structured grid generation, unstructured grid generation, hybrid grid generation and use of virtual parts libraries in large parametric analysis projects. The analysis is geared towards comparing the effective turn around time for specific grid generation and CFD projects. The conclusion was made that a single grid generation methodology is not universally suited for all CFD applications due to both limitations in grid generation and flow solver technology. A new geometric modeling and grid generation tool, CFD-GEOM, is introduced to effectively integrate the geometric modeling process to the various grid generation methodologies including structured, unstructured, and hybrid procedures. The full integration of the geometric modeling and grid generation allows implementation of extremely efficient updating procedures, a necessary requirement for large parametric analysis projects. The concept of using virtual parts libraries in conjunction with hybrid grids for large parametric analysis projects is also introduced to improve the efficiency of the applied CFD engineer.
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.
Grid generation for general 2-D regions using hyperbolic equations
NASA Technical Reports Server (NTRS)
Cordova, Jeffrey Q.; Barth, Timothy J.
1988-01-01
A method for applying a hyperbolic grid generation scheme to the construction of meshes in general 2-D regions has been developed. This approach, which follows the theory developed by Steger and Chaussee (1980) and the algorithm outlined by Kinsey and Barth (1984), is based on improving local grid control. This is accomplished by adding an angle control source term to the equations and using a new algorithm for computing the volume source term. These modifications lead to superior methods for fixing the 'local' problems of hyperbolic grid generation, namely, propagation of initial discontinuities and formation of grid shocks (crossing grid lines). More importantly, a method for solving the global problem of constraining the grid with more than one boundary (internal grid generation) has been developed. These algorithms have been implemented in an interactive grid generation program and the results for several geometries are presented and discussed.
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.
An adaptive Cartesian grid generation method for Dirty geometry
NASA Astrophysics Data System (ADS)
Wang, Z. J.; Srinivasan, Kumar
2002-07-01
Traditional structured and unstructured grid generation methods need a water-tight boundary surface grid to start. Therefore, these methods are named boundary to interior (B2I) approaches. Although these methods have achieved great success in fluid flow simulations, the grid generation process can still be very time consuming if non-water-tight geometries are given. Significant user time can be taken to repair or clean a dirty geometry with cracks, overlaps or invalid manifolds before grid generation can take place. In this paper, we advocate a different approach in grid generation, namely the interior to boundary (I2B) approach. With an I2B approach, the computational grid is first generated inside the computational domain. Then this grid is intelligently connected to the boundary, and the boundary grid is a result of this connection. A significant advantage of the I2B approach is that dirty geometries can be handled without cleaning or repairing, dramatically reducing grid generation time. An I2B adaptive Cartesian grid generation method is developed in this paper to handle dirty geometries without geometry repair. Comparing with a B2I approach, the grid generation time with the I2B approach for a complex automotive engine can be reduced by three orders of magnitude. Copyright
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.
Generation of unstructured grids and Euler solutions for complex geometries
NASA Technical Reports Server (NTRS)
Loehner, Rainald; Parikh, Paresh; Salas, Manuel D.
1989-01-01
Algorithms are described for the generation and adaptation of unstructured grids in two and three dimensions, as well as Euler solvers for unstructured grids. The main purpose is to demonstrate how unstructured grids may be employed advantageously for the economic simulation of both geometrically as well as physically complex flow fields.
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.
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.
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.
Numerical grid generation in 3D Euler-flow simulation
NASA Astrophysics Data System (ADS)
Boerstoel, J. W.
1988-04-01
The technical problems with grid generation are analyzed and an overview of proposed solutions is given. The usefulness of grid-generation techniques, for the numerical simulation of Euler (and Navier-Stokes) flows around complex three-dimensional aerodynamic configurations, is illustrated. It is shown that the core of the grid-generation problem is a topology problem. The following remarks are sketched: grid generation is a subtask in a numerical simulation of a flow in industrial and research environments; the design requirements of a grid generation concern the geometrical imput, the desired grid as output, the technical means to control grid resolution and quality and turnaround time performance; the construction of a blocked grid can be subdivided in a block-decomposition task and a grid-point distribution task. A technique for using connectivity relations to define conventions about local coordinate systems in edges, faces and blocks is presented. Experiences are reported and an example concerning a 96-blocked grid around a complex aerodynamic configuration is given. Concepts for improvements in the presented technique are discussed.
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.
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.
Grid generation and inviscid flow computation about cranked-winged airplane geometries
NASA Technical Reports Server (NTRS)
Eriksson, L.-E.; Smith, R. E.; Wiese, M. R.; Farr, N.
1987-01-01
An algebraic grid generation procedure that defines a patched multiple-block grid system suitable for fighter-type aircraft geometries with fuselage and engine inlet, canard or horizontal tail, cranked delta wing and vertical fin has been developed. The grid generation is based on transfinite interpolation and requires little computational power. A finite-volume Euler solver using explicit Runge-Kutta time-stepping has been adapted to this grid system and implemented on the VPS-32 vector processor with a high degree of vectorization. Grids are presented for an experimental aircraft with fuselage, canard, 70-20-cranked wing, and vertical fin. Computed inviscid compressible flow solutions are presented for Mach 2 at 3.79, 7 and 10 deg angles of attack. Conmparisons of the 3.79 deg computed solutions are made with available full-potential flow and Euler flow solutions on the same configuration but with another grid system. The occurrence of an unsteady solution in the 10 deg angle of attack case is discussed.
Hyperbolic Methods for Surface and Field Grid Generation
NASA Technical Reports Server (NTRS)
Chan, William M.; VanDalsem, William R. (Technical Monitor)
1996-01-01
This chapter describes the use of hyperbolic partial differential equation methods for structured surface grid generation and field grid generation. While the surface grid generation equations are inherently three dimensional, the field grid generation equations can be formulated in two or three dimensions. The governing equations are derived from orthogonality relations and cell area/volume constraints; and are solved numerically by marching from an initial curve or surface. The marching step size and marching distance can be prescribedly the user. Exact specifications of the side and outer boundaries are not possible with a one sweep marching scheme but limited control is achievable. Excellent orthogonality and grid clustering characteristics are provided by hyperbolic methods with one to two orders of magnitude savings in time over typical elliptic methods. Since hyperbolic grid generation methods do not require the exact specifications of the side and outer boundaries of a grid, these methods are particularly well suited for the overlapping grid approach for solving problems on complex configurations. Grid generation software based on hyperbolic methods and their applications on several complex configurations will be described.
The turbulent flow generated by inhomogeneous multiscale grids
NASA Astrophysics Data System (ADS)
Zheng, Shaokai; Bruce, Paul J. K.; Graham, J. Michael R.; Vassilicos, John Christos
2015-11-01
A group of inhomogeneous multiscale grids have been designed and tested in a low speed wind tunnel in an attempt to generate bespoke turbulent shear flows. Cross-wire anemometry measurements were performed in different planes parallel to the grid and at various streamwise locations to study turbulence development behind each of the different geometry grids. Two spatially separated single hot wires were also used to measure transverse integral length scale at selected locations. Results are compared to previous studies of shearless mixing layer grids and fractal grids, including mean flow profiles and turbulence statistics.
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.
Grid generation for a complex aircraft configuration
NASA Technical Reports Server (NTRS)
Bruns, Jim
1992-01-01
The procedure used to create a grid around the F/A-18 fighter aircraft is presented. This work was done for the NASA High Alpha Technology Program. As part of this program, LeRC is numerically and experimentally investigating the flow in the F/A-18 inlet duct at high angles of attack. A grid was needed which could be used to calculate both the external and internal flow around the F/A-18. The grid had to be compatible with the computational fluid dynamics (CFD) codes PARC3D and CFL3D. The programs used to create this grid were I3GVIRGO and GRIDGEN. A surface definition used to create the grid was obtained from McDonnell Aircraft Company (MCAIR) and was composed of numerous files each containing a point definition of a portion of the aircraft. These files were read into the geometry manipulation program I3GVIRGO, where they were modified and grouped into smaller GRIDGEN database files. Next, the block outlines and boundary conditions were specified in the GRIDBLOCK program. The GRIDGEN2D program was used to create the surface grid on the block faces, and GRIDGEN3D was used to create the full 3-D grid.
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.
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
Investigation of advancing front method for generating unstructured grid
NASA Astrophysics Data System (ADS)
Thomas, A. M.; Tiwari, S. N.
1992-06-01
The advancing front technique is used to generate an unstructured grid about simple aerodynamic geometries. Unstructured grids are generated using VGRID2D and VGRID3D software. Specific problems considered are a NACA 0012 airfoil, a bi-plane consisting of two NACA 0012 airfoil, a four element airfoil in its landing configuration, and an ONERA M6 wing. Inviscid time dependent solutions are computed on these geometries using USM3D and the results are compared with standard test results obtained by other investigators. A grid convergence study is conducted for the NACA 0012 airfoil and compared with a structured grid. A structured grid is generated using GRIDGEN software and inviscid solutions computed using CFL3D flow solver. The results obtained by unstructured grid for NACA 0012 airfoil showed an asymmetric distribution of flow quantities, and a fine distribution of grid was required to remove this asymmetry. On the other hand, the structured grid predicted a very symmetric distribution, but when the total number of points were compared to obtain the same results it was seen that structured grid required more grid points.
Investigation of advancing front method for generating unstructured grid
NASA Technical Reports Server (NTRS)
Thomas, A. M.; Tiwari, S. N.
1992-01-01
The advancing front technique is used to generate an unstructured grid about simple aerodynamic geometries. Unstructured grids are generated using VGRID2D and VGRID3D software. Specific problems considered are a NACA 0012 airfoil, a bi-plane consisting of two NACA 0012 airfoil, a four element airfoil in its landing configuration, and an ONERA M6 wing. Inviscid time dependent solutions are computed on these geometries using USM3D and the results are compared with standard test results obtained by other investigators. A grid convergence study is conducted for the NACA 0012 airfoil and compared with a structured grid. A structured grid is generated using GRIDGEN software and inviscid solutions computed using CFL3D flow solver. The results obtained by unstructured grid for NACA 0012 airfoil showed an asymmetric distribution of flow quantities, and a fine distribution of grid was required to remove this asymmetry. On the other hand, the structured grid predicted a very symmetric distribution, but when the total number of points were compared to obtain the same results it was seen that structured grid required more grid points.
Fast Generation of body conforming grids for 3-D
NASA Technical Reports Server (NTRS)
Dulikravich, O.
1980-01-01
A fast algorithm was developed for accurately generating boundary conforming, three dimensional, consecutively refined, computational grids applicable to arbitrary axial turbomachinery geometry. The method is based on using a single analytic function to generate two dimensional grids on a number of coaxial axisymmetric surfaces positioned between the hub and the shroud. These grids are of the "O" type and are characterized by quasi-orthogonality, geometric periodicity, and an adequate resolution throughout the flowfield. Due to the built in additional nonorthogonal coordinate stretching and shearing, the grid lines leaving the trailing of the blade end at downstream infinity, thus simplifying the numerical treatment of the three dimensional trailing vortex sheet.
Adaptive Grid Generation for Numerical Solution of Partial Differential Equations.
1983-12-01
RETURN 65 Bibliography 1. Thompson , J . F ., "A Survey of Grid Generation Tecniques in Computational Fluid Dynamics," AIAA Paper No. 83-0447, 1-36...edited by K. N. Ghia and U. Ghia. ASME FED, 5: 35-47 (1983). 3. Thompson , J . F ., Thames, F. C., and Mastin, C. W., "Automated Numerical Generation...Equations," Numerical Grid Generation, Edited by J. F. Thompson. New York: North Holland, 1982. 10. Thompson , J . F ., and Mastin, C. W., "Grid Generation
3D automatic Cartesian grid generation for Euler flows
NASA Technical Reports Server (NTRS)
Melton, John E.; Enomoto, Francis Y.; Berger, Marsha J.
1993-01-01
We describe a Cartesian grid strategy for the study of three dimensional inviscid flows about arbitrary geometries that uses both conventional and CAD/CAM surface geometry databases. Initial applications of the technique are presented. The elimination of the body-fitted constraint allows the grid generation process to be automated, significantly reducing the time and effort required to develop suitable computational grids for inviscid flowfield simulations.
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.
On central ideals of finitely generated binary (-1,1)-algebras
Pchelintsev, S V
2002-04-30
In 1975 the author proved that the centre of a free finitely generated (-1,1)-algebra contains a non-zero ideal of the whole algebra. Filippov proved that in a free alternative algebra of rank {>=}4 there exists a trivial ideal contained in the associative centre. Il'tyakov established that the associative nucleus of a free alternative algebra of rank 3 coincides with the ideal of identities of the Cayley-Dickson algebra. In the present paper the above-mentioned theorem of the author is extended to free finitely generated binary (-1,1)-algebras. Theorem. The centre of a free finitely generated binary (-1,1)-algebra of rank {>=}3 over a field of characteristic distinct from 2 and 3 contains a non-zero ideal of the whole algebra. As a by-product, we shall prove that the T-ideal generated by the function (z,x,(x,x,y)) in a free binary (-1,1)-algebra of finite rank is soluble. We deduce from this that the basis rank of the variety of binary (-1,1)-algebras is infinite.
Grid generation using differential systems techniques
NASA Technical Reports Server (NTRS)
Thompson, J. F.; Mastin, C. W.
1980-01-01
The errors in approximating the derivatives of a function by traditional central differences at grid points of a curvilinear coordinate system were examined. The implications concerning the accuracy of the numerical solution of a partial differential equation are explained by considering several numerical examples. Although this study only considers the two dimensional case, the techniques and implications are equally valid for three dimensional grids. An interesting feature of the error analysis is its simplicity. Most of the results follow by merely working with the truncation terms of some power series expansion. These series expansions also give rise to higher order difference approximations which can significantly reduce error when the grid spacing changes rapidly, as might be the case in problems with shock waves or thin boundary layers.
Methods for prismatic/tetrahedral grid generation and adaptation
NASA Technical Reports Server (NTRS)
Kallinderis, Y.
1995-01-01
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.
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.
A Survey on Next-generation Power Grid Data Architecture
You, Shutang; Zhu, Dr. Lin; Liu, Yong; Liu, Yilu; Shankar, Mallikarjun; Robertson, Russell; King Jr, Thomas J
2015-01-01
The operation and control of power grids will increasingly rely on data. A high-speed, reliable, flexible and secure data architecture is the prerequisite of the next-generation power grid. This paper summarizes the challenges in collecting and utilizing power grid data, and then provides reference data architecture for future power grids. Based on the data architecture deployment, related research on data architecture is reviewed and summarized in several categories including data measurement/actuation, data transmission, data service layer, data utilization, as well as two cross-cutting issues, interoperability and cyber security. Research gaps and future work are also presented.
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.
Interconnection of a photovoltaic power generation system with the grid
NASA Astrophysics Data System (ADS)
Corbefin, R.; Vacelet, G.
Converting photovoltaic system-generated power into a form compatible with grid-furnished power and simultaneously ensuring that maximal power is drawn from the solar system is discussed. A converter is interposed between the solar-derived electricity and the grid lines, allowing the user to apply the power to a load, feed excess power to the grid, and receive power from the grid when the photovoltaic output is too low to fill demand. A dc-ac converter is described, with microprocessor controlled transistorized switching to adapt the solar output to the load amplitude on demand, while maintaining constant voltage. An adaptor allows the converter to take its amplitude, phase, and frequency regulation from the grid, and also assures that power will flow only toward the grid.
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.
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.
Interactive generation of unstructured grids for three dimensional problems
NASA Technical Reports Server (NTRS)
Lohner, Rainald; Parikh, Paresh; Gumbert, Clyde
1988-01-01
The present interactive grid-generation capability for unstructured grids substantially bases itself on the performance available in the most advanced workstations, in order to obviate much of the input, error-checking, and output process burden associated with the generation of grids in three dimensions. The illustrative examples presented encompass the B-747 wing-fuselage configuration, a generic wing-fuselage-tail pathfinder configuration in a wind tunnel, and a generic train configuration in which surface data are not required to have very high accuracy, but many configurations must be analyzed rapidly.
Generating MODFLOW grids from boundary representation solid models.
Jones, Norman L; Budge, Trevor J; Lemon, Alan M; Zundel, Alan K
2002-01-01
Complex stratigraphy can be difficult to simulate in MODFLOW models. MODFLOW uses a structured grid that requires that each grid layer be continuous throughout the model domain. This makes it difficult to explicitly represent common features such as pinchouts and embedded seams in a MODFLOW model. In this paper, we describe a method for automatically generating MODFLOW-compatible grids from boundary-representation solid models. Solid models are data structures developed originally for computer-aided design applications that define the geometry of three-dimensional objects. Solid models can be used to represent arbitrarily complex stratigraphy. The elevations defined by the solids are then extracted from the solids in a manner that preserves the continuous-layer requirement imposed by MODFLOW. Two basic approaches are described: The first method adjusts the MODFLOW grid dimensions (layer elevations) to fit the solid model boundaries, and the second method creates a regular MODFLOW grid and adjusts the material properties to match the changes in stratigraphy. One of the main benefits of using solid models to define stratigraphy for MODFLOW models is that it provides a grid-independent definition of the layer elevations that can be used to immediately re-create the MODFLOW grid geometry after any change to the grid resolution.
On an approach for computing the generating functions of the characters of simple Lie algebras
NASA Astrophysics Data System (ADS)
Fernández Núñez, José; García Fuertes, Wifredo; Perelomov, Askold M.
2014-04-01
We describe a general approach to obtain the generating functions of the characters of simple Lie algebras which is based on the theory of the quantum trigonometric Calogero-Sutherland model. We show how the method works in practice by means of a few examples involving some low rank classical algebras.
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.
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 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.
