TBGG- INTERACTIVE ALGEBRAIC GRID GENERATION
NASA Technical Reports Server (NTRS)
Smith, R. E.
1994-01-01
TBGG, Two-Boundary Grid Generation, applies an interactive algebraic grid generation technique in two dimensions. The program incorporates mathematical equations that relate the computational domain to the physical domain. TBGG has application to a variety of problems using finite difference techniques, such as computational fluid dynamics. Examples include the creation of a C-type grid about an airfoil and a nozzle configuration in which no left or right boundaries are specified. The underlying two-boundary technique of grid generation is based on Hermite cubic interpolation between two fixed, nonintersecting boundaries. The boundaries are defined by two ordered sets of points, referred to as the top and bottom. Left and right side boundaries may also be specified, and call upon linear blending functions to conform interior interpolation to the side boundaries. Spacing between physical grid coordinates is determined as a function of boundary data and uniformly spaced computational coordinates. Control functions relating computational coordinates to parametric intermediate variables that affect the distance between grid points are embedded in the interpolation formulas. A versatile control function technique with smooth cubic spline functions is also presented. The TBGG program is written in FORTRAN 77. It works best in an interactive graphics environment where computational displays and user responses are quickly exchanged. The program has been implemented on a CDC Cyber 170 series computer using NOS 2.4 operating system, with a central memory requirement of 151,700 (octal) 60 bit words. TBGG requires a Tektronix 4015 terminal and the DI-3000 Graphics Library of Precision Visuals, Inc. TBGG was developed in 1986.
A grid spacing control technique for algebraic grid generation methods
NASA Technical Reports Server (NTRS)
Smith, R. E.; Kudlinski, R. A.; Everton, E. L.
1982-01-01
A technique which controls the spacing of grid points in algebraically defined coordinate transformations is described. The technique is based on the generation of control functions which map a uniformly distributed computational grid onto parametric variables defining the physical grid. The control functions are smoothed cubic splines. Sets of control points are input for each coordinate directions to outline the control functions. Smoothed cubic spline functions are then generated to approximate the input data. The technique works best in an interactive graphics environment where control inputs and grid displays are nearly instantaneous. The technique is illustrated with the two-boundary grid generation algorithm.
Structured adaptive grid generation using algebraic methods
NASA Technical Reports Server (NTRS)
Yang, Jiann-Cherng; Soni, Bharat K.; Roger, R. P.; Chan, Stephen C.
1993-01-01
The accuracy of the numerical algorithm depends not only on the formal order of approximation but also on the distribution of grid points in the computational domain. Grid adaptation is a procedure which allows optimal grid redistribution as the solution progresses. It offers the prospect of accurate flow field simulations without the use of an excessively timely, computationally expensive, grid. Grid adaptive schemes are divided into two basic categories: differential and algebraic. The differential method is based on a variational approach where a function which contains a measure of grid smoothness, orthogonality and volume variation is minimized by using a variational principle. This approach provided a solid mathematical basis for the adaptive method, but the Euler-Lagrange equations must be solved in addition to the original governing equations. On the other hand, the algebraic method requires much less computational effort, but the grid may not be smooth. The algebraic techniques are based on devising an algorithm where the grid movement is governed by estimates of the local error in the numerical solution. This is achieved by requiring the points in the large error regions to attract other points and points in the low error region to repel other points. The development of a fast, efficient, and robust algebraic adaptive algorithm for structured flow simulation applications is presented. This development is accomplished in a three step process. The first step is to define an adaptive weighting mesh (distribution mesh) on the basis of the equidistribution law applied to the flow field solution. The second, and probably the most crucial step, is to redistribute grid points in the computational domain according to the aforementioned weighting mesh. The third and the last step is to reevaluate the flow property by an appropriate search/interpolate scheme at the new grid locations. The adaptive weighting mesh provides the information on the desired concentration
Algebraic grid generation with corner singularities
NASA Technical Reports Server (NTRS)
Vinokur, M.; Lombard, C. K.
1983-01-01
A simple noniterative algebraic procedure is presented for generating smooth computational meshes on a quadrilateral topology. Coordinate distribution and normal derivative are provided on all boundaries, one of which may include a slope discontinuity. The boundary conditions are sufficient to guarantee continuity of global meshes formed of joined patches generated by the procedure. The method extends to 3-D. The procedure involves a synthesis of prior techniques stretching functions, cubic blending functions, and transfinite interpolation - to which is added the functional form of the corner solution. The procedure introduces the concept of generalized blending, which is implemented as an automatic scaling of the boundary derivatives for effective interpolation. Some implications of the treatment at boundaries for techniques solving elliptic PDE's are discussed in an Appendix.