Orthogonal grid generation in two dimensional space
NASA Astrophysics Data System (ADS)
Theodoropoulos, T.; Bergeles, G.; Athanassiadis, N.
A generalization of a numerical technique for orthogonal mapping, used by Ryskin and Leal (1983) for the construction of boundary-fitted curvilinear coordinate systems in two-dimensional space, is proposed. The boundary-fitted orthogonal curvilinear coordinates are assumed to transform to Cartesian coordinates by Laplace equations. The scale factors involved in the Laplace equations are computed on boundaries and estimated on internal points by means of an interpolation formula. Three types of boundary conditions have been tested: Dirichlet, Cauchy-Riemann, and pseudo-Dirichlet. It is shown that, using this method, grids appropriate for the calculation of flow fields over sharp edges, complex boundary shapes, etc., can be easily constructed. Examples on various geometries are presented, together with a convenient method to check the orthogonality of the resulting meshes.
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.
Surface grid generation for complex three-dimensional geometries
NASA Astrophysics Data System (ADS)
Luh, Raymond Ching-Chung
1988-10-01
An outline is presented for the creation of surface grids from primitive geometry data such as obtained from CAD/CAM systems. The general procedure is applicable to any geometry including full aircraft with wing, nacelle, and empennage. When developed in an interactive graphics environment, a code based on this procedure is expected to substantially improve the turn around time for generating surface grids on complex geometries. Results are shown for a general hypersonic airplane geometry.
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.
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.
Wingridder - an interactive grid generator for TOUGH2
Pan, Lehua
2003-03-27
The TOUGH (Transport Of Unsaturated Groundwater and Heat) family of codes has great flexibility in handling the variety of grid information required to describe a complex subsurface system. However, designing and generating such a grid can be a tedious and error-prone process. This is especially true when the number of cells and connections is very large. As a user-friendly, efficient, and effective grid generating software, 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. It can also output additional grid information for various purposes in either graphic format or plain text format. It has user-friendly graphical user interfaces, along with an easy-to-use interactive design and plot tools. Many important features, such as inclined faults and offset, layering structure, local refinements, and embedded engineering structures, can be represented in the grid.
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.
Geometry definition and grid generation for a complete fighter aircraft
NASA Technical Reports Server (NTRS)
Edwards, Thomas 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. A procedure for performing the geometry definition of a fighter aircraft that makes use of a commercial computer-aided design/computer-aided manufacturing system is presented. 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.
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.
NASA Astrophysics Data System (ADS)
Choi, D.; Knight, C. J.
1991-06-01
A method to generate H and O-H grid systems for 3D gas turbine geometries has been developed. It is a simple procedure which solves a set of elliptic equations starting from an initial grid system generated algebraically. This grid generation procedure is for 3D Navier-Stokes analysis based on the scalar or diagonalized form of approximate factorization. The grids generated by this procedure have been applied to 3D heat transfer calculations and compared with experimental results. Detailed comparisons are given for both H and O-H grid topologies, considering the Low Aspect Ratio Turbine (LART) and using a two-equation turbulence model with viscous sublayer resolution.
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.
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.
Turbulent premixed flames on fractal-grid-generated turbulence
NASA Astrophysics Data System (ADS)
Soulopoulos, N.; Kerl, J.; Sponfeldner, T.; Beyrau, F.; Hardalupas, Y.; Taylor, A. M. K. P.; Vassilicos, J. C.
2013-12-01
A space-filling, low blockage fractal grid is used as a novel turbulence generator in a premixed turbulent flame stabilized by a rod. The study compares the flame behaviour with a fractal grid to the behaviour when a standard square mesh grid with the same effective mesh size and solidity as the fractal grid is used. The isothermal gas flow turbulence characteristics, including mean flow velocity and rms of velocity fluctuations and Taylor length, were evaluated from hot-wire measurements. The behaviour of the flames was assessed with direct chemiluminescence emission from the flame and high-speed OH-laser-induced fluorescence. The characteristics of the two flames are considered in terms of turbulent flame thickness, local flame curvature and turbulent flame speed. It is found that, for the same flow rate and stoichiometry and at the same distance downstream of the location of the grid, fractal-grid-generated turbulence leads to a more turbulent flame with enhanced burning rate and increased flame surface area.
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.
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.
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.
Applications of Differential Topology to Grid Generation.
1985-11-25
Calculations," AIAA 22nd Aerospace Sciences Meeting, Reno, Nevada, 1984. 3. Thompson , J . F ., Thames, F. C. , and Mastin, C. M., "Automatic Numerical Generation...14 (1974), 299-319. 4. Thames, F. C., Thompson , J . F ., Mastin, C. W., and Walker, R. L., "Numerical Solutions for Viscous and Potential Flow about
Mesh Generation via Local Bisection Refinement of Triangulated Grids
2015-06-01
UNCLASSIFIED Mesh Generation via Local Bisection Refinement of Triangulated Grids Jason R. Looker Joint and Operations Analysis Division Defence...Science and Technology Organisation DSTO–TR–3095 ABSTRACT This report provides a comprehensive implementation of an unstructured mesh generation method...relatively simple to implement, has the capacity to quickly generate a refined mesh with triangles that rapidly change size over a short distance, and does
Explicit Generation of Orthogonal Grids for Ocean Models
NASA Astrophysics Data System (ADS)
Murray, Ross J.
1996-07-01
Several explicit methods are proposed for generating global orthogonal curvilinear grids for ocean modelling. The methods are based on the conformal properties of stereographic and Mercator map projections and have been developed with the specific object of removing the North Pole from the ocean domain. Some of the configurations, in addition to overcoming the pole problem, have very attractive resolution properties in the polar regions. Two of the constructions are geometrical in nature, while a third is based on the superposition of potential fields generated by discrete coordinate poles. The methods described here differ from those commonly employed in engineering problems in that grid line control is exercised by the placement of a finite number of singularities, and no specific condition is placed upon the fitting of coordinate lines to physical boundaries. The grids produced are accordingly of global construction and have smooth variations in grid size. Being of analytical or semi-analytical formulation, the grids may be generated quickly and without the need for advanced software.
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
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.
International Conference on Numerical Grid Generation in Computational Fluid Dynamics
1989-04-30
Sao Vicente 225 Washington, D.C. 20059 22453 Rio de Janerlo-- RJ BRA A.S. Dvinsky Haiqing Gong Creare Inc. University of Delaware Etna Road P.O. Box...Fulselage- Mounted Nacelle 77S /Pylon Configuration N. D. Halsey Zonal Grid Generation for Fighter Aircraft 785 E. H. Atta Geometric Modelling of
A Parallel Computational Fluid Dynamics Unstructured Grid Generator
1993-12-01
Vol 11. 953-961. Philadelphia: SIAM, 1993. Holey, J. Andrew and Oscar H. Ibarra . "Triangulation, Veronoi Diagram, and Convex Hull in k-Space on Mesh...rIdhner, Rainald, Jose Camberos, and Marshall Merriam. "Parallel Unstructured Grid Generation," in Unstructured Scientific Computation on Scalable
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.
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.
A few Lie algebras and their applications for generating integrable hierarchies of evolution types
NASA Astrophysics Data System (ADS)
Zhang, Yufeng; Feng, Binlu
2011-08-01
A Lie algebra consisting of 3 × 3 matrices is introduced, whose induced Lie algebra by using an inverted linear transformation is obtained as well. As for application examples, we obtain a unified integrable model of the integrable couplings of the AKNS hierarchy, the D-AKNS hierarchy and the TD hierarchy as well as their induced integrable hierarchies. These integrable couplings are different from those results obtained before. However, the Hamiltonian structures of the integrable couplings cannot be obtained by using the quadratic-form identity or the variational identity. For solving the problem, we construct a higher-dimensional subalgebra R and its reduced algebra Q of the Lie algebra A2 by decomposing the induced Lie algebra and then again making some linear combinations. The subalgebras of the Lie algebras R and Q do not satisfy the relation ( G=G1⊕G2,[G1,G2]⊂G2), but we can deduce integrable couplings, which indicates that the above condition is not necessary to generate integrable couplings. As for application example, an expanding integrable model of the AKNS hierarchy is obtained whose Hamiltonian structure is generated by the trace identity. Finally, we give another Lie algebras which can be decomposed into two simple Lie subalgebras for which a nonlinear integrable coupling of the classical Boussinesq-Burgers (CBB) hierarchy is obtained.
On the generating function of weight multiplicities for the representations of the Lie algebra C2
NASA Astrophysics Data System (ADS)
Fernández-Núñez, José; García-Fuertes, Wifredo; Perelomov, Askold M.
2015-04-01
We use the generating function of the characters of C2 to obtain a generating function for the multiplicities of the weights entering in the irreducible representations of that simple Lie algebra. From this generating function, we derive some recurrence relations among the multiplicities and a simple graphical recipe to compute them.
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.
The Next-Generation Power Electronics Technology for Smart Grids
NASA Astrophysics Data System (ADS)
Akagi, Hirofumi
This paper presents an overview of the next-generation power electronics technology for the Japanese-version smart grid. It focuses on a grid-level battery energy storage system, a grid-level STATCOM (STATic synchronous COMpensator), and a 6.6-kV BTB (Back-To-Back) system for power flow control between two power distribution feeders. These power electronic devices play an important role in achieving load frequency control and voltage regulation. Their circuit configurations based on modular multilevel cascade PWM converters are characterized by flexible system design, low voltage steps, and low EMI (Electro-Magnetic Interference) emission. Their downscaled laboratory models are designed, constructed, and tested to verify the viability and effectiveness of the circuit configurations and control methods.
Integrating Renewable Generation into Grid Operations: Four International Experiences
Weimar, Mark R.; Mylrea, Michael E.; Levin, Todd; Botterud, Audun; O'Shaughnessy, Eric; Bird, Lori
2016-04-22
International experiences with power sector restructuring and the resultant impacts on bulk power grid operations and planning may provide insight into policy questions for the evolving United States power grid as resource mixes are changing in response to fuel prices, an aging generation fleet and to meet climate goals. Australia, Germany, Japan and the UK were selected to represent a range in the level and attributes of electricity industry liberalization in order to draw comparisons across a variety of regions in the United States such as California, ERCOT, the Southwest Power Pool and the Southeast Reliability Region. The study draws conclusions through a literature review of the four case study countries with regards to the changing resource mix and the electricity industry sector structure and their impact on grid operations and planning. This paper derives lessons learned and synthesizes implications for the United States based on answers to the above questions and the challenges faced by the four selected countries. Each country was examined to determine the challenges to their bulk power sector based on their changing resource mix, market structure, policies driving the changing resource mix, and policies driving restructuring. Each countries’ approach to solving those changes was examined, as well as how each country’s market structure either exacerbated or mitigated the approaches to solving the challenges to their bulk power grid operations and planning. All countries’ policies encourage renewable energy generation. One significant finding included the low- to zero-marginal cost of intermittent renewables and its potential negative impact on long-term resource adequacy. No dominant solution has emerged although a capacity market was introduced in the UK and is being contemplated in Japan. Germany has proposed the Energy Market 2.0 to encourage flexible generation investment. The grid operator in Australia proposed several approaches to maintaining
Eggs illusion: Local shape deformation generated by a grid pattern.
Qian, Kun; Mitsudo, Hiroyuki
2016-12-01
In this study, we report a new visual shape illusion, the eggs illusion, in which circular disks located at the midpoints between adjacent grid intersections are perceived as being deformed to ellipses. In Experiment 1, we examined the eggs illusion by using a matching method and found that grid luminance and patch size play a critical role in producing the illusory deformation. In Experiment 2, we employed several types of elliptic or circular patches to examine the conditions in which the illusory deformation was cancelled or weakened. We observed that the illusory deformation was dependent on local grid orientation. Based on these results, we found several common features between the eggs illusion and the scintillating grid illusion. This resemblance suggests a possibility that similar mechanisms underlie the two phenomena. In addition to the scintillating grid illusion, we also considered several known perceptual phenomena that might be related to the eggs illusion, i.e., the apparent size illusion, the shape-contrast effect, and the Orbison illusion. Finally, we discuss the role of orientation processing in generating the eggs illusion.
Computations and generation of elements on the Hopf algebra of Feynman graphs
NASA Astrophysics Data System (ADS)
Borinsky, Michael
2015-05-01
Two programs, feyngen and feyncop, were developed. feyngen is designed to generate high loop order Feynman graphs for Yang-Mills, QED and ϕk theories. feyncop can compute the coproduct of these graphs on the underlying Hopf algebra of Feynman graphs. The programs can be validated by exploiting zero dimensional field theory combinatorics and identities on the Hopf algebra which follow from the renormalizability of the theories. A benchmark for both programs was made.
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.
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.
High-resolution subgrid models: background, grid generation, and implementation
NASA Astrophysics Data System (ADS)
Sehili, Aissa; Lang, Günther; Lippert, Christoph
2014-04-01
The basic idea of subgrid models is the use of available high-resolution bathymetric data at subgrid level in computations that are performed on relatively coarse grids allowing large time steps. For that purpose, an algorithm that correctly represents the precise mass balance in regions where wetting and drying occur was derived by Casulli (Int J Numer Method Fluids 60:391-408, 2009) and Casulli and Stelling (Int J Numer Method Fluids 67:441-449, 2010). Computational grid cells are permitted to be wet, partially wet, or dry, and no drying threshold is needed. Based on the subgrid technique, practical applications involving various scenarios were implemented including an operational forecast model for water level, salinity, and temperature of the Elbe Estuary in Germany. The grid generation procedure allows a detailed boundary fitting at subgrid level. The computational grid is made of flow-aligned quadrilaterals including few triangles where necessary. User-defined grid subdivision at subgrid level allows a correct representation of the volume up to measurement accuracy. Bottom friction requires a particular treatment. Based on the conveyance approach, an appropriate empirical correction was worked out. The aforementioned features make the subgrid technique very efficient, robust, and accurate. Comparison of predicted water levels with the comparatively highly resolved classical unstructured grid model shows very good agreement. The speedup in computational performance due to the use of the subgrid technique is about a factor of 20. A typical daily forecast can be carried out in less than 10 min on a standard PC-like hardware. The subgrid technique is therefore a promising framework to perform accurate temporal and spatial large-scale simulations of coastal and estuarine flow and transport processes at low computational cost.
Atmospheric wind field conditions generated by active grids
NASA Astrophysics Data System (ADS)
Knebel, Pascal; Kittel, Achim; Peinke, Joachim
2011-08-01
An active grid for turbulence generation of several rotatable axes with surmounted vanes that can be driven via stepper or servo motors is presented. We investigate the impact of different excitation protocols for the grid. Using such protocols that already have the intermittent structure of turbulence, higher intermittent flows can be achieved. This concept can also be used to generate turbulent flows of high turbulence intensities (>25%) exhibiting integral length scales beyond the typical size of the test section of the wind tunnel. Similar two-point correlations measured by the intermittent statistics of velocity increments that are characteristic for flows of high Reynolds number, i.e. in the atmospheric boundary layer, can be reproduced.
NASA Astrophysics Data System (ADS)
Mikhalev, A. V.; Pinchuk, I. A.
2005-06-01
The structure of Steinberg conformal algebras is studied; these are analogues of Steinberg groups (algebras, superalgebras).A Steinberg conformal algebra is defined as an abstract algebra by a system of generators and relations between the generators. It is proved that a Steinberg conformal algebra is the universal central extension of the corresponding conformal Lie algebra; the kernel of this extension is calculated.
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.
Adaptive Unstructured Grid Generation for Modeling of Coastal Margins
1999-09-30
applied to the 2+1D simulations of the barotropic circulation in the Tagus estuary (Fortunato et al. 1997). The approach, denoted localized sigma...analysis. Application to the Tagus does not appear to have produced new pathologies relative to a conventional sigma-coordinate discretization, and reduced...particular, adopt and provide additional testbeds and technical feedback for our grid generation software. The Columbia River estuary and plume have provided
Interfacing a small thermophotovoltaic generator to the grid
NASA Astrophysics Data System (ADS)
Durisch, W.; Grob, B.; Mayor, J.-C.; Panitz, J.-C.; Rosselet, A.
1999-03-01
A prototype thermophotovoltaic generator and grid-interfacing device have been developed to demonstrate the feasibility of grid-connected operation. For this purpose a conventional butane burner (rated power 1.35 kWth) was equipped with a ceramic composite emitter made of rare earth oxides. A water layer between emitter and photocells was used to protect the photocells against overheating. It absorbs the nonconvertible emitter radiation and is heated up thereby. The hot water so produced in larger units of this type could be used in a primary recirculation loop to transfer heat to a secondary domestic hot water system. For the photovoltaic generator, commercial grade silicon solar cells with 16% efficiency (under standard test conditions) were used. With the radiation of the emitter, a current of 4.6 A at a maximum power point voltage of 3.3 V was produced, corresponding to a DC output of 15 W and a thermal to DC power conversion efficiency of 1.1%. A specially developed high efficiency DC/DC converter and a modified, commercially available inverter were used to feed the generated power to the local grid. Under the experimental conditions in question the DC/DC-converter and the grid-inverter had efficiencies of 98 and 91%, respectively resulting in an overall interface efficiency of 89%. From modeling of the measured electrical characteristics of the photo cell generator under solar and emitter radiation, it is concluded that the photo current was about three times higher under the filtered emitter radiation. Under these conditions the electrical losses of the photocells were significantly higher than under sunlight.
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.
NASA Technical Reports Server (NTRS)
Sorenson, R. L.
1986-01-01
An elliptic grid-generation method for finite-difference computations about complex aerodynamic configurations is developed. A zonal approach is used, which involves first making a coarse global grid filling the entire physical domain and then subdividing regions of that grid to make the individual zone grids. The 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.
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.
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.
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.
NASA Astrophysics Data System (ADS)
Garriz, J. A.
1985-01-01
A code is described which demonstrates the versatility of the differential equations method of grid generation for generating boundary-fitted grids. Two problems from the field of solid mechanics are used to show the code's utility. The problem of successively generating grids for a geometry which changes with time is illustrated with the case of an ablating solid rocket propellant grain. On a more quantitative basis, the problem of successively generating grids whose grid points automatically position or 'adapt' themselves in order to resolve gradients of interest in an evolving solution is illustrated with the classic case of analyzing the state of stress in an axially loaded, rectangular plate with a centered circular hole.
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.
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
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.
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.
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.
NASA Astrophysics Data System (ADS)
Etingof, Pavel; Rains, Eric
2016-10-01
Generalized power sums are linear combinations of ith powers of coordinates. We consider subalgebras of the polynomial algebra generated by generalized power sums, and study when such algebras are Cohen-Macaulay. It turns out that the Cohen-Macaulay property of such algebras is rare, and tends to be related to quantum integrability and representation theory of Cherednik algebras. Using representation theoretic results and deformation theory, we establish Cohen-Macaulayness of the algebra of q, t-deformed power sums defined by Sergeev and Veselov, and of some generalizations of this algebra, proving a conjecture of Brookner, Corwin, Etingof, and Sam. We also apply representation-theoretic techniques to studying m-quasi-invariants of deformed Calogero-Moser systems. In an appendix to this paper, M. Feigin uses representation theory of Cherednik algebras to compute Hilbert series for such quasi-invariants, and show that in the case of one light particle, the ring of quasi-invariants is Gorenstein.
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.
Surface grid generation for flowfield applications using B-spline surfaces
NASA Technical Reports Server (NTRS)
Atwood, Christopher A.; Vogel, Jerald M.
1989-01-01
The adequate discretization of the flowfield domain in structured grid techniques depends on the body surface, the zones, and the interior grid. Attention is presently given to the problem of obtaining a versatile surface-definition and grid-generation technique; a general surface grid-generation technique is presented which develops three-dimensional patches from point data. The grid is generated on a two-dimensional field on the basis of either a direct or inverse interpolation procedure. It is then mapped onto physical space to yield the surface grid.
Efficient generation of generalized Monkhorst-Pack grids through the use of informatics
NASA Astrophysics Data System (ADS)
Wisesa, Pandu; McGill, Kyle A.; Mueller, Tim
2016-04-01
We present a method for rapidly generating efficient k -point grids for Brillouin zone integration by using a database of precalculated grids. Benchmark results on 102 randomly selected materials indicate that for well-converged calculations, the grids generated by our method have fewer than half as many irreducible k -points as Monkhorst-Pack grids generated using a more conventional method, significantly accelerating the calculation of properties of crystalline materials.
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.
Irregular Grid Generation and Rapid 3D Color Display Algorithm
Wilson D. Chin, Ph.D.
2000-05-10
Computationally efficient and fast methods for irregular grid generation are developed to accurately characterize wellbore and fracture boundaries, and farfield reservoir boundaries, in oil and gas petroleum fields. Advanced reservoir simulation techniques are developed for oilfields described by such ''boundary conforming'' mesh systems. Very rapid, three-dimensional color display algorithms are also developed that allow users to ''interrogate'' 3D earth cubes using ''slice, rotate, and zoom'' functions. Based on expert system ideas, the new methods operate much faster than existing display methodologies and do not require sophisticated computer hardware or software. They are designed to operate with PC based applications.
Explicit generators in rectangular affine W-algebras of type A
NASA Astrophysics Data System (ADS)
Arakawa, Tomoyuki; Molev, Alexander
2016-10-01
We produce in an explicit form free generators of the affine W-algebra of type A associated with a nilpotent matrix whose Jordan blocks are of the same size. This includes the principal nilpotent case and we thus recover the quantum Miura transformation of Fateev and Lukyanov.
Explicit generators in rectangular affine W-algebras of type A
NASA Astrophysics Data System (ADS)
Arakawa, Tomoyuki; Molev, Alexander
2017-01-01
We produce in an explicit form free generators of the affine W-algebra of type A associated with a nilpotent matrix whose Jordan blocks are of the same size. This includes the principal nilpotent case and we thus recover the quantum Miura transformation of Fateev and Lukyanov.
Generation of a multi-component aircraft grid system using NGP and Begger
Lijewski, L.E.; Belk, D.M.
1996-12-31
Generation of a multiple component aircraft grid system is presented. A hybrid system of blocked and overset grids axe generated using NGP and overlap communications established with the Beggar code. Techniques for gridding wing-flap and fuselage-flap gap regions axe discussed. Steady-state subsonic flow solutions are presented.
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,…
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.
Electric Grid Expansion Planning with High Levels of Variable Generation
Hadley, Stanton W.; You, Shutang; Shankar, Mallikarjun; Liu, Yilu
2016-02-01
Renewables are taking a large proportion of generation capacity in U.S. power grids. As their randomness has increasing influence on power system operation, it is necessary to consider their impact on system expansion planning. To this end, this project studies the generation and transmission expansion co-optimization problem of the US Eastern Interconnection (EI) power grid with a high wind power penetration rate. In this project, the generation and transmission expansion problem for the EI system is modeled as a mixed-integer programming (MIP) problem. This study analyzed a time series creation method to capture the diversity of load and wind power across balancing regions in the EI system. The obtained time series can be easily introduced into the MIP co-optimization problem and then solved robustly through available MIP solvers. Simulation results show that the proposed time series generation method and the expansion co-optimization model and can improve the expansion result significantly after considering the diversity of wind and load across EI regions. The improved expansion plan that combines generation and transmission will aid system planners and policy makers to maximize the social welfare. This study shows that modelling load and wind variations and diversities across balancing regions will produce significantly different expansion result compared with former studies. For example, if wind is modeled in more details (by increasing the number of wind output levels) so that more wind blocks are considered in expansion planning, transmission expansion will be larger and the expansion timing will be earlier. Regarding generation expansion, more wind scenarios will slightly reduce wind generation expansion in the EI system and increase the expansion of other generation such as gas. Also, adopting detailed wind scenarios will reveal that it may be uneconomic to expand transmission networks for transmitting a large amount of wind power through a long distance
Generic polyhedron grid generation for solving partial differential equations on spherical surfaces
NASA Astrophysics Data System (ADS)
Oldham, D.; Davies, J. H.; Phillips, T. N.
2012-02-01
A new method for generating a numerical grid on a spherical surface is presented. This method allows the grid to be based on several different regular polyhedrons (including octahedron, cube, icosahedron, and rhombic dodecahedron). The type of polyhedron on which the grid is based can be changed by altering only a few input parameters. Each polygon face can then be subdivided using a mapping technique that is described. An advantage of this new grid is that it gives increased flexibility in terms of the total number of nodes in the system. It also makes comparison between different numerical grids easier and simplifies the transfer of code/data between numerical simulators with different grids. This generic grid is then used to solve Poisson's equation on a spherical surface using a spectral element implementation for a range of actual grids. The generic grid allows us to quickly compare the actual grids and illustrates its utility.
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.
PLUTO 3-D Grid Generator (User’s Manual)
1991-06-01
PLUTO (Poisson Laplace U TFI Orthogonal), is a three dimensional gridding and smoothing program developed in-house at WL/FIMM. Its purpose is to: (1...spacing, smoothness and orthogonality, and (4) output grids in user selected ascii or binary formats. Initial grids are established by PLUTO with a three
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.
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.
NASA Technical Reports Server (NTRS)
Sorenson, R. L.; Steger, J. L.
1980-01-01
A method for generating boundary-fitted, curvilinear, two dimensional grids by the use of the Poisson equations is presented. Grids of C-type and O-type were made about airfoils and other shapes, with circular, rectangular, cascade-type, and other outer boundary shapes. Both viscous and inviscid spacings were used. In all cases, two important types of grid control can be exercised at both inner and outer boundaries. First is arbitrary control of the distances between the boundaries and the adjacent lines of the same coordinate family, i.e., stand-off distances. Second is arbitrary control of the angles with which lines of the opposite coordinate family intersect the boundaries. Thus, both grid cell size (or aspect ratio) and grid cell skewness are controlled at boundaries. Reasonable cell size and shape are ensured even in cases wherein extreme boundary shapes would tend to cause skewness or poorly controlled grid spacing. An inherent feature of the Poisson equations is that lines in the interior of the grid smoothly connect the boundary points (the grid mapping functions are second order differentiable).
1988-05-16
THOMPSON , J . F ., WARSI, Z.U.A., and MASTIN, C.W., Numerical Grid Genera- tion: Foundations and Applications, North-Holland, Amsterdam, 1985. 2. THOMPSON...Coordinate Generation’, in Numerical Grid Generation, Ed. Thompson , J . F ., 1982, pp. 41-77. 10. WARSI, Z.U.A., and ZIEBARTH, J.P., ’Numerical Generation of
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.
Grid generation on and about a cranked-wing fighter aircraft configuration
NASA Technical Reports Server (NTRS)
Smith, Robert E.; Pitts, Joan I.; Eriksson, Lars-Erik; Wiese, Michael R.
1988-01-01
Experiences at the NASA Langley Research Center generating grids about a cranked wing fighter aircraft configuration is described. A single block planar grid about the fuselage and canard used with a finite difference Navier-Stokes solver is also described. A dual block nonplanar grid about the complete configuration and used with a finite volume Euler solver is presented. The very important aspect of computing the aircraft surface grid, starting with a standardized model description, is also presented.
Three-dimensional adaptive grid generation for body-fitted coordinate system
NASA Technical Reports Server (NTRS)
Chen, S. C.
1988-01-01
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.
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.
NASA Technical Reports Server (NTRS)
Nakamura, S.
1982-01-01
A fast method for generating three-dimensional grids for fuselage-wing transonic flow calculations using parabolic difference equations is described. No iterative scheme is used in the three-dimensional sense; grids are generated from one grid surface to the next starting from the fuselage surface. The computational procedure is similar to the iterative solution of the two-dimensional heat conduction equation. The proposed method is at least 10 times faster than the elliptic grid generation method and has much smaller memory requirements. Results are presented for a fuselage and wing of NACA-0012 section and thickness ratio of 10 percent. Although only H-grids are demonstrated, the present technique should be applicable to C-grids and O-grids in three dimensions.
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.
NASA Technical Reports Server (NTRS)
Cheng, Zheming; Eiseman, Peter R.
1995-01-01
With examples, we illustrate how implicitly specified surfaces can be used for grid generation with GridPro/az3000. The particular examples address two questions: (1) How do you model intersecting tubes with fillets? and (2) How do you generate grids inside the intersected tubes? The implication is much more general. With the results in a forthcoming paper which develops an easy-to-follow procedure for implicit surface modeling, we provide a powerful means for rapid prototyping in grid generation.
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.
Emissions & Generation Resource Integrated Database (eGRID) Questions and Answers
eGRID is a comprehensive source of data on the environmental characteristics of almost all electric power generated in the United States. eGRID is based on available plant-specific data for all U.S. electricity generating plants that report data.
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.
Automatic multi-block grid generation for high-lift configuration wings
NASA Technical Reports Server (NTRS)
Kim, Byoungsoo; Eberhardt, Scott
1995-01-01
A new method for automatic multi-block grid generation is described. The method combines the Modified Advancing Front Method as a Predictor with an elliptic scheme as a corrector. It advances a collection of cells by one cell height in the outward direction using Modified Advancing Front Method, and then corrects newly-obtained cell positions by solving elliptic equations. This predictor-corrector type scheme is repeatedly applied until the field of interest is filled with hexahedral grid cells. Given the configuration surface grid, the scheme produces block layouts as well as grid cells with overall smoothness as its output. The present method saves human-time and reduces the burden on the user in generating grids for general 3-D configurations. It was used to generate multi-block grids for wings in their high-lift configuration.
Grid generation and compressible flow computations about a high-speed civil transport configuration
NASA Technical Reports Server (NTRS)
Abolhassani, J. S.; Stewart, J. E.; Farr, N.; Smith, R. E.; Kerr, P. W.; Everton, E. L.
1991-01-01
Techniques and software are discussed for generating grids about a high-speed civil transport configuration. The configuration is defined by a computer-aided design system in wing, fuselage, tail and engine-nacelle components. Grid topology and the surfaces outlining the blocks of the topology are computed with interactive software. The volume grid is computed using software based on transfinite interpolation and Lagrangian blending functions. Several volume grids for inviscid and viscous flow have been generated using this system of codes. Demonstration flowfields around this vehicle are described.
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.
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).
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.
A development of grid generation procedure for multicomponent aerodynamic configuration
NASA Technical Reports Server (NTRS)
Chen, H. C.
1981-01-01
Two approaches for solving the transonic flow in a multi-block grid were explored. The first approach examines a method involving "zonal decomposition" wherein block boundaries are treated as true boundary surfaces separating interfacing grids. The issues investigated involve techniques for matching solutions at a block boundary. A feasibility study was completed and the results are presented. The second approach involves overlapping grids for differencing across a block boundary near an artificially induced coordinate singularity occurring at a fictitious corner. This approach selects a set of neighboring nodes for the fictitious corner such that the resulting physical cells for a node are topologically the same as any other node on the airfoil surface.
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...
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.
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.
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.
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.
NASA Astrophysics Data System (ADS)
Boerstoel, J. W.
1986-08-01
Aproaches to grid generation are analyzed. A grid-generation procedure for complex aircraft configurations could be based on a combination of three subprocesses: decomposition of the flow domain into 100 hexahedronal blocks; trilinear transfinite interpolation to generate initial grid point distributions; and elliptic mesh-size tuning and smoothing. To get insight into this procedure, mathematical models of the subprocesses were worked out. The results of the analysis are technical concepts required or desirable in the grid-generation procedure.
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.
An analytical approach to grid sensitivity analysis. [of NACA wing sections
NASA Technical Reports Server (NTRS)
Sadrehaghighi, Ideen; Smith, Robert E.; Tiwari, Surendra 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.
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.
Generation of three-dimensional unstructured grids by the advancing-front method
NASA Technical Reports Server (NTRS)
Lohner, Rainald; Parikh, Paresh
1988-01-01
The generation of three-dimensional unstructured grids using the advancing-front technique is described. While this generation technique has been shown to be effective for the generation of unstructured grids in two dimensions, its extension to three-dimensional regions required the development of surface definition software and sophisticated data structures to avoid excessive CPU-time overheads for the search operations involved. After obtaining an initial triangulation of the surfaces, tetrahedrons are generated by successively deleting faces from the generation front. Details of the mesh generation algorithm are given, together with examples and timings.
DIRAC3 - the new generation of the LHCb grid software
NASA Astrophysics Data System (ADS)
Tsaregorodtsev, A.; Brook, N.; Casajus Ramo, A.; Charpentier, Ph; Closier, J.; Cowan, G.; Graciani Diaz, R.; Lanciotti, E.; Mathe, Z.; Nandakumar, R.; Paterson, S.; Romanovsky, V.; Santinelli, R.; Sapunov, M.; Smith, A. C.; Seco Miguelez, M.; Zhelezov, A.
2010-04-01
DIRAC, the LHCb community Grid solution, was considerably reengineered in order to meet all the requirements for processing the data coming from the LHCb experiment. It is covering all the tasks starting with raw data transportation from the experiment area to the grid storage, data processing up to the final user analysis. The reengineered DIRAC3 version of the system includes a fully grid security compliant framework for building service oriented distributed systems; complete Pilot Job framework for creating efficient workload management systems; several subsystems to manage high level operations like data production and distribution management. The user interfaces of the DIRAC3 system providing rich command line and scripting tools are complemented by a full-featured Web portal providing users with a secure access to all the details of the system status and ongoing activities. We will present an overview of the DIRAC3 architecture, new innovative features and the achieved performance. Extending DIRAC3 to manage computing resources beyond the WLCG grid will be discussed. Experience with using DIRAC3 by other user communities than LHCb and in other application domains than High Energy Physics will be shown to demonstrate the general-purpose nature of the system.
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
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.
NASA Astrophysics Data System (ADS)
Miao, Qian; Hu, Xiao-Rui; Chen, Yong
2014-02-01
We present a Maple computer algebra package, ONEOptimal, which can calculate one-dimensional optimal system of finite dimensional Lie algebra for nonlinear equations automatically based on Olver's theory. The core of this theory is viewing the Killing form of the Lie algebra as an invariant for the adjoint representation. Some examples are given to demonstrate the validity and efficiency of the program.
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.
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.
Grid generation for microaerodynamics simulations of the Cassini-Huygens space probe
Haeuser, J.; Xia, Y.; Spel, M.
1996-12-31
With the advent of parallel computers substantially more complex fluid flow problems can be tackled. Complete aircraft configurations, complex turbine geometries, or flows including combustion have been computed in the automotive industry. Consequently, geometries of high complexity are now of interest as well as very large meshes, for instance, computations of up to 30 million grid points have been performed. Clearly, grid generation codes have to be capable to handle this new class of applications. Convential grid generation techniques derived from CAD systems that interactively work on the CAD data to generate first the surface grids and then the volume grids are not useful for these large and complex meshes. The user has to perform tens of thousands of mouse clicks with no or little reusability of his input. Moreover, a separation of topology and geometry is not possible. An aircraft, for example, has a certain topology, but different geometry data describe different aircraft types. The topology definition is a certain amount of work, since it describes the resulting grid line configuration. Once the topology has been described, it can be reused for a whole class of applications. One step further would be the definition of objects that can be translated, rotated and multiplied. These features could be used to build an application specific data base that can be employed by the design engineer to quickly generate the grids needed.