Algebraic grid generation for wing-fuselage bodies
NASA Technical Reports Server (NTRS)
Smith, R. E.; Everton, E. L.; Kudlinski, R. A.
1984-01-01
An algebraic procedure for the generation of boundary-fitted grids about wing-fuselage configurations is presented. A wing-fuselage configuration is specified by cross sections and mathematically represented by Coons' patches. A configuration is divided into sections so that several grid blocks that either adjoin each other or partially overlap each other can be generated, and each grid has six surfaces that map into a computational cube. Grids are first determined on the six boundary surfaces and then in the interior. Grid curves that are on the surface of the configuration are derived using plane-patch intersections, and single-valued functions relating approximate arc lengths along the curves to computational coordinates define the distribution of grid points. The two-boundary technique and transfinite interpolation are used to determine the boundary surface grids that are not on the configuration, and transfinite interpolation with linear blending functions is used to determine the interior grids.
Algebraic grid generation about wing-fuselage bodies
NASA Technical Reports Server (NTRS)
Smith, R.E.; Kudlinski, R. A.; Everton, E. L.; Wiese, M. R.
1987-01-01
An algebraic procedure for generating boundary-fitted grids about wing-fuselage configurations is presented. A wing-fuselage configuration consists of two aircraft components specified by cross sections and mathematically represented by Coons' patches. Several grid blocks are constructed to cover the entire region surrounding the configuration, and each grid block maps into a computational cube. Grid points are first determined on the six boundary surfaces of a block and then in the interior. Grid points on the surface of the configuration are derived from the intersection of planes with the Coons' patch definition. Approximate arc length distributions along the resulting grid curves concentrate and disperse grid points. The two-boundary technique and transfinite interpolation are used to determine grid points on the remaining boundary surfaces and block interiors.
Algebraic grid generation with control points
NASA Technical Reports Server (NTRS)
Eiseman, Peter R.; Choo, Yung K.; Smith, Robert E.
1992-01-01
The control-point form (CPF) formulation is an algebraically defined class of coordinate transformations by means of which the interior form of the coordinates can be manipulated in the local fashion, and any boundary can be either specified or manipulated in a similar manner. Currently, the most intense activity involving CPF is with such graphic interactive codes as TurboI and TurboT, for which detailed illustrative examples are given; these have furnished experience on whose basis future interactive strategies can be developed.
Algebraic grid generation about wing-fuselage bodies
NASA Technical Reports Server (NTRS)
Smith, R. E.
1986-01-01
An algebraic procedure for the generation of boundary-fitted grids about wing-fuselage configurations is presented. A wing-fuselage configuration is specified by cross sections and mathematically represented by Coons' patches. A configuration is divided into sections so that several grid blocks that either adjoin each other or partially overlap each other can be generated. Each grid has six exterior surfaces that map into a computational cube. Grids are first determined on the six boundary surfaces and then in the interior. Grid curves that are on the surface of the configuration are derived from the intersection of planes with the Coons' patch definition. Single-valued functions relating approximate arc lengths along the grid curves to a computational coordinate define the distribution of grid points. The two-boundary technique and transfinite interpolation are used to determine the boundary surface grids that are not on the configuration, and transfinite interpolation with linear blending functions is used to determine the interior grid.
Algebraic surface grid generation in three-dimensional space
NASA Technical Reports Server (NTRS)
Warsi, Saif
1992-01-01
An interactive program for algebraic generation of structured surface grids in three dimensional space was developed on the IRIS4D series workstations. Interactive tools are available to ease construction of edge curves and surfaces in 3-D space. Addition, removal, or redistribution of points at arbitrary locations on a general 3-D surface or curve is possible. Also, redistribution of surface grid points may be accomplished through use of conventional surface splines or a method called 'surface constrained transfinite interpolation'. This method allows the user to redistribute the grid points on the edges of a surface patch; the effect of the redistribution is then propagated to the remainder of the surface through a transfinite interpolation procedure where the grid points will be constrained to lie on the surface. The program was written to be highly functional and easy to use. A host of utilities are available to ease the grid generation process. Generality of the program allows the creation of single and multizonal surface grids according to the user requirements. The program communicates with the user through popup menus, windows, and the mouse.
On the applications of algebraic grid generation methods based on transfinite interpolation
NASA Technical Reports Server (NTRS)
Nguyen, Hung Lee
1989-01-01
Algebraic grid generation methods based on transfinite interpolation called the two-boundary and four-boundary methods are applied for generating grids with highly complex boundaries. These methods yield grid point distributions that allow for accurate application to regions of sharp gradients in the physical domain or time-dependent problems with small length scale phenomena. Algebraic grids are derived using the two-boundary and four-boundary methods for applications in both two- and three-dimensional domains. Grids are developed for distinctly different geometrical problems and the two-boundary and four-boundary methods are demonstrated to be applicable to a wide class of geometries.