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 Astrophysics Data System (ADS)
Iga, Shin-ichi
2017-02-01
An equatorially enhanced grid is applicable to atmospheric general circulation simulations with better representations of the cumulus convection active in the tropics. This study improved the topology of previously proposed equatorially enhanced grids (Iga, 2015) [1], which had extremely large grid intervals around the poles. The proposed grids in this study are of a triangular mesh and are generated by a spring dynamics method with stretching around singular points, which are connected to five or seven neighboring grid points. The latitudinal distribution of resolution is nearly proportional to the combination of the map factors of the Mercator, Lambert conformal conic, and polar stereographic projections. The resolution contrast between the equator and pole is 2.3 ∼ 4.5 for the sampled cases, which is much smaller than that for the LML grids. This improvement requires only a small amount of additional grid resources, less than 11% of the total. The proposed grids are also examined with shallow water tests, and were found to perform better than the previous LML grids.
Euler and N-S grid generation for Halis configuration with body flap
Haeuser, J.; Xia, Y.; Muylaert, J.
1996-12-31
The purpose of this paper is two fold. First, a high quality grid for the Halis geometry has been generated. The grid is optimized with regard to smoothness, orthogonality, and skewness. In particular, the grid is almost orthogonal on fixed boundaries to simplify the usage of turbulence models. Second, a topology has been designed that aligns the grid with the expected streamline distribution as much as possible to improve the accuracy of the numerical solution, and, at the same time, allows the reduction of the number of grid points needed. This is an important aspect in driving down computing time. For a flow adapted grid topology the number of blocks is higher than for a simple topology. Consequently, the number of points per block is smaller. In addition, the number of grid points may differ substantially from block to block. This feature has two consequences. First, an advanced topology cannot be used by codes that rely on large blocks, for instance, codes that ran on vector computers demanding long vector lengths. This type of topology will also be difficult for codes using the mult-grid technique because grid coarsening win be less effective for smaller blocks.
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.
NASA Astrophysics Data System (ADS)
Yamashita, Koji; Sakamoto, Orie; Kitauchi, Yoshihiro; Nanahara, Toshiya; Inoue, Toshio; Shiohama, Tomohiro; Fukuda, Hitoshi
Integrating of wind power generation into small islands has been one of the demonstration projects in Okinawa prefecture. Since such integration could deteriorate power quality including frequency in an island grid, a frequency stabilizing system using flywheels has been installed into a small island. In order to establish a proper frequency stabilizing scheme for the small island, an accurate model of a diesel generator including governor is vital. Therefore, the model was developed based on the measured values of generator dump tests. A new frequency stabilizing scheme was also developed through time-domain simulation of the island grid model which consists of the above-mentioned diesel generator model and an equivalent load change representing wind power variation. The proper parameters of the scheme were derived considering role sharing between the diesel generators and the flywheels. The developed stabilizing scheme was applied to the flywheels in the island grid and revealed great performance for mitigating frequency variation.
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.
Extent of cortical generators visible on the scalp: effect of a subdural grid.
von Ellenrieder, Nicolás; Beltrachini, Leandro; Muravchik, Carlos H; Gotman, Jean
2014-11-01
The effect of the non-conducting substrate of a subdural grid on the scalp electric potential distribution is studied through simulations. Using a detailed head model and the finite element method we show that the governing physics equations predict an important attenuation in the scalp potential for generators located under the grid, and an amplification for generators located under holes in the skull filled with conductive media. These effects are spatially localized and do not cancel each other. A 4 × 8 cm grid can produce attenuations of 2 to 3 times, and an 8 × 8 cm grid attenuation of up to 8 times. As a consequence, when there is no subdural grid, generators of 4 to 8 cm(2) produce scalp potentials of the same maximum amplitude as generators of 10 to 20 cm(2) under the center of a subdural grid. This means that the minimum cortical extents necessary to produce visible scalp activity determined from simultaneous scalp and subdural recordings can be overestimations.
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.
ERIC Educational Resources Information Center
Lee, Kerry; Ng, Ee Lynn; Ng, Swee Fong
2009-01-01
Solving algebraic word problems involves multiple cognitive phases. The authors used a multitask approach to examine the extent to which working memory and executive functioning are associated with generating problem models and producing solutions. They tested 255 11-year-olds on working memory (Counting Recall, Letter Memory, and Keep Track),…
Brislawn, K.; Brown, D.; Chesshire, G.; Henshaw, W.
1997-01-01
Overture is a library containing classes for grids, overlapping grid generation and the discretization and solution of PDEs on overlapping grids. This document describes the Overture grid classes, including classes for single grids and classes for collections of grids.
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).
The three-dimensional Multi-Block Advanced Grid Generation System (3DMAGGS)
NASA Astrophysics Data System (ADS)
Alter, Stephen J.; Weilmuenster, Kenneth J.
1993-05-01
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).
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.
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.
Simplified clustering of nonorthogonal grids generated by elliptic partial differential equations
NASA Technical Reports Server (NTRS)
Sorenson, R. L.; Steger, J. L.
1977-01-01
A simple clustering transformation is combined with the Thompson, Thames, and Mastin (TTM) method of generating computational grids to produce controlled mesh spacings. For various practical grids, the resulting hybrid scheme is easier to apply than the inhomogeneous clustering terms included in the TTM method for this purpose. The technique is illustrated in application to airfoil problems, and listings of a FORTRAN computer code for this usage are included.
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.
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.
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.
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.
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.
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.
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.
A General Curvilinear Grid Generation Program for Projectile Configurations
1981-10-01
of Comp. Physics, Vol. 8, 1971, pp. 392-408. 7. Thompson , J . F ., Thames, F. C, and Mastin, C. M., "Automatic Numerical... J . F ., Thames, F. C, and Mastin, C. M., "Automatic Numerical Generation of Body-Fitted Curvilinear Coordinate System for Field Con- taining any...34Development of a General Finite Difference Approximation for a General Domain". Journal of Comp. Physics, Vol. 8, 1971, pp. 392-408. 7. Thompson
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.
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.
NASA Astrophysics Data System (ADS)
Mueller, Tim; Wisesa, Pandu
The calculation of many material properties requires the evaluation of an integral over the Brillouin zone, which is commonly approximated by sampling a regular grid of points, known as k-points, in reciprocal space. We have developed an automated tool for generating k-point grids that significantly accelerates the calculation of material properties compared to commonly used methods. Our tool, which is being made freely available to the public, is capable of generating highly efficient k-point grids in a fraction of a second for any crystalline material. We present an overview of our method, benchmark results, and a discussion of how it can be integrated into a high-throughput computing environment.
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.
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 Astrophysics Data System (ADS)
Barrett, James
The incorporation of small, privately owned generation operating in parallel with, and supplying power to, the distribution network is becoming more widespread. This method of operation does however have problems associated with it. In particular, a loss of the connection to the main utility supply which leaves a portion of the utility load connected to the embedded generator will result in a power island. This situation presents possible dangers to utility personnel and the public, complications for smooth system operation and probable plant damage should the two systems be reconnected out-of-synchronism. Loss of Grid (or Islanding), as this situation is known, is the subject of this thesis. The work begins by detailing the requirements for operation of generation embedded in the utility supply with particular attention drawn to the requirements for a loss of grid protection scheme. The mathematical basis for a new loss of grid protection algorithm is developed and the inclusion of the algorithm in an integrated generator protection scheme described. A detailed description is given on the implementation of the new algorithm in a microprocessor based relay hardware to allow practical tests on small embedded generation facilities, including an in-house multiple generator test facility. The results obtained from the practical tests are compared with those obtained from simulation studies carried out in previous work and the differences are discussed. The performance of the algorithm is enhanced from the theoretical algorithm developed using the simulation results with simple filtering together with pattern recognition techniques. This provides stability during severe load fluctuations under parallel operation and system fault conditions and improved performance under normal operating conditions and for loss of grid detection. In addition to operating for a loss of grid connection, the algorithm will respond to load fluctuations which occur within a power island
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.
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.
Tian, Tian; Chernyakhovskiy, Ilya; Brancucci Martinez-Anido, Carlo
2016-04-01
This document is the Spanish version of 'Greening the Grid- Forecasting Wind and Solar Generation Improving System Operations'. It discusses improving system operations with forecasting with 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.
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.
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.
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.
NASA Astrophysics Data System (ADS)
Zhang, Yufeng; Tam, Honwah; Wu, Lixin
2015-10-01
We deduce a set of integrable equations under the framework of zero curvature equations and obtain two sets of integrable soliton equations, which can be reduced to some new integrable equations including the generalised nonlinear Schrödinger (NLS) equation. Under the case where the isospectral functions are one-order polynomials in the parameter λ, we generate a set of rational integrable equations, which are reduced to the loop soliton equation. Under the case where the derivative λt of the spectral parameter λ is a quadratic algebraic curve in λ, we derive a set of variable-coefficient integrable equations. In addition, we discretise a pair of isospectral problems introduced through the Lie algebra given by us for which a set of new semi-discrete nonlinear equations are available; furthermore, the semi-discrete MKdV equation and the Hirota lattice equation are followed to produce, respectively. Finally, we apply the Lie algebra to introduce a set of operator Lax pairs with an operator, and then through the Tu scheme and the binomial-residue representation method proposed by us, we generate a 2+1-dimensional integrable hierarchy of evolution equations, which reduces to a generalised 2+1-dimensional Davey-Stewartson (DS) equation.
NASA Astrophysics Data System (ADS)
Aydin, Sinan
2014-08-01
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 student-generated examples regarding the concepts. With the help of these examples, we have analysed students' understanding of linear dependence/independence and determined the effect of the example-generation process on student understanding of linear algebra. In addition, we identified some difficulties that were experienced by students learning the concepts of linear dependence/independence. In this study, APOS (action-process-object-schema) theory is the main tool utilized to explain students' written responses. It was also used with regard to the interview questions that were posed to students with the purpose of identifying possible difficulties with linear dependence/independence and observing the adequacy of the relations that students might form between different elements of the genetic decomposition of linear dependence/independence concepts. The findings of this study confirmed that many students do not have appropriate mental structures at object and schema levels. Moreover, in order to ensure the success of such exercises, students must be encouraged to review and validate their responses to the example requests.
NASA Astrophysics Data System (ADS)
Matone, Marco
2016-11-01
Recently it has been introduced an algorithm for the Baker-Campbell-Hausdorff (BCH) formula, which extends the Van-Brunt and Visser recent results, leading to new closed forms of BCH formula. More recently, it has been shown that there are 13 types of such commutator algebras. We show, by providing the explicit solutions, that these include the generators of the semisimple complex Lie algebras. More precisely, for any pair, X, Y of the Cartan-Weyl basis, we find W, linear combination of X, Y, such that exp (X) exp (Y)=exp (W). The derivation of such closed forms follows, in part, by using the above mentioned recent results. The complete derivation is provided by considering the structure of the root system. Furthermore, if X, Y, and Z are three generators of the Cartan-Weyl basis, we find, for a wide class of cases, W, a linear combination of X, Y and Z, such that exp (X) exp (Y) exp (Z)=exp (W). It turns out that the relevant commutator algebras are type 1c-i, type 4 and type 5. A key result concerns an iterative application of the algorithm leading to relevant extensions of the cases admitting closed forms of the BCH formula. Here we provide the main steps of such an iteration that will be developed in a forthcoming paper.
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.
Noncommutative algebras, nano-structures, and quantum dynamics generated by resonances. III
NASA Astrophysics Data System (ADS)
Karasev, M.
2006-04-01
Quantum geometry, algebras with nonlinear commutation relations, representation theory, the coherent transform, and operator averaging are used to solve the perturbation problem for wave (quantum) systems near a resonance equilibrium point or a resonance equilibrium ray in two and three-dimensional spaces.
Meanings Generated while Using Algebraic-Like Formalism to Construct and Control Animated Models
ERIC Educational Resources Information Center
Kynigos, Chronis; Psycharis, Giorgos; Moustaki, Foteini
2010-01-01
This paper reports on a design experiment conducted to explore the construction of meanings by 17 year old students, emerging from their interpretations and uses of algebraic like formalism. The students worked collaboratively in groups of two or three, using MoPiX, a constructionist computational environment with which they could create concrete…
ERIC Educational Resources Information Center
Grassl, R.; Mingus, T. T. Y.
2007-01-01
Experiences in designing and teaching a reformed abstract algebra course are described. This effort was partially a result of a five year statewide National Science Foundation (NSF) grant entitled the Rocky Mountain Teacher Enhancement Collaborative. The major thrust of this grant was to implement reform in core mathematics courses that would…
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.
Three-Dimensional Optimal Shape Design in Heat Transfer Based on Body-fitted Grid Generation
NASA Astrophysics Data System (ADS)
Mohebbi, Farzad; Sellier, Mathieu
2013-10-01
This paper is concerned with an optimal shape design (shape optimization) problem in heat transfer. As an inverse steady-state heat transfer problem, given a body locally heated by a specified heat flux and exposed to convective heat transfer on parts of its boundary, the aim is to find the optimal shape of this body such that the temperature is constant on a desired subset of its boundary. The numerical method to achieve this aim consists of a three-dimensional elliptic grid generation technique to generate a mesh over the body and solve for a heat conduction equation. This paper describes a novel sensitivity analysis scheme to compute the sensitivity of the temperatures to variation of grid node positions and the conjugate gradient method (CGM) is used as an optimization algorithm to minimize the difference between the computed temperature on the boundary and desired temperature. The elliptic grid generation technique allows us to map the physical domain (body) onto a fixed computational domain and to discretize the heat conduction equation using the finite difference method (FDM).
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.
NASA Astrophysics Data System (ADS)
Daniel, Michael T.
Here in the early 21st century humanity is continuing to seek improved quality of life for citizens throughout the world. This global advancement is providing more people than ever with access to state-of-the-art services in areas such as transportation, entertainment, computing, communication, and so on. Providing these services to an ever-growing population while considering the constraints levied by continuing climate change will require new frontiers of clean energy to be developed. At the time of this writing, offshore wind has been proven as both a politically and economically agreeable source of clean, sustainable energy by northern European nations with many wind farms deployed in the North, Baltic, and Irish Seas. Modern offshore wind farms are equipped with an electrical system within the farm itself to aggregate the energy from all turbines in the farm before it is transmitted to shore. This collection grid is traditionally a 3-phase medium voltage alternating current (MVAC) system. Due to reactive power and other practical constraints, it is preferable to use a medium voltage direct current (MVDC) collection grid when siting farms >150 km from shore. To date, no offshore wind farm features an MVDC collection grid. However, MVDC collection grids are expected to be deployed with future offshore wind farms as they are sited further out to sea. In this work it is assumed that many future offshore wind farms may utilize an MVDC collection grid to aggregate electrical energy generated by individual wind turbines. As such, this work presents both per-phase and per-pole power electronic converter systems suitable for interfacing individual wind turbines to such an MVDC collection grid. Both interfaces are shown to provide high input power factor at the wind turbine while providing DC output current to the MVDC grid. Common mode voltage stress and circulating currents are investigated, and mitigation strategies are provided for both interfaces. A power sharing
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.
Generation of reproducible turbulent inflows for wind tunnel applications using active grids
NASA Astrophysics Data System (ADS)
Kroeger, Lars; Guelker, Gerd; Peinke, Joachim
2016-11-01
Turbulent flows are omnipresent in nature. In the case of wind energy applications, reproducible measurements in situ are quite difficult, therefore research in turbulence demands for experimental setups with reproducible turbulent flow fields. To simulate the situation from the outside in a wind tunnel an active grid can be used. It consists of horizontal and vertical rotating axes with attached square flaps which could be moved individually. This dynamically driven setup and the possibility to repeat the motions of the active grid axes permits to generate reproducible, statistically well defined turbulence with a wide range of statistical behavior. The objective of this work is to create turbulence with two active grids of different dimensions, to establish comparable setups in our available wind tunnel facilities. In this study the wake of the active grids was investigated by high speed PIV and hotwire measurements. To determine the similarities and limitations between the setups of different dimensions the hotwire data is compared using higher order statistics, increment analysis and the power spectra. The PIV data is used to observe spatial correlations and the prevailing length scales in the turbulent wakes. First results regarding this comparison are shown.
Research on grid connection control technology of double fed wind generator
NASA Astrophysics Data System (ADS)
Ling, Li
2017-01-01
The composition and working principle of variable speed constant frequency doubly fed wind power generation system is discussed in this thesis. On the basis of theoretical analysis and control on the modeling, the doubly fed wind power generation simulation control system is designed based on a TMS320F2407 digital signal processor (DSP), and has done a large amount of experimental research, which mainly include, variable speed constant frequency, constant pressure, Grid connected control experiment. The running results show that the design of simulation control system is reasonable and can meet the need of experimental research.
Yu, Zhaoyuan; Yuan, Linwang; Luo, Wen; Feng, Linyao; Lv, Guonian
2015-12-30
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.
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
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…
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.
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.
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.
NASA Astrophysics Data System (ADS)
Obara, Shin'ya
The fuel cell micro-grid is expected as a distributed power supply with little environmental impact. However, if a micro-grid is installed in an urban area, a generation efficiency of less than 21% on an all-year basis is expected. Generally, in planning an electric power network using a micro-grid, all the target buildings are connected and electric power is supplied. In this paper, a micro-grid is divided into multiple and each is optimized for the purpose of maximization of power generation efficiency. In the cooperation management of a micro-grid, large fluctuations in load, or increases and decreases in a building, can be followed with a grid using a system-interconnection device. The system proposed in this paper obtained results with high generation efficiency (from 21.1% to 27.6%) compared with the central system (generation efficiency is 20.6% to 24.8%) of a fuel cell micro-grid.