NASA Technical Reports Server (NTRS)
Shih, T. I.-P.; Roelke, R. J.; Steinthorsson, E.
1991-01-01
In order to study numerically details of the flow and heat transfer within coolant passages of turbine blades, a method must first be developed to generate grid systems within the very complicated geometries involved. In this study, a grid generation package was developed that is capable of generating the required grid systems. The package developed is based on an algebraic grid generation technique that permits the user considerable control over how grid points are to be distributed in a very explicit way. These controls include orthogonality of grid lines next to boundary surfaces and ability to cluster about arbitrary points, lines, and surfaces. This paper describes that grid generation package and shows how it can be used to generate grid systems within complicated-shaped coolant passages via an example.
An algebraic grid generation technique for multi body launch vehicle configurations
Balu, R.; Unnikrishnan, C.
1996-12-31
A simple algebraic grid generation method is used to generate three dimensional computational grids over multi body launch vehicle configurations. Sample grids for various configurations like, axisymmetric bodies with fins and multi body launch vehicles having a number of strap-on boosters, are presented. These grids appear to be of comparative quality to those generated by sophisticated techniques like Poisson`s equation solutions, which take enormous computing times. Viscous flow simulations using the present grids are found to be quite satisfactory for practical purposes.
Two and three dimensional grid generation by an algebraic homotopy procedure
NASA Technical Reports Server (NTRS)
Moitra, Anutosh
1990-01-01
An algebraic method for generating two- and three-dimensional grid systems for aerospace vehicles is presented. The method is based on algebraic procedures derived from homotopic relations for blending between inner and outer boundaries of any given configuration. Stable properties of homotopic maps have been exploited to provide near-orthogonality and specified constant spacing at the inner boundary. The method has been successfully applied to analytically generated blended wing-body configurations as well as discretely defined geometries such as the High-Speed Civil Transport Aircraft. Grid examples representative of the capabilities of the method are presented.
NASA Technical Reports Server (NTRS)
Moitra, Anutosh
1989-01-01
A fast and versatile procedure for algebraically generating boundary conforming computational grids for use with finite-volume Euler flow solvers is presented. A semi-analytic homotopic procedure is used to generate the grids. Grids generated in two-dimensional planes are stacked to produce quasi-three-dimensional grid systems. The body surface and outer boundary are described in terms of surface parameters. An interpolation scheme is used to blend between the body surface and the outer boundary in order to determine the field points. The method, albeit developed for analytically generated body geometries is equally applicable to other classes of geometries. The method can be used for both internal and external flow configurations, the only constraint being that the body geometries be specified in two-dimensional cross-sections stationed along the longitudinal axis of the configuration. Techniques for controlling various grid parameters, e.g., clustering and orthogonality are described. Techniques for treating problems arising in algebraic grid generation for geometries with sharp corners are addressed. A set of representative grid systems generated by this method is included. Results of flow computations using these grids are presented for validation of the effectiveness of the method.
Implementation of control point form of algebraic grid-generation technique
NASA Technical Reports Server (NTRS)
Choo, Yung K.; Miller, David P.; Reno, Charles J.
1991-01-01
The control point form (CPF) provides explicit control of physical grid shape and grid spacing through the movement of the control points. The control point array, called a control net, is a space grid type arrangement of locations in physical space with an index for each direction. As an algebraic method CPF is efficient and works well with interactive computer graphics. A family of menu-driven, interactive grid-generation computer codes (TURBO) is being developed by using CPF. Key features of TurboI (a TURBO member) are discussed and typical results are presented. TurboI runs on any IRIS 4D series workstation.
A three-dimensional algebraic grid generation scheme for gas turbine combustors with inclined slots
NASA Technical Reports Server (NTRS)
Yang, S. L.; Cline, M. C.; Chen, R.; Chang, Y. L.
1993-01-01
A 3D algebraic grid generation scheme is presented for generating the grid points inside gas turbine combustors with inclined slots. The scheme is based on the 2D transfinite interpolation method. Since the scheme is a 2D approach, it is very efficient and can easily be extended to gas turbine combustors with either dilution hole or slot configurations. To demonstrate the feasibility and the usefulness of the technique, a numerical study of the quick-quench/lean-combustion (QQ/LC) zones of a staged turbine combustor is given. Preliminary results illustrate some of the major features of the flow and temperature fields in the QQ/LC zones. Formation of co- and counter-rotating bulk flow and shape temperature fields can be observed clearly, and the resulting patterns are consistent with experimental observations typical of the confined slanted jet-in-cross flow. Numerical solutions show the method to be an efficient and reliable tool for generating computational grids for analyzing gas turbine combustors with slanted slots.