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 Cartesian Grid Generation Method Considering a Complicated Cell Geometry at the Body Surface
NASA Astrophysics Data System (ADS)
Lahur, Paulus R.; Nakamura, Yoshiaki
A cell-splitting method for Cartesian grid generation that has the capability of taking into account the cases of thin body and sharp edge is proposed in this paper. Such cases are frequently found when solving the flow around a very thin wing, such as that of a supersonic transport (SST). The method has also been extended to treat the problem of multiple solid regions within a cell, which is sometimes encountered at a highly curved body surface. Validation of the method proposed here is carried out on a sharp, thin double wedge in a supersonic flow, where significant improvements in accuracy are achieved at the cost of a small increase in the number of cells. Furthermore, application of the present method to a model of SST shows its effectiveness on a three-dimensional, realistic geometry. As a result of making a pseudo-planar approximation for body surface elements, the total number of body surface elements was reduced by a factor of about 3.2 in this application. Local grid refinement by relocating grid cells to a curved surface is also proposed, so that a more accurate solution is obtained with a reasonable number of cells.
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.
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.
NASA Astrophysics Data System (ADS)
Chatterjee, A.; Ghoshal, S. P.; Mukherjee, V.
In this paper, a conventional thermal power system equipped with automatic voltage regulator, IEEE type dual input power system stabilizer (PSS) PSS3B and integral controlled automatic generation control loop is considered. A distributed generation (DG) system consisting of aqua electrolyzer, photovoltaic cells, diesel engine generator, and some other energy storage devices like flywheel energy storage system and battery energy storage system is modeled. This hybrid distributed system is connected to the grid. While integrating this DG with the onventional thermal power system, improved transient performance is noticed. Further improvement in the transient performance of this grid connected DG is observed with the usage of superconducting magnetic energy storage device. The different tunable parameters of the proposed hybrid power system model are optimized by artificial bee colony (ABC) algorithm. The optimal solutions offered by the ABC algorithm are compared with those offered by genetic algorithm (GA). It is also revealed that the optimizing performance of the ABC is better than the GA for this specific application.
Computation and analysis of rotor-noise generation in grid turbulence
NASA Astrophysics Data System (ADS)
Wang, Junye; Wang, Kan; Wang, Meng
2016-11-01
The noise of a ten-bladed rotor interacting with a grid-generated turbulent flow at low Mach number is computed using large-eddy simulation and the Ffowcs Williams-Hawkings extension to Lighthill's theory. The grid turbulence is approximated as convected homogeneous and isotropic turbulence generated by a separate simulation and provided as inflow boundary conditions. The sound pressure spectrum predicted by the simulation exhibits overall agreement with previous experimental measurements in terms of the spectral shape and level. The turbulence ingestion noise is broadband with small peaks at the blade passing frequency and its harmonics. It is significantly stronger than the rotor self-noise generated by blade trailing-edge vortex shedding. Consistent with experimental observations, decreasing the rotor advance ratio at fixed mean inflow velocity leads to an increase in the sound pressure level. Different levels of acoustic compactness assumptions are examined, and the results indicate that the blade chord is acoustically compact over the frequency range of interest. Blade to blade correlations of the acoustic dipole sources are shown to be small. Supported by ONR Grant N00014-14-1-0129.
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.
Computing confidence intervals on solution costs for stochastic grid generation expansion problems.
Woodruff, David L..; Watson, Jean-Paul
2010-12-01
A range of core operations and planning problems for the national electrical grid are naturally formulated and solved as stochastic programming problems, which minimize expected costs subject to a range of uncertain outcomes relating to, for example, uncertain demands or generator output. A critical decision issue relating to such stochastic programs is: How many scenarios are required to ensure a specific error bound on the solution cost? Scenarios are the key mechanism used to sample from the uncertainty space, and the number of scenarios drives computational difficultly. We explore this question in the context of a long-term grid generation expansion problem, using a bounding procedure introduced by Mak, Morton, and Wood. We discuss experimental results using problem formulations independently minimizing expected cost and down-side risk. Our results indicate that we can use a surprisingly small number of scenarios to yield tight error bounds in the case of expected cost minimization, which has key practical implications. In contrast, error bounds in the case of risk minimization are significantly larger, suggesting more research is required in this area in order to achieve rigorous solutions for decision makers.
A fundamental approach to the problem of domain decomposition in structured grid generation
NASA Astrophysics Data System (ADS)
Piperni, Pasquale
2003-10-01
A new approach is presented for the automation of structured grid generation in multiply-connected domains. In this approach, the domain decomposition problem is cast as a classical boundary value problem in which the mesh topology is defined through the imposition of appropriate boundary conditions on the domain boundaries. The automation of the domain decomposition process is achieved by transferring it from the physical space to the topological space, where it is amenable to a rigorous solution. Once the domain is decomposed in the topological space, the mesh is generated in the physical space via the solution of a non-linear elliptic partial differential operator which takes into account the curvature of the physical space. The forms of the decomposition surfaces are obtained as part of the solution of the differential operator. The latter is solved iteratively in a system of overlapping sub-domains in which the decomposition surfaces are left floating, and in which only the shape of the domain boundaries and the point distribution thereon influence the form of the final mesh. It is shown that the proper representation of domain curvature is an essential element to the success of the domain decomposition strategy. In any curved space, the curvature of the decomposition surfaces must closely mirror the curvature of the space in order to yield a high quality mesh. Since the decomposition of the multiply-connected domain is done in the topological space, the curvature of the physical space must be re-injected into the system through the solution of an appropriate differential operator. A new mathematical formulation is derived for this purpose and takes the form of a new forcing function in the elliptic grid generation equations. This new Curvature term is completely general and can be applied to both two- and three-dimensional domains of arbitrary shape. The combination of the new grid generation equations and the domain decomposition strategy provides a
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.
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
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.
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.
Optimal Shape Design in Heat Transfer Based on Body-Fitted Grid Generation
NASA Astrophysics Data System (ADS)
Mohebbi, Farzad; Sellier, Mathieu
2013-04-01
This paper deals with an inverse steady-state heat transfer problem. We develop in this work a new numerical methodology to infer the shape a heated body should have for the temperature distribution on part of its boundary to match a prescribed one. This new numerical methodology solves this shape optimization problem using body-fitted grid generation to map the unknown optimal shape onto a fixed computational domain. This mapping enables a simple discretization of the Heat Equation using finite differences and allows us to remesh the physical domain, which varies at each optimization iteration. A novel aspect of this work is the sensitivity analysis, which is expressed explicitly in the fixed computational domain. This allows a very efficient evaluation of the sensitivities. The Conjugate Gradient method is used to minimize the objective function and this work proposes an efficient redistribution method to maintain the quality of the mesh throughout the optimization procedure.
Interaction of a highly flexible cantilever beam with grid-generated turbulent flow
NASA Astrophysics Data System (ADS)
Goushcha, Oleg; Andreopoulos, Yiannis
2016-11-01
Experiments have been performed to study the fluid-structure interaction of a flexible cantilever beam with the free end facing upstream in anisotropic turbulent flow. Velocity fluctuations in the wind tunnel flow were generated by a turbulence grid. Time-Resolved Particle Image Velocimetry (TR-PIV) techniques were used to acquire velocity data on the plane of a CW laser illumination. Forces exerted on the beam were estimated based on the PIV data by analytically solving the Pressure Poisson Equation (PPE). Two types of interaction were observed. At a lower Reynolds number, fluid forces excite the beam into oscillations of small magnitude. At higher Reynolds number, the excitation is stronger, deflecting the beam sufficiently to cause flow separation and vortex shedding on one side of the beam. The resultant vortices exert additional forces on the beam producing large magnitude oscillations of the beam.
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.
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.
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
Experimental Investigation of Statistical Moments of Travel Time in Grid-Generated Turbulence
NASA Astrophysics Data System (ADS)
Durgin, William; Meleschi, Shangari; Andreeva, Tatiana
2003-11-01
Experimental Investigation of Statistical Moments of Travel Time in Grid-Generated Turbulence W.W. Durgin, S.B. Meleschi and T.A. Andreeva ABSTRACT. An experimental technique for investigation of the behavior of acoustic waves propagation through a turbulent medium is discussed. The present study utilizes the ultrasonic travel-time technique to diagnose a 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. Experimental investigation is performed under well-controlled laboratory conditions using a data acquisition and control system featuring a high-speed analog to digital conversion card that enables fine resolution of ultrasonic signals. Experimental data confirm numerical and theoretical predictions of a nonlinear increase of the first-order travel time variance with propagation distance. This behavior seems to be closely related to the occurrence of first caustics [Kulkarny and White, Blanc-Benon et al, 1991, 1995]. With increased turbulent intensity the distance at which the first caustic occurs, decreases. Numerically the phenomena was explored by Blanc-Benon and Juvé [1990], Juvé et al, 1991; Karweit et al [1991]; and their probability of appearance in a random field theoretically by Kulkarny and White [1982], Klyatskin [1993], Blanc-Benon et al, [1995]. Current work seeks to illustrate the correspondence between flow parameters and the first appearance of non-linearity in the travel time variance. Expansion of experimental controls to include flow temperature references and rigid transducer supports adds to the integrity of the determined travel times.
NASA Astrophysics Data System (ADS)
Oh, H. J.; Kang, I. S.
1994-05-01
A new numerical scheme is proposed for generating an orthogonal grid in a simply-connected 2D domain. The scheme is based on the idea of decomposition of a global orthogonal transform into consecutive mappings of a conformal mapping and an auxiliary orthogonal mapping, which was suggested by Kang and Leal (J, Comput. Phys.102, 78 (1992)). The method is non-iterative and flexible in the adjustment of grid spacing The grid spacing can be controlled mainly by specification of the boundary correspondence up to three sides of the boundary. The method is also equipped with a control function that provides further degrees of freedom in the grid spacing adjustment. From a mathematical viewpoint, the proposed scheme can also be regarded as a numerical implementation of the constructive proof for the existence of a solution of the orthogonal mapping problem in an arbitrary simply-connected domain under the condition that the boundary correspondence is specified on three sides.
NASA Astrophysics Data System (ADS)
Oh, H. J.; Kang, I. S.
1994-05-01
A new numerical scheme is proposed for generating an orthogonal grid in a simply-connected 2D domain. The scheme is based on the idea of decomposition of a global orthogonal transform into consecutive mappings of a conformal mapping and an auxiliary orthogonal mapping which was suggested by Kang and Leal (J. Comput. Phys. 102, 78 (1992)). The method is non-iterative and flexible in the adjustment of grid spacing. The grid spacing can be controlled mainly by specification of the boundary correspondence up to three sides of the boundary. The method is also equipped with a control function that provides further degrees of freedom in the grid spacing adjustment. From a mathematical viewpoint, the proposed scheme can also be regarded as a numerical implementation of the constructive proof for the existence of a solution of the orthogonal mapping problem in an arbitrary simply-connected domain under the condition that the boundary correspondence is specified on three sides.
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.
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.
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…
Ruberti, M.; Averbukh, V.; Decleva, P.
2014-10-28
We present the first implementation of the ab initio many-body Green's function method, algebraic diagrammatic construction (ADC), in the B-spline single-electron basis. B-spline versions of the first order [ADC(1)] and second order [ADC(2)] schemes for the polarization propagator are developed and applied to the ab initio calculation of static (photoionization cross-sections) and dynamic (high-order harmonic generation spectra) quantities. We show that the cross-section features that pose a challenge for the Gaussian basis calculations, such as Cooper minima and high-energy tails, are found to be reproduced by the B-spline ADC in a very good agreement with the experiment. We also present the first dynamic B-spline ADC results, showing that the effect of the Cooper minimum on the high-order harmonic generation spectrum of Ar is correctly predicted by the time-dependent ADC calculation in the B-spline basis. The present development paves the way for the application of the B-spline ADC to both energy- and time-resolved theoretical studies of many-electron phenomena in atoms, molecules, and clusters.
Ruberti, M; Averbukh, V; Decleva, P
2014-10-28
We present the first implementation of the ab initio many-body Green's function method, algebraic diagrammatic construction (ADC), in the B-spline single-electron basis. B-spline versions of the first order [ADC(1)] and second order [ADC(2)] schemes for the polarization propagator are developed and applied to the ab initio calculation of static (photoionization cross-sections) and dynamic (high-order harmonic generation spectra) quantities. We show that the cross-section features that pose a challenge for the Gaussian basis calculations, such as Cooper minima and high-energy tails, are found to be reproduced by the B-spline ADC in a very good agreement with the experiment. We also present the first dynamic B-spline ADC results, showing that the effect of the Cooper minimum on the high-order harmonic generation spectrum of Ar is correctly predicted by the time-dependent ADC calculation in the B-spline basis. The present development paves the way for the application of the B-spline ADC to both energy- and time-resolved theoretical studies of many-electron phenomena in atoms, molecules, and clusters.
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.
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.
The Generation Of Quantum Turbulence In 3He-B By A Vibrating Grid At Low Temperatures
Bradley, D. I.; Fisher, S. N.; Guenault, A. M.; Haley, R. P.; Matthews, C. J.; Pickett, G. R.; Tsepelin, V.; Zaki, K.
2006-09-07
We have measured the onset of quantum turbulence generated by a vibrating grid resonator in 3He-B. Our measurements were carried out in the low temperature regime where the normal fluid component is very dilute and can be described as a gas of ballistic quasiparticles. Consequently, the normal fluid component can not participate in turbulence generation. We have measured the onset of turbulence from the grid motion using two nearby vibrating wire resonators. The vibrating wires show a reduction in thermal quasiparticle damping due to Andreev reflection in the surrounding turbulent velocity field. Our measurements reveal a transition in the transient behavior of the onset of the vorticity signal at the vibrating wire resonators as a function of the grid velocity.
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
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.
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
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.
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.
Narayanan, S.S.Y.; Murthy, B.K.; Rao, G.S.
1995-12-31
The presence of forced oscillations occurring in a Wells Turbine driven grid-connected induction generator enables one to seek a solution by considering the analogy between the dynamics of the Wells turbine driven systems with those associated with diesel-engine driven generators or electric motors driving reciprocating compressors, where also such forced oscillations occur, although there they occur in synchronism with shaft-position or speed. This difference is taken into account and the hunting network theory, which has hitherto been applied to the dynamic analysis of motors driving reciprocating compressors, is here applied to analyze the dynamics of a Wells Turbine driven grid-connected induction generator. The method enables the generator current, power and slip to be predicted from a knowledge of the shaft-torque harmonics. The result is compared with that obtained through d-q analysis.
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)
Sorenson, R. L.
1980-01-01
A method for generating two dimensional finite difference grids about airfoils and other shapes by the use of the Poisson differential equation is developed. The inhomogeneous terms are automatically chosen such that two important effects are imposed on the grid at both the inner and outer boundaries. The first effect is control of the spacing between mesh points along mesh lines intersecting the boundaries. The second effect is control of the angles with which mesh lines intersect the boundaries. A FORTRAN computer program has been written to use this method. A description of the program, a discussion of the control parameters, and a set of sample cases are included.
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.
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.
NASA Technical Reports Server (NTRS)
Su, T. Y.; Appleby, R. A.; Chen, H. C.
1991-01-01
The BCON is a menu-driven graphics interface program whose input consists of strings or arrays of points generated from a computer aided design (CAD) tool or any other surface geometry source. The user needs to design the block topology and prepare the surface geometry definition and surface grids separately. The BCON generates input files that contain the block definitions and the block relationships required for generating a multiblock volume grid with the EAGLE grid generation package. The BCON also generates the block boundary conditions file which is used along with the block relationship file as input for the general multiblock Euler (GMBE) code (GMBE, volumes 1 and 3).
Algebraic Nonlinear Collective Motion
NASA Astrophysics Data System (ADS)
Troupe, J.; Rosensteel, G.
1998-11-01
Finite-dimensional Lie algebras of vector fields determine geometrical collective models in quantum and classical physics. Every set of vector fields on Euclidean space that generates the Lie algebra sl(3, R) and contains the angular momentum algebra so(3) is determined. The subset of divergence-free sl(3, R) vector fields is proven to be indexed by a real numberΛ. TheΛ=0 solution is the linear representation that corresponds to the Riemann ellipsoidal model. The nonlinear group action on Euclidean space transforms a certain family of deformed droplets among themselves. For positiveΛ, the droplets have a neck that becomes more pronounced asΛincreases; for negativeΛ, the droplets contain a spherical bubble of radius |Λ|1/3. The nonlinear vector field algebra is extended to the nonlinear general collective motion algebra gcm(3) which includes the inertia tensor. The quantum algebraic models of nonlinear nuclear collective motion are given by irreducible unitary representations of the nonlinear gcm(3) Lie algebra. These representations model fissioning isotopes (Λ>0) and bubble and two-fluid nuclei (Λ<0).
NASA Astrophysics Data System (ADS)
Bilgili, Ata; Smith, Keston W.; Lynch, Daniel R.
2006-06-01
A brief summary of Delaunay unstructured triangular grid refinement algorithms, including the recent "off-centers" method, is provided and mesh generation requirements that are imperative to meet the criteria of the circulation modeling community are defined. A Matlab public-domain two-dimensional (2-D) mesh generation package (BatTri) based on these requirements is then presented and its efficiency shown through examples. BatTri consists of a graphical mesh editing interface and several bathymetry-based refinement algorithms, complemented by a set of diagnostic utilities to check and improve grid quality. The final output mesh node locations, node depths and element incidence list are obtained starting from only a basic set of bathymetric data. This simple but efficient setup allows fast interactive mesh customization and provides circulation modelers with problem-specific flexibility while satisfying the usual requirements on mesh size and element quality. A test of the "off-centers" method performed on 100 domains with randomly generated coastline and bathymetry shows an overall 25% reduction in the number of elements with only slight decrease in element quality. More importantly, this shows that BatTri is easily upgradeable to meet the future demands by the addition of new grid generation algorithms and Delaunay refinement schemes as they are made available.
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
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.
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.
Bicovariant quantum algebras and quantum Lie algebras
NASA Astrophysics Data System (ADS)
Schupp, Peter; Watts, Paul; Zumino, Bruno
1993-10-01
A bicovariant calculus of differential operators on a quantum group is constructed in a natural way, using invariant maps from Fun(mathfrak{G}_q ) to U q g, given by elements of the pure braid group. These operators—the “reflection matrix” Y≡L + SL - being a special case—generate algebras that linearly close under adjoint actions, i.e. they form generalized Lie algebras. We establish the connection between the Hopf algebra formulation of the calculus and a formulation in compact matrix form which is quite powerful for actual computations and as applications we find the quantum determinant and an orthogonality relation for Y in SO q (N).
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.
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.…
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.
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.
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)
Vorobev, Viktor V.; Tyukhtin, Andrey V.; Galyamin, Sergey N.
2017-04-01
Surface waves generated by a charged-particle bunch at the semi-infinite planar periodic wire structure are analyzed. It is supposed that the bunch moves parallel to the edge of the structure. The influence of the grid is described by the averaged boundary conditions. The analytical results are given for a general case, which takes into account the finite period and wires radius. It is shown that the surface waves excited by the bunch propagate along wires with the speed of light in vacuum. The number and the structure of these surface waves depend on relative location of the bunch path and the grid. One type of wave is always excited, but its magnitude decreases with distance from the bunch path to the structure edge. If the bunch projection falls on the half-plane occupied by wires, then additionally three surface waves are generated: two of them are equivalent to ones excited by the bunch moving along infinite wire grid and another one represents the surface wave reflected from the edge. The analysis of the surface waves shows that their structure allows for determination of the length of the bunch. Typical numerical results are presented.
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.
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.
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.
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.
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.
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.
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.
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.
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 Astrophysics Data System (ADS)
Durka, R.
2017-04-01
The S-expansion framework is analyzed in the context of a freedom in closing the multiplication tables for the abelian semigroups. Including the possibility of the zero element in the resonant decomposition, and associating the Lorentz generator with the semigroup identity element, leads to a wide class of the expanded Lie algebras introducing interesting modifications to the gauge gravity theories. Among the results, we find all the Maxwell algebras of type {{B}m} , {{C}m} , and the recently introduced {{D}m} . The additional new examples complete the resulting generalization of the bosonic enlargements for an arbitrary number of the Lorentz-like and translational-like generators. Some further prospects concerning enlarging the algebras are discussed, along with providing all the necessary constituents for constructing the gravity actions based on the obtained results.
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.
Effects of a curved vocal tract with grid-generated tongue profile on low-order formants
Milenkovic, Paul H.; Yaddanapudi, Srikanth; Vorperian, Houri K.; Kent, Raymond D.
2010-01-01
A hyperbolic grid-generation algorithm allows investigation of the effect of vocal-tract curvature on low-order formants. A smooth two-dimensional (2D) curve represents the combined lower lip, tongue, and anterior pharyngeal wall profile as displacements from the combined upper lip, palate, and posterior pharyngeal wall outline. The algorithm is able to generate tongue displacements beyond the local radius of strongly curved sections of the palate. The 2D grid, along with transverse profiles of the lip, oral-pharyngeal, and epilarynx regions, specifies a vocal conduit from which an effective area function may be determined using corrections to acoustic parameters resulting from duct curvature; the effective area function in turn determines formant frequencies through an acoustic transmission-line calculation. Results of the corrected transmission line are compared with a three-dimensional finite element model. The observed effects of the curved vocal tract on formants F1 and F2 are in order of importance, as follows: (1) reduction in midline distances owing to curvature of the palate and the bend joining the palate to the pharynx, (2) the curvature correction to areas and section lengths, and (3) adjustments to the palate-tongue distance required to produce smooth tongue shapes at large displacements from the palate. PMID:20136222
Effects of a curved vocal tract with grid-generated tongue profile on low-order formants.
Milenkovic, Paul H; Yaddanapudi, Srikanth; Vorperian, Houri K; Kent, Raymond D
2010-02-01
A hyperbolic grid-generation algorithm allows investigation of the effect of vocal-tract curvature on low-order formants. A smooth two-dimensional (2D) curve represents the combined lower lip, tongue, and anterior pharyngeal wall profile as displacements from the combined upper lip, palate, and posterior pharyngeal wall outline. The algorithm is able to generate tongue displacements beyond the local radius of strongly curved sections of the palate. The 2D grid, along with transverse profiles of the lip, oral-pharyngeal, and epilarynx regions, specifies a vocal conduit from which an effective area function may be determined using corrections to acoustic parameters resulting from duct curvature; the effective area function in turn determines formant frequencies through an acoustic transmission-line calculation. Results of the corrected transmission line are compared with a three-dimensional finite element model. The observed effects of the curved vocal tract on formants F1 and F2 are in order of importance, as follows: (1) reduction in midline distances owing to curvature of the palate and the bend joining the palate to the pharynx, (2) the curvature correction to areas and section lengths, and (3) adjustments to the palate-tongue distance required to produce smooth tongue shapes at large displacements from the palate.
Algebraic mesh quality metrics
KNUPP,PATRICK
2000-04-24
Quality metrics for structured and unstructured mesh generation are placed within an algebraic framework to form a mathematical theory of mesh quality metrics. The theory, based on the Jacobian and related matrices, provides a means of constructing, classifying, and evaluating mesh quality metrics. The Jacobian matrix is factored into geometrically meaningful parts. A nodally-invariant Jacobian matrix can be defined for simplicial elements using a weight matrix derived from the Jacobian matrix of an ideal reference element. Scale and orientation-invariant algebraic mesh quality metrics are defined. the singular value decomposition is used to study relationships between metrics. Equivalence of the element condition number and mean ratio metrics is proved. Condition number is shown to measure the distance of an element to the set of degenerate elements. Algebraic measures for skew, length ratio, shape, volume, and orientation are defined abstractly, with specific examples given. Combined metrics for shape and volume, shape-volume-orientation are algebraically defined and examples of such metrics are given. Algebraic mesh quality metrics are extended to non-simplical elements. A series of numerical tests verify the theoretical properties of the metrics defined.
NASA Technical Reports Server (NTRS)
Mulligan, Jeffrey B.
2017-01-01
A color algebra refers to a system for computing sums and products of colors, analogous to additive and subtractive color mixtures. We would like it to match the well-defined algebra of spectral functions describing lights and surface reflectances, but an exact correspondence is impossible after the spectra have been projected to a three-dimensional color space, because of metamerism physically different spectra can produce the same color sensation. Metameric spectra are interchangeable for the purposes of addition, but not multiplication, so any color algebra is necessarily an approximation to physical reality. Nevertheless, because the majority of naturally-occurring spectra are well-behaved (e.g., continuous and slowly-varying), color algebras can be formulated that are largely accurate and agree well with human intuition. Here we explore the family of algebras that result from associating each color with a member of a three-dimensional manifold of spectra. This association can be used to construct a color product, defined as the color of the spectrum of the wavelength-wise product of the spectra associated with the two input colors. The choice of the spectral manifold determines the behavior of the resulting system, and certain special subspaces allow computational efficiencies. The resulting systems can be used to improve computer graphic rendering techniques, and to model various perceptual phenomena such as color constancy.
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.
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.
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.
3D Composite Grids Using Bezier Curves and Surfaces in Component Adaptive Methods
1993-08-01
bounding curves, an algebraic grid generation method, such as transfinite interpolation of these curves, results in a definition of the interior of...dependent variables is assembled and solved iteratively. The interior generated by the transfinite interpolation technique is used as the initial guess...The boundaries of the face are first parameterized in this fashion Transfinite interpolation is then employed first to obtain a parameterization of
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)
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.
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-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.
ERIC Educational Resources Information Center
Capani, Antonio; De Dominicis, Gabriel
This paper proposes a model for a general interface between people and Computer Algebra Systems (CAS). The main features in the CAS interface are data navigation and the possibility of accessing powerful remote machines. This model is based on the idea of session management, in which the main engine of the tool enables interactions with the…
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
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)
Zhou, Yi; Nagata, Koji; Sakai, Yasuhiko; Ito, Yasumasa; Hayase, Toshiyuki
2015-07-01
Direct numerical simulations were performed to investigate the topological evolution of turbulence generated by a single square grid. Immediately behind the single square grid (i.e., in the irrotational dissipation region), the conditional mean trajectories (CMTs) of R and Q are distinctly different from those in homogeneous isotropic turbulence (HIT), where R and Q are the third and second invariants, respectively, of the velocity gradient tensor. In this region, the non-local influence of the pressure Hessian is dominant, which causes irrotational viscous dissipation. The anisotropic part of the pressure Hessian may be responsible for the irrotational viscous dissipation found at the turbulent/nonturbulent interface in turbulent jets [C. B. da Silva and J. C. F. Pereira, "Invariants of the velocity-gradient, rate-of-strain, and rate-of-rotation tensors across the turbulent/nonturbulent interface in jets," Phys. Fluids 20, 055101 (2008) and Watanabe et al., "Vortex stretching and compression near the turbulent/non-turbulent interface in a planar jet," J. Fluid Mech. 758, 754 (2014)]. In the transition region, the CMTs of R and Q gradually acquire an evolution pattern similar to that in HIT. The expansion of the (R, Q) map at Q > 0 is associated with the effects of the restricted Euler term. Finally, in the fully turbulent region, the CMTs of R and Q demonstrate a clockwise evolution toward a point close to the origin. However, the cyclic spiraling seen in HIT is not found. The lack of the cyclic evolution may be attributed to the considerably large effect of the viscous term owing to the relatively small local Reynolds number. On average, the combined influences of the restricted Euler term and anisotropic part of the pressure Hessian contribute to the generation of small-scale motions, and the viscous term tends to remove small-scale motions.
Etingov, Pavel; Makarov, PNNL Yuri; Subbarao, PNNL Kris; PNNL,
2014-03-03
RUT software is designed for use by the Balancing Authorities to predict and display additional requirements caused by the variability and uncertainty in load and generation. The prediction is made for the next operating hours as well as for the next day. The tool predicts possible deficiencies in generation capability and ramping capability. This deficiency of balancing resources can cause serious risks to power system stability and also impact real-time market energy prices. The tool dynamically and adaptively correlates changing system conditions with the additional balancing needs triggered by the interplay between forecasted and actual load and output of variable resources. The assessment is performed using a specially developed probabilistic algorithm incorporating multiple sources of uncertainty including wind, solar and load forecast errors. The tool evaluates required generation for a worst case scenario, with a user-specified confidence level.
Symplectic Clifford Algebraic Field Theory.
NASA Astrophysics Data System (ADS)
Dixon, Geoffrey Moore
We develop a mathematical framework on which is built a theory of fermion, scalar, and gauge vector fields. This field theory is shown to be equivalent to the original Weinberg-Salam model of weak and electromagnetic interactions, but since the new framework is more rigid than that on which the original Weinberg-Salam model was built, a concomitant reduction in the number of assumptions lying outside of the framework has resulted. In particular, parity violation is actually hiding within our framework, and with little difficulty we are able to manifest it. The mathematical framework upon which we build our field theory is arrived at along two separate paths. The first is by the marriage of a Clifford algebra and a Lie superalgebra, the result being called a super Clifford algebra. The second is by providing a new characterization for a Clifford algebra employing its generators and a symmetric array of metric coefficients. Subsequently we generalize this characterization to the case of an antisymmetric array of metric coefficients, and we call the algebra which results a symplectic Clifford algebra. It is upon one of these that we build our field theory, and it is shown that this symplectic Clifford algebra is a particular subalgebra of a super Clifford algebra. The final ingredient is the operation of bracketing which involves treating the elements of our algebra as endomorphisms of a particular inner product space, and employing this space and its inner product to provide us with maps from our algebra to the reals. It is this operation which enables us to manifest the parity violation hiding in our algebra.
1987-07-01
subregions and then Joining them to obtain the coordinates in the integrated surface. 4 REFERENCES 1. THOMPSON , J . F ., WARSI, Z.U.A., and MASTIN, C.W... Thompson , J . F ., 1982, pp. 41-77. 10. WARSI, Z.U.A., and ZIEBARTH, J.P., ’Numerical Generation of Three-Dimen- sional Coordinates Between Bodies of
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.
2009-03-01
IEEE Spectrum Online Article, "Re-engineering Iraq,” Feb. 2006.)....................................................................5 Figure 5...Capstone Microturbines (Source: Capstone Turbine Coorperation) ..............12 Figure 6: Caterpillar Model 3406C 300kW Reciprocating Diesel...Generator (Source: Caterpillar ) .......................................................................................................13 Figure 7
Bradley, D. I.; Fisher, S. N.; Guenault, A. M.; Haley, R. P.; Matthews, C. J.; Pickett, G. R.; Tsepelin, V.; Zaki, K.
2006-09-07
We describe measurements of the decay of quantum turbulence produced by a vibrating grid in superfluid 3He-B at low temperatures. Two nearby NbTi vibrating wire resonators at different distances from the grid are used to detect the turbulence via a reduction in the quasiparticle damping owing to Andreev reflection by the flow around the vortex lines. The decay time constant of this turbulence, after stopping the grid motion, is longer at the wire furthest from the grid. This suggests that either the tangle evolves and moves away from the grid once the grid motion has been stopped, or that there is a faster decay mechanism in operation close to the grid.
Hasegawa, J.; Yoshida, M.; Ogawa, M.; Oguri, Y.; Nakajima, M.; Horioka, K.; Kwan, J.
2003-08-01
We examined grid-controlled extraction for a laser ion source using a KrF laser. By using grid-controlled extraction in the over-dense regime, we found that the ion beam current waveforms were stabilized more significantly as the grid bias raised from -90 V to -280 V. The normalized emittance of 0.08 {pi}mm-mrad measured without the grid control was improved to 0.06 {pi}mm-mrad with the grid control. In contrast to this observation, the grid bias disturbed the pattern of the beam extracted in the source-limited regime. Fast extraction was carried out using a high-voltage pulse with a rise time of {approx} 100 ns. The grid control suppressed successfully the beam pedestal originating from the plasma pre-filled in the extraction gap.
Deformed Kac Moody and Virasoro algebras
NASA Astrophysics Data System (ADS)
Balachandran, A. P.; Queiroz, A. R.; Marques, A. M.; Teotonio-Sobrinho, P.
2007-07-01
Whenever the group {\\bb R}^n acts on an algebra {\\cal A} , there is a method to twist \\cal A to a new algebra {\\cal A}_\\theta which depends on an antisymmetric matrix θ (θμν = -θνμ = constant). The Groenewold-Moyal plane {\\cal A}_\\theta({\\bb R}^{d+1}) is an example of such a twisted algebra. We give a general construction to realize this twist in terms of {\\cal A} itself and certain 'charge' operators Qμ. For {\\cal A}_\\theta({\\bb R}^{d+1}), Q_\\mu are translation generators. This construction is then applied to twist the oscillators realizing the Kac-Moody (KM) algebra as well as the KM currents. They give different deformations of the KM algebra. From one of the deformations of the KM algebra, we construct, via the Sugawara construction, the Virasoro algebra. These deformations have an implication for statistics as well.
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.
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
You, Shutang; Hadley, Stanton W.; Shankar, Mallikarjun; ...
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
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 method 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.
Jayet Bray, Laurence C; Quoy, Mathias; Harris, Frederick C; Goodman, Philip H
2010-01-01
Hippocampal "place cells" and the precession of their extracellularly recorded spiking during traversal of a "place field" are well-established phenomena. More recent experiments describe associated entorhinal "grid cell" firing, but to date only conceptual models have been offered to explain the potential interactions among entorhinal cortex (EC) and hippocampus. To better understand not only spatial navigation, but mechanisms of episodic and semantic memory consolidation and reconsolidation, more detailed physiological models are needed to guide confirmatory experiments. Here, we report the results of a putative entorhinal-hippocampal circuit level model that incorporates recurrent asynchronous-irregular non-linear (RAIN) dynamics, in the context of recent in vivo findings showing specific intracellular-extracellular precession disparities and place field destabilization by entorhinal lesioning. In particular, during computer-simulated rodent maze navigation, our model demonstrate asymmetric ramp-like depolarization, increased theta power, and frequency (that can explain the phase precession disparity), and a role for STDP and K(AHP) channels. Additionally, we propose distinct roles for two entorhinal cell populations projecting to hippocampus. Grid cell populations transiently trigger place field activity, while tonic "suppression-generating cell" populations minimize aberrant place cell activation, and limit the number of active place cells during traversal of a given field. Applied to place-cell RAIN networks, this tonic suppression explains an otherwise seemingly discordant association with overall increased firing. The findings of this circuit level model suggest in vivo and in vitro experiments that could refute or support the proposed mechanisms of place cell dynamics and modulating influences of EC.
NASA Astrophysics Data System (ADS)
King, Nelson E.; Liu, Brent; Zhou, Zheng; Documet, Jorge; Huang, H. K.
2005-04-01
Grid Computing represents the latest and most exciting technology to evolve from the familiar realm of parallel, peer-to-peer and client-server models that can address the problem of fault-tolerant storage for backup and recovery of clinical images. We have researched and developed a novel Data Grid testbed involving several federated PAC systems based on grid architecture. By integrating a grid computing architecture to the DICOM environment, a failed PACS archive can recover its image data from others in the federation in a timely and seamless fashion. The design reflects the five-layer architecture of grid computing: Fabric, Resource, Connectivity, Collective, and Application Layers. The testbed Data Grid architecture representing three federated PAC systems, the Fault-Tolerant PACS archive server at the Image Processing and Informatics Laboratory, Marina del Rey, the clinical PACS at Saint John's Health Center, Santa Monica, and the clinical PACS at the Healthcare Consultation Center II, USC Health Science Campus, will be presented. The successful demonstration of the Data Grid in the testbed will provide an understanding of the Data Grid concept in clinical image data backup as well as establishment of benchmarks for performance from future grid technology improvements and serve as a road map for expanded research into large enterprise and federation level data grids to guarantee 99.999 % up time.