Algebraic grid generation using tensor product B-splines. Ph.D. Thesis
NASA Technical Reports Server (NTRS)
Saunders, B. V.
1985-01-01
Finite difference methods are more successful if the accompanying grid has lines which are smooth and nearly orthogonal. The development of an algorithm which produces such a grid when given the boundary description. Topological considerations in structuring the grid generation mapping are discussed. The concept of the degree of a mapping and how it can be used to determine what requirements are necessary if a mapping is to produce a suitable grid is examined. The grid generation algorithm uses a mapping composed of bicubic B-splines. Boundary coefficients are chosen so that the splines produce Schoenberg's variation diminishing spline approximation to the boundary. Interior coefficients are initially chosen to give a variation diminishing approximation to the transfinite bilinear interpolant of the function mapping the boundary of the unit square onto the boundary grid. The practicality of optimizing the grid by minimizing a functional involving the Jacobian of the grid generation mapping at each interior grid point and the dot product of vectors tangent to the grid lines is investigated. Grids generated by using the algorithm are presented.
Structured and unstructured grid generation.
Thompson, J F; Weatherill, N P
1992-01-01
Current techniques in composite-block-structured grid generation and unstructured grid generation for general 3D geometries are summarized, including both algebraic and elliptic generation procedures for the former and Delaunay tessellations for the latter. Citations of relevant theory are given. Examples of applications for several geometries are included. PMID:1424687
Barnhill, R.E.; Farin, G.; Hamann, B.
1995-12-31
This paper provides a basic overview of NURBS and their application to numerical grid generation. Curve/surface smoothing, accelerated grid generation, and the use of NURBS in a practical grid generation system are discussed.
Interactive solution-adaptive grid generation
NASA Technical Reports Server (NTRS)
Choo, Yung K.; Henderson, Todd L.
1992-01-01
TURBO-AD is an interactive solution-adaptive grid generation program under development. The program combines an interactive algebraic grid generation technique and a solution-adaptive grid generation technique into a single interactive solution-adaptive grid generation package. The control point form uses a sparse collection of control points to algebraically generate a field grid. This technique provides local grid control capability and is well suited to interactive work due to its speed and efficiency. A mapping from the physical domain to a parametric domain was used to improve difficulties that had been encountered near outwardly concave boundaries in the control point technique. Therefore, all grid modifications are performed on a unit square in the parametric domain, and the new adapted grid in the parametric domain is then mapped back to the physical domain. The grid adaptation is achieved by first adapting the control points to a numerical solution in the parametric domain using control sources obtained from flow properties. Then a new modified grid is generated from the adapted control net. This solution-adaptive grid generation process is efficient because the number of control points is much less than the number of grid points and the generation of a new grid from the adapted control net is an efficient algebraic process. TURBO-AD provides the user with both local and global grid controls.
Interactive solution-adaptive grid generation procedure
NASA Technical Reports Server (NTRS)
Henderson, Todd L.; Choo, Yung K.; Lee, Ki D.
1992-01-01
TURBO-AD is an interactive solution adaptive grid generation program under development. The program combines an interactive algebraic grid generation technique and a solution adaptive grid generation technique into a single interactive package. The control point form uses a sparse collection of control points to algebraically generate a field grid. This technique provides local grid control capability and is well suited to interactive work due to its speed and efficiency. A mapping from the physical domain to a parametric domain was used to improve difficulties encountered near outwardly concave boundaries in the control point technique. Therefore, all grid modifications are performed on the unit square in the parametric domain, and the new adapted grid is then mapped back to the physical domain. The grid adaption is achieved by adapting the control points to a numerical solution in the parametric domain using control sources obtained from the flow properties. Then a new modified grid is generated from the adapted control net. This process is efficient because the number of control points is much less than the number of grid points and the generation of the grid is an efficient algebraic process. TURBO-AD provides the user with both local and global controls.
Barnette, Daniel W.
2002-01-01
The present invention provides a method of grid generation that uses the geometry of the problem space and the governing relations to generate a grid. The method can generate a grid with minimized discretization errors, and with minimal user interaction. The method of the present invention comprises assigning grid cell locations so that, when the governing relations are discretized using the grid, at least some of the discretization errors are substantially zero. Conventional grid generation is driven by the problem space geometry; grid generation according to the present invention is driven by problem space geometry and by governing relations. The present invention accordingly can provide two significant benefits: more efficient and accurate modeling since discretization errors are minimized, and reduced cost grid generation since less human interaction is required.
An interactive grid generation technique for turbomachinery
NASA Technical Reports Server