Super short term forecasting of photovoltaic power generation output in micro grid
NASA Astrophysics Data System (ADS)
Gong, Cheng; Ma, Longfei; Chi, Zhongjun; Zhang, Baoqun; Jiao, Ran; Yang, Bing; Chen, Jianshu; Zeng, Shuang
2017-01-01
The prediction model combining data mining and support vector machine (SVM) was built. Which provide information of photovoltaic (PV) power generation output for economic operation and optimal control of micro gird, and which reduce influence of power system from PV fluctuation. Because of the characteristic which output of PV rely on radiation intensity, ambient temperature, cloudiness, etc., so data mining was brought in. This technology can deal with large amounts of historical data and eliminate superfluous data, by using fuzzy classifier of daily type and grey related degree. The model of SVM was built, which can dock with information from data mining. Based on measured data from a small PV station, the prediction model was tested. The numerical example shows that the prediction model is fast and accurate.
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.
Quantum Q systems: from cluster algebras to quantum current algebras
NASA Astrophysics Data System (ADS)
Di Francesco, Philippe; Kedem, Rinat
2017-02-01
This paper gives a new algebraic interpretation for the algebra generated by the quantum cluster variables of the A_r quantum Q-system (Di Francesco and Kedem in Int Math Res Not IMRN 10:2593-2642, 2014). We show that the algebra can be described as a quotient of the localization of the quantum algebra U_{√{q}}({n}[u,u^{-1}])subset U_{√{q}}(widehat{{sl}}_2), in the Drinfeld presentation. The generating current is made up of a subset of the cluster variables which satisfy the Q-system, which we call fundamental. The other cluster variables are given by a quantum determinant-type formula, and are polynomials in the fundamental generators. The conserved quantities of the discrete evolution (Di Francesco and Kedem in Adv Math 228(1):97-152, 2011) described by quantum Q-system generate the Cartan currents at level 0, in a non-standard polarization. The rest of the quantum affine algebra is also described in terms of cluster variables.
NASA Astrophysics Data System (ADS)
Kato, Takeyoshi; Yamawaki, Hiroshi; Suzuoki, Yasuo
Power output fluctuation of photovoltaic power generation systems (PVSs) may cause negative impacts on the existing electric power system when the penetration of PVSs is quite large. A micro-grid consisting of clustered PVSs and a battery system would be one of the promising measures against negative impacts of clustered PVSs, while the capacity of battery system should be reduced as much as possible from the economic point of view. Because of the difference in output fluctuation among PVSs in the various locations, the total output fluctuations of PVSs would be relaxed due to the so-called “smoothing-effect”. By using data on solar irradiance simultaneously observed at five points, this study evaluates the total output fluctuation of several micro-grids and the required capacity of battery system, taking the smoothing effect into account. The main results are as follows. The balancing control is accomplished with the acceptable error by using the small capacity of battery system, while small output fluctuation still remains in each micro-grid. In such the situation, because the total fluctuation of five micro-grids is not so large, the acceptable error in balancing control can be increased by a few percentages, resulting in reduction in the required maximum power of battery system by a few ten percentages.
Lie algebras of classical and stochastic electrodynamics
NASA Astrophysics Data System (ADS)
Neto, J. J. Soares; Vianna, J. D. M.
1994-03-01
The Lie algebras associated with infinitesimal symmetry transformations of third-order differential equations of interest to classical electrodynamics and stochastic electrodynamics have been obtained. The structure constants for a general case are presented and the Lie algebra for each particular application is easily achieved. By the method used here it is not necessary to know the explicit expressions of the infinitesimal generators in order to determine the structure constants of the Lie algebra.
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.
NASA Astrophysics Data System (ADS)
Vaninsky, Alexander
2011-04-01
This article introduces a trigonometric field (TF) that extends the field of real numbers by adding two new elements: sin and cos - satisfying an axiom sin2 + cos2 = 1. It is shown that by assigning meaningful names to particular elements of the field, all known trigonometric identities may be introduced and proved. Two different interpretations of the TF are discussed with many others potentially possible. The main objective of this article is to introduce a broader view of trigonometry that can serve as motivation for mathematics students and teachers to study and teach abstract algebraic structures.
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
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.
Mehrotra, Sanjay
2016-09-07
The support from this grant resulted in seven published papers and a technical report. Two papers are published in SIAM J. on Optimization [87, 88]; two papers are published in IEEE Transactions on Power Systems [77, 78]; one paper is published in Smart Grid [79]; one paper is published in Computational Optimization and Applications [44] and one in INFORMS J. on Computing [67]). The works in [44, 67, 87, 88] were funded primarily by this DOE grant. The applied papers in [77, 78, 79] were also supported through a subcontract from the Argonne National Lab. We start by presenting our main research results on the scenario generation problem in Sections 1–2. We present our algorithmic results on interior point methods for convex optimization problems in Section 3. We describe a new ‘central’ cutting surface algorithm developed for solving large scale convex programming problems (as is the case with our proposed research) with semi-infinite number of constraints in Section 4. In Sections 5–6 we present our work on two application problems of interest to DOE.
Derive Workshop Matrix Algebra and Linear Algebra.
ERIC Educational Resources Information Center
Townsley Kulich, Lisa; Victor, Barbara
This document presents the course content for a workshop that integrates the use of the computer algebra system Derive with topics in matrix and linear algebra. The first section is a guide to using Derive that provides information on how to write algebraic expressions, make graphs, save files, edit, define functions, differentiate expressions,…
2016-03-24
diamonds and hexagons, and anything in between. Each of these cases has also been studied under a previous program...tensor to a map of the surface. Figure 16. One of the cell types studies is the diamond shaped cell. The impedance matches that of the...of effective rectangular cells created from the moment of inertia method. Figure 16 and figure 17 show two examples, for an elongated diamond
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.
Grid flexibility and patching techniques
NASA Technical Reports Server (NTRS)
Keith, T. G.; Smith, L. W.; Yung, C. N.; Barthelson, S. H.; Dewitt, K. J.
1984-01-01
The numerical determination of combustor flowfields is of great value to the combustor designer. An a priori knowledge of the flow behavior can speed the combustor design process and reduce the number of experimental test rigs required to arrive at an optimal design. Even 2-D steady incompressible isothermal flow predictions are of use; many codes of this kind are available, each employing different techniques to surmount the difficulties arising from the nonlinearity of the governing equations and from typically irregular combustor geometries. Mapping techniques (algebraic and elliptic PDE), and adaptive grid methods (both multi-grid and grid embedding) as applied to axisymmetric combustors are discussed.
Upper bound for the length of commutative algebras
NASA Astrophysics Data System (ADS)
Markova, Ol'ga V.
2009-12-01
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.
Quantum walled Brauer algebra: commuting families, Baxterization, and representations
NASA Astrophysics Data System (ADS)
Semikhatov, A. M.; Tipunin, I. Yu
2017-02-01
For the quantum walled Brauer algebra, we construct its Specht modules and (for generic parameters of the algebra) seminormal modules. The latter construction yields the spectrum of a commuting family of Jucys-Murphy elements. We also propose a Baxterization prescription; it involves representing the quantum walled Brauer algebra in terms of morphisms in a braided monoidal category and introducing parameters into these morphisms, which allows constructing a ‘universal transfer matrix’ that generates commuting elements of the algebra.
Dynamical algebras for Poeschl-Teller Hamiltonian hierarchies
Kuru, S.; Negro, J.
2009-12-15
The dynamical algebras of the trigonometric and hyperbolic symmetric Poeschl-Teller Hamiltonian hierarchies are obtained. A kind of discrete-differential realizations of these algebras are found which are isomorphic to so(3, 2) Lie algebras. In order to get them, first the relation between ladder and factor operators is investigated. In particular, the action of the ladder operators on normalized eigenfunctions is found explicitly. Then, the whole dynamical algebras are generated in a straightforward way.
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
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.
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.
Algebraic orbifold conformal field theories
Xu, Feng
2000-01-01
The unitary rational orbifold conformal field theories in the algebraic quantum field theory and subfactor theory framework are formulated. Under general conditions, it is shown that the orbifold of a given unitary rational conformal field theory generates a unitary modular category. Many new unitary modular categories are obtained. It is also shown that the irreducible representations of orbifolds of rank one lattice vertex operator algebras give rise to unitary modular categories and determine the corresponding modular matrices, which has been conjectured for some time. PMID:11106383
Flow solution on a dual-block grid around an airplane
NASA Technical Reports Server (NTRS)
Eriksson, Lars-Erik
1987-01-01
The compressible flow around a complex fighter-aircraft configuration (fuselage, cranked delta wing, canard, and inlet) is simulated numerically using a novel grid scheme and a finite-volume Euler solver. The patched dual-block grid is generated by an algebraic procedure based on transfinite interpolation, and the explicit Runge-Kutta time-stepping Euler solver is implemented with a high degree of vectorization on a Cyber 205 processor. Results are presented in extensive graphs and diagrams and characterized in detail. The concentration of grid points near the wing apex in the present scheme is shown to facilitate capture of the vortex generated by the leading edge at high angles of attack and modeling of its interaction with the canard wake.
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.
Gauged Ads-Maxwell Algebra and Gravity
NASA Astrophysics Data System (ADS)
Durka, R.; Kowalski-Glikman, J.; Szczachor, M.
We deform the anti-de Sitter algebra by adding additional generators {Z}ab, forming in this way the negative cosmological constant counterpart of the Maxwell algebra. We gauge this algebra and construct a dynamical model with the help of a constrained BF theory. It turns out that the resulting theory is described by the Einstein-Cartan action with Holst term, and the gauge fields associated with the Maxwell generators {Z}ab appear only in topological terms that do not influence dynamical field equations. We briefly comment on the extension of this construction, which would lead to a nontrivial Maxwell fields dynamics.
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)
Bewley, Thomas; Cessna, Joseph; Belitz, Paul
2008-11-01
The abstract field of n-dimensional sphere packing theory is well developed (for a comprehensive review, see Sphere Packings, Lattices and Groups by Conway and Sloane). This theory forms the theoretical underpinning of the error-correcting codes used in both deep space communications and in computer memory. The present work extends this elegant theory to two important and immensely practical problems in computational fluid dynamics: (a) the generation of efficient grids for the coordination of grid-based derivative-free optimization algorithms in n dimensions, and (b) the effective n-dimensional interconnection of massively-parallel clusters of computational nodes. As we will illustrate and quantify, the first problem benefits tremendously from dense sphere packings with large kissing numbers >> 2n, whereas the latter problem benefits tremendously from rare sphere packings with kissing number = n+1.
2016-01-14
The electric power grid has been rightly celebrated as the single most important engineering feat of the 20th century. The grid powers our homes, offices, hospitals, and schools; and, increasingly, it powers our favorite devices from smartphones to HDTVs. With those and other modern innovations and challenges, our grid will need to evolve. Grid modernization efforts will help the grid make full use of today’s advanced technologies and serve our needs in the 21st century. While the vast majority of upgrades are implemented by private sector energy companies that own and operate the grid, DOE has been investing in technologies that are revolutionizing the way we generate, store and transmit power.
Investigation of three-dimensional mesh generation with precise controls
NASA Astrophysics Data System (ADS)
Eiseman, Peter R.
1989-01-01
In the grant, a number of accomplishments were made in a variety of ways and in a variety of topics. The ways in which this was achieved were in oral communication with others, in the organization of conferences, in the journal publications, in the direction of graduate studies, and in the computer demonstration of theoretical developments. The topics include a study of shock-vortex interaction and a number of studies in grid generation. Those studies covered algebraic and interactive aspects here converged with the establishment of a powerful control point formulation for arbitrary grid generation.
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.
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…
ERIC Educational Resources Information Center
Miller, L. Diane; England, David A.
1989-01-01
Describes a study in a large metropolitan high school to ascertain what influence the use of regular writing in algebra classes would have on students' attitudes towards algebra and their skills in algebra. Reports the simpler and more direct the writing topics the better. (MVL)
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.
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…
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…
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.
Ackermann, Doreen; Wang, Weiqun; Streipert, Benjamin; Geib, Birgit; Grün, Lothar; König, Simone
2012-05-01
The comparison of proteins separated on 2DE is difficult due to gel-to-gel variability. Here, a method named comparative fluorescence gel electrophoresis (CoFGE) is presented, which allows the generation of an artificial protein grid in parallel to the separation of an analytical sample on the same gel. Different fluorescent stains are used to distinguish sample and marker on the gel. The technology combines elements of 1DE and 2DE. Special gel combs with V-shaped wells are placed in a stacking gel above the pI strip. Proteins separated on the pI strip are electrophoresed at the same time as marker proteins (commercially available purified protein of different molecular weight) placed in V-wells. In that way, grids providing approximately 100 nodes as landmarks for the determination of protein spot coordinates are generated. Data analysis is possible with commercial 2DE software capable of warping. The method improves comparability of 2DE protein gels, because they are generated in combination with regular in-gel anchor points formed by protein standards. This was shown here for two comparative experiments with three gels each using Escherichia coli lysate. For a set of 47 well-defined samples spots, the deviation of the coordinates was improved from 7% to less than 1% applying warping using the marker grid. Conclusively, as long as the same protein markers, the same size of pI-strips and the same technology are used, gel matching is reproducibly possible. This is an important advancement for projects involving comparison of 2DE-gels produced over several years and in different laboratories.
1990-12-01
NUMBERS Interactive EAGLE: An Interactive Surface Mesh and Three- Dimensional Grid Generation System PE6SB07F i 6 AUTHOR(S) Dietzo W. E. and Evans, S...Development Center/DO Air Force Systems Command Arnold AFB, TN 37389-5000 REPORT NUMBER AEDC-TR-90-2S 10 SPONSORING/MONITORING AGENCY REPORT NUMBER 11...CLASSIFICATION 19 SECURITY CLASSIFICATION OF REPORT I OF THIS PAGE OF ABSTRACT UNCLASSIFIED U N C L A S S I F I E D UNCLASSIFIED 15 NUMBER OF PAGES 171 16
Discrete Minimal Surface Algebras
NASA Astrophysics Data System (ADS)
Arnlind, Joakim; Hoppe, Jens
2010-05-01
We consider discrete minimal surface algebras (DMSA) as generalized noncommutative analogues of minimal surfaces in higher dimensional spheres. These algebras appear naturally in membrane theory, where sequences of their representations are used as a regularization. After showing that the defining relations of the algebra are consistent, and that one can compute a basis of the enveloping algebra, we give several explicit examples of DMSAs in terms of subsets of sln (any semi-simple Lie algebra providing a trivial example by itself). A special class of DMSAs are Yang-Mills algebras. The representation graph is introduced to study representations of DMSAs of dimension d ≤ 4, and properties of representations are related to properties of graphs. The representation graph of a tensor product is (generically) the Cartesian product of the corresponding graphs. We provide explicit examples of irreducible representations and, for coinciding eigenvalues, classify all the unitary representations of the corresponding algebras.
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.
Dynamical systems and quantum bicrossproduct algebras
NASA Astrophysics Data System (ADS)
Arratia, Oscar; del Olmo, Mariano A.
2002-06-01
We present a unified study of some aspects of quantum bicrossproduct algebras of inhomogeneous Lie algebras, such as Poincaré, Galilei and Euclidean in N dimensions. The action associated with the bicrossproduct structure allows us to obtain a nonlinear action over a new group linked to the translations. This new nonlinear action associates a dynamical system with each generator which is the object of our study.
Superintegrability in Two Dimensions and the Racah-Wilson Algebra
NASA Astrophysics Data System (ADS)
Genest, Vincent X.; Vinet, Luc; Zhedanov, Alexei
2014-08-01
The analysis of the most general second-order superintegrable system in two dimensions: the generic 3-parameter model on the 2-sphere is cast in the framework of the Racah problem for the algebra. The Hamiltonian of the 3-parameter system and the generators of its quadratic symmetry algebra are seen to correspond to the total and intermediate Casimir operators of the combination of three algebras, respectively. The construction makes explicit the isomorphism between the Racah-Wilson algebra, which is the fundamental algebraic structure behind the Racah problem for , and the invariance algebra of the generic 3-parameter system. It also provides an explanation for the occurrence of the Racah polynomials as overlap coefficients in this context. The irreducible representations of the Racah-Wilson algebra are reviewed as well as their connection with the Askey scheme of classical orthogonal polynomials.
NASA Astrophysics Data System (ADS)
El-Sayed, Abeer Galal; Obara, Shin'ya
In this study, the combined system of a solid-oxide fuel cell (SOFC) and a proton-exchange membrane fuel cell (PEFC) is developed. The proposed system consists of a SOFC-PEFC combined system and a photovoltaic system (PV) as the energy supply to a micro-grid. The exhaust heat of the SOFC is used for the steam reforming of the bio-ethanol gas with time shift utilization of the exhaust heat of the SOFC in optional time. The SOFC-PEFC combined system with the PV was introduced in a micro-grid of 30 residences in Sapporo, Japan. The operation plan of the system has three cases: without solar power, with 50% and with 100% of solar output power. Moreover, three types of system operation of using the SOFC independent operation, PEFC independent operation and SOFC-PEFC combined system are used to supply the demand side. A comparative study between the types of system operation is presented. The power generation efficiency is investigated for different load patterns: average load pattern, compressed load pattern and extended load pattern. This paper reported that the power generation efficiencies of the proposedsystem in consideration of these load patterns are 27% to 48%.
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.
Conformal current algebra in two dimensions
NASA Astrophysics Data System (ADS)
Ashok, Sujay K.; Benichou, Raphael; Troost, Jan
2009-06-01
We construct a non-chiral current algebra in two dimensions consistent with conformal invariance. We show that the conformal current algebra is realized in non-linear sigma-models on supergroup manifolds with vanishing Killing form, with or without a Wess-Zumino term. The current algebra is computed using two distinct methods. First we exploit special algebraic properties of supergroups to compute the exact two- and three-point functions of the currents and from them we infer the current algebra. The algebra is also calculated by using conformal perturbation theory about the Wess-Zumino-Witten point and resumming the perturbation series. We also prove that these models realize a non-chiral Kac-Moody algebra and construct an infinite set of commuting operators that is closed under the action of the Kac-Moody generators. The supergroup models that we consider include models with applications to statistical mechanics, condensed matter and string theory. In particular, our results may help to systematically solve and clarify the quantum integrability of PSU(n|n) models and their cosets, which appear prominently in string worldsheet models on anti-deSitter spaces.
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"…
Prediction of Algebraic Instabilities
NASA Astrophysics Data System (ADS)
Zaretzky, Paula; King, Kristina; Hill, Nicole; Keithley, Kimberlee; Barlow, Nathaniel; Weinstein, Steven; Cromer, Michael
2016-11-01
A widely unexplored type of hydrodynamic instability is examined - large-time algebraic growth. Such growth occurs on the threshold of (exponentially) neutral stability. A new methodology is provided for predicting the algebraic growth rate of an initial disturbance, when applied to the governing differential equation (or dispersion relation) describing wave propagation in dispersive media. Several types of algebraic instabilities are explored in the context of both linear and nonlinear waves.
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)
Clifford Algebras, Random Graphs, and Quantum Random Variables
NASA Astrophysics Data System (ADS)
Schott, René; Staples, G. Stacey
2008-08-01
For fixed n > 0, the space of finite graphs on n vertices is canonically associated with an abelian, nilpotent-generated subalgebra of the Clifford algebra {C}l2n,2n which is canonically isomorphic to the 2n-particle fermion algebra. Using the generators of the subalgebra, an algebraic probability space of "Clifford adjacency matrices" associated with finite graphs is defined. Each Clifford adjacency matrix is a quantum random variable whose mth moment corresponds to the number of m-cycles in the graph G. Each matrix admits a canonical "quantum decomposition" into a sum of three algebraic random variables: a = aΔ + aΥ + aΛ, where aΔ is classical while aΥ and aΛ are quantum. Moreover, within the Clifford algebra context the NP problem of cycle enumeration is reduced to matrix multiplication, requiring no more than n4 Clifford (geo-metric) multiplications within the algebra.
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
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.
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…
Parastatistics Algebras and Combinatorics
NASA Astrophysics Data System (ADS)
Popov, T.
2005-03-01
We consider the algebras spanned by the creation parafermionic and parabosonic operators which give rise to generalized parastatistics Fock spaces. The basis of such a generalized Fock space can be labelled by Young tableaux which are combinatorial objects. By means of quantum deformations a nice combinatorial structure of the algebra of the plactic monoid that lies behind the parastatistics is revealed.
Algebraic Reasoning through Patterns
ERIC Educational Resources Information Center
Rivera, F. D.; Becker, Joanne Rossi
2009-01-01
This article presents the results of a three-year study that explores students' performance on patterning tasks involving prealgebra and algebra. The findings, insights, and issues drawn from the study are intended to help teach prealgebra and algebra. In the remainder of the article, the authors take a more global view of the three-year study on…
Learning Activity Package, Algebra.
ERIC Educational Resources Information Center
Evans, Diane
A set of ten teacher-prepared Learning Activity Packages (LAPs) in beginning algebra and nine in intermediate algebra, these units cover sets, properties of operations, number systems, open expressions, solution sets of equations and inequalities in one and two variables, exponents, factoring and polynomials, relations and functions, radicals,…
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
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 dissertation,…
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…
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.
Cartan-Weyl 3-algebras and the BLG theory. I: classification of Cartan-Weyl 3-algebras
NASA Astrophysics Data System (ADS)
Chu, Chong-Sun
2010-10-01
As Lie algebras of compact connected Lie groups, semisimple Lie algebras have wide applications in the description of continuous symmetries of physical systems. Mathematically, semisimple Lie algebra admits a Cartan-Weyl basis of generators which consists of a Cartan subalgebra of mutually commuting generators H I and a number of step generators E α that are characterized by a root space of non-degenerate one-forms α. This simple decomposition in terms of the root space allows for a complete classification of semisimple Lie algebras. In this paper, we introduce the analogous concept of a Cartan-Weyl Lie 3-algebra. We analyze their structure and obtain a complete classification of them. Many known examples of metric Lie 3-algebras (e.g. the Lorentzian 3-algebras) are special cases of the Cartan-Weyl 3-algebras. Due to their elegant and simple structure, we speculate that Cartan-Weyl 3-algebras may be useful for describing some kinds of generalized symmetries. As an application, we consider their use in the Bagger-Lambert-Gustavsson (BLG) theory.
ERIC Educational Resources Information Center
Barrington, Linda; Carter, Jacky
2003-01-01
Proposes that narrow columns provide a flexible system of organization for designers. Notes that grids serve the content on the pages, help to develop a layout that will clearly direct the reader to information; and prevent visual monotony. Concludes when grid layouts are used, school publications look as good as professional ones. (PM)
NASA Astrophysics Data System (ADS)
Camera, Corrado; Bruggeman, Adriana; Hadjinicolaou, Panos; Michaelides, Silas; Lange, Manfred A.
2015-04-01
Space-time variability of precipitation plays a key role as a driver of many processes in different environmental fields like hydrology, ecology, biology, agriculture, and natural hazards. The objective of this study was to compare two approaches for statistical downscaling of precipitation from climate models. The study was applied to the island of Cyprus, an orographically complex terrain. The first approach makes use of a spatial temporal Neyman-Scott Rectangular Pulses (NSRP) model and a previously tested interpolation scheme (Camera et al., 2014). The second approach is based on the use of the single site NSRP model and a simplified gridded scheme based on scaling coefficients obtained from past observations. The rainfall generators were evaluated on the period 1980-2010. Both approaches were subsequently used to downscale three RCMs from the EU ENSEMBLE project to calculate climate projections (2020-2050). The main advantage of the spatial-temporal approach is that it allows creating spatially consistent daily maps of precipitation. On the other hand, due to the assumptions made using a stochastic generator based on homogeneous Poisson processes, it shows a smoothing out of all the rainfall statistics (except mean and variance) all over the study area. This leads to high errors when analyzing indices related to extremes. Examples are the number of days with rainfall over 50 mm (R50 - mean error 65%), the 95th percentile value of rainy days (RT95 - mean error 19%), and the mean annual rainfall recorded on days with rainfall above the 95th percentile (RA95 - mean error 22%). The single site approach excludes the possibility of using the created gridded data sets for case studies involving spatial connection between grid cells (e.g. hydrologic modelling), but it leads to a better reproduction of rainfall statistics and properties. The errors for the extreme indices are in fact much lower: 17% for R50, 4% for RT95, and 2% for RA95. Future projections show a
NASA Technical Reports Server (NTRS)
Banks, D. W.; Hafez, M. M.
1996-01-01
Grid adaptation for structured meshes is the art of using information from an existing, but poorly resolved, solution to automatically redistribute the grid points in such a way as to improve the resolution in regions of high error, and thus the quality of the solution. This involves: (1) generate a grid vis some standard algorithm, (2) calculate a solution on this grid, (3) adapt the grid to this solution, (4) recalculate the solution on this adapted grid, and (5) repeat steps 3 and 4 to satisfaction. Steps 3 and 4 can be repeated until some 'optimal' grid is converged to but typically this is not worth the effort and just two or three repeat calculations are necessary. They also may be repeated every 5-10 time steps for unsteady calculations.
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.
Magnetic translation algebra with or without magnetic field
NASA Astrophysics Data System (ADS)
Mudry, Christopher; Chamon, Claudio
2013-03-01
The magnetic translation algebra plays an important role in the quantum Hall effect. Murthy and Shankar have shown how to realize this algebra using fermionic bilinears defined on a two-dimensional square lattice. We show that, in any dimension d, it is always possible to close the magnetic translation algebra using fermionic bilinears, be it in the continuum or on the lattice. We also show that these generators are complete in even, but not odd, dimensions, in the sense that any fermionic Hamiltonian in even dimensions that conserves particle number can be represented in terms of the generators of this algebra, whether or not time-reversal symmetry is broken. As an example, we reproduce the f-sum rule of interacting electrons at vanishing magnetic field using this representation. We also show that interactions can significantly change the bare band width of lattice Hamiltonians when represented in terms of the generators of the magnetic translation algebra.
Grid-free 3D multiple spot generation with an efficient single-plane FFT-based algorithm.
Engström, David; Frank, Anders; Backsten, Jan; Goksör, Mattias; Bengtsson, Jörgen
2009-06-08
Algorithms based on the fast Fourier transform (FFT) for the design of spot-generating computer generated holograms (CGHs) typically only make use of a few sample positions in the propagated field. We have developed a new design method that much better utilizes the information-carrying capacity of the sampled propagated field. In this way design tasks which are difficult to accomplish with conventional FFT-based design methods, such as spot positioning at non-sample positions and/or spot positioning in 3D, are solved as easily as any standard design task using a conventional method. The new design method is based on a projection optimization, similar to that in the commonly used Gerchberg-Saxton algorithm, and the vastly improved design freedom comes at virtually no extra computational cost compared to the conventional design. Several different design tasks were demonstrated experimentally with a liquid crystal spatial light modulator, showing highly accurate creation of the desired field distributions.
Conformal manifolds in four dimensions and chiral algebras
NASA Astrophysics Data System (ADS)
Buican, Matthew; Nishinaka, Takahiro
2016-11-01
Any { N }=2 superconformal field theory (SCFT) in four dimensions has a sector of operators related to a two-dimensional chiral algebra containing a Virasoro sub-algebra. Moreover, there are well-known examples of isolated SCFTs whose chiral algebra is a Virasoro algebra. In this note, we consider the chiral algebras associated with interacting { N }=2 SCFTs possessing an exactly marginal deformation that can be interpreted as a gauge coupling (i.e., at special points on the resulting conformal manifolds, free gauge fields appear that decouple from isolated SCFT building blocks). At any point on these conformal manifolds, we argue that the associated chiral algebras possess at least three generators. In addition, we show that there are examples of SCFTs realizing such a minimal chiral algebra: they are certain points on the conformal manifold obtained by considering the low-energy limit of type IIB string theory on the three complex-dimensional hypersurface singularity {x}13+{x}23+{x}33+α {x}1{x}2{x}3+{w}2=0. The associated chiral algebra is the { A }(6) theory of Feigin, Feigin, and Tipunin. As byproducts of our work, we argue that (i) a collection of isolated theories can be conformally gauged only if there is a SUSY moduli space associated with the corresponding symmetry current moment maps in each sector, and (ii) { N }=2 SCFTs with a≥slant c have hidden fermionic symmetries (in the sense of fermionic chiral algebra generators).
Chain models on hecke algebra for corner type representations
NASA Astrophysics Data System (ADS)
Isaev, A. P.; Ogievetsky, O. V.; Os'kin, A. F.
2008-04-01
We consider the integrable open chain models formulated in terms of generators of the Hecke algebra. The spectrum of Hamiltonians for the open Hecke chains of finite size with free boundary conditions is deduced for special (comer type) irreducible representations of the Hecke algebra.
Algebraic invariants for homotopy types
NASA Astrophysics Data System (ADS)
Blanc, David
1999-11-01
We define a sequence of purely algebraic invariants - namely, classes in the Quillen cohomology of the [Pi]-algebra [pi][low asterisk]X - for distinguishing between different homotopy types of spaces. Another sequence of such cohomology classes allows one to decide whether a given abstract [Pi]-algebra can be realized as the homotopy [Pi]-algebra of a space.
NASA Astrophysics Data System (ADS)
Collier, A. M.; Hannigan, M.; Masson, N.; Piedrahita, R.; Gordon, J. L.; Russel, M.
2014-12-01
For the past several years, our research group has been developing low-cost (for reference, each unit costs under $1000) next generation air quality monitors, which utilize metal-oxide semiconductor sensors and non-dispersive infrared sensors to collect data on various gaseous pollutants. The pollutants of focus for this deployment were CO2, O3, and NO2. Additional data collected by the monitors includes temperature, humidity, wind speed and direction, and some information on hydrocarbon levels. A main focus of our research has been sensor characterization and exploring research applications of the technology. During summer 2014, the DISCOVER-AQ and FRAPPE sampling campaigns provided our group with the opportunity to deploy twenty monitors throughout the sampling region with the Boulder Atmospheric Observatory Tower in Erie CO at the center of our monitoring area. Thirteen of these monitors were located at ground-level within an approximately 10 by 10 km grid cell, and the rest were outside of this area at various distances. This placement was intended to provide information on pollutant variability, specifically ozone, within a remote-sensing sized grid cell. Additionally, the availability of reference monitors in the field provided opportunities for co-location during the deployment and hence, opportunities to quantify monitor performance. Analysis will include both an evaluation of low-cost sensor performance and a look at temporal and spatial variability. For example, land-use regression modeling will be used to explore population density, distance to roadways, and distance to oil and gas activity as covariates. Additionally, we will explore how the spatial distribution varies with time and look for temporal patterns.
Choi, Woo-Young; Lai, Jih-Sheng
2010-04-15
This paper presents a high-efficiency grid-connected photovoltaic (PV) module integrated converter (MIC) system with reduced PV current variation. The proposed PV MIC system consists of a high-efficiency step-up DC-DC converter and a single-phase full-bridge DC-AC inverter. An active-clamping flyback converter with a voltage-doubler rectifier is proposed for the step-up DC-DC converter. The proposed step-up DC-DC converter reduces the switching losses by eliminating the reverse-recovery current of the output rectifying diodes. To reduce the PV current variation introduced by the grid-connected inverter, a PV current variation reduction method is also suggested. The suggested PV current variation reduction method reduces the PV current variation without any additional components. Moreover, for centralized power control of distributed PV MIC systems, a PV power control scheme with both a central control level and a local control level is presented. The central PV power control level controls the whole power production by sending out reference power signals to each individual PV MIC system. The proposed step-up DC-DC converter achieves a high-efficiency of 97.5% at 260 W output power to generate the DC-link voltage of 350 V from the PV voltage of 36.1 V. The PV MIC system including the DC-DC converter and the DC-AC inverter achieves a high-efficiency of 95% with the PV current ripple less than 3% variation of the rated PV current. (author)
Smart Grid Integration Laboratory
Troxell, Wade
2011-12-22
The initial federal funding for the Colorado State University Smart Grid Integration Laboratory is through a Congressionally Directed Project (CDP), DE-OE0000070 Smart Grid Integration Laboratory. The original program requested in three one-year increments for staff acquisition, curriculum development, and instrumentation all which will benefit the Laboratory. This report focuses on the initial phase of staff acquisition which was directed and administered by DOE NETL/ West Virginia under Project Officer Tom George. Using this CDP funding, we have developed the leadership and intellectual capacity for the SGIC. This was accomplished by investing (hiring) a core team of Smart Grid Systems engineering faculty focused on education, research, and innovation of a secure and smart grid infrastructure. The Smart Grid Integration Laboratory will be housed with the separately funded Integrid Laboratory as part of CSU's overall Smart Grid Integration Center (SGIC). The period of performance of this grant was 10/1/2009 to 9/30/2011 which included one no cost extension due to time delays in faculty hiring. The Smart Grid Integration Laboratory's focus is to build foundations to help graduate and undergraduates acquire systems engineering knowledge; conduct innovative research; and team externally with grid smart organizations. Using the results of the separately funded Smart Grid Workforce Education Workshop (May 2009) sponsored by the City of Fort Collins, Northern Colorado Clean Energy Cluster, Colorado State University Continuing Education, Spirae, and Siemens has been used to guide the hiring of faculty, program curriculum and education plan. This project develops faculty leaders with the intellectual capacity to inspire its students to become leaders that substantially contribute to the development and maintenance of Smart Grid infrastructure through topics such as: (1) Distributed energy systems modeling and control; (2) Energy and power conversion; (3) Simulation of
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.
Pseudo-Riemannian Novikov algebras
NASA Astrophysics Data System (ADS)
Chen, Zhiqi; Zhu, Fuhai
2008-08-01
Novikov algebras were introduced in connection with the Poisson brackets of hydrodynamic-type and Hamiltonian operators in formal variational calculus. Pseudo-Riemannian Novikov algebras denote Novikov algebras with non-degenerate invariant symmetric bilinear forms. In this paper, we find that there is a remarkable geometry on pseudo-Riemannian Novikov algebras, and give a special class of pseudo-Riemannian Novikov algebras.
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 Technical Reports Server (NTRS)
Popovic, Zorana B.; Kim, Moonil; Rutledge, David B.
1988-01-01
Loading a two-dimensional grid with active devices offers a means of combining the power of solid-state oscillators in the microwave and millimeter-wave range. The grid structure allows a large number of negative resistance devices to be combined. This approach is attractive because the active devices do not require an external locking signal, and the combining is done in free space. In addition, the loaded grid is a planar structure amenable to monolithic integration. Measurements on a 25-MESFET grid at 9.7 GHz show power-combining and frequency-locking without an external locking signal, with an ERP of 37 W. Experimental far-field patterns agree with theoretical results obtained using reciprocity.
NASA Astrophysics Data System (ADS)
Markarian, Nikita
2017-03-01
We introduce Weyl n-algebras and show how their factorization complex may be used to define invariants of manifolds. In the appendix, we heuristically explain why these invariants must be perturbative Chern-Simons invariants.
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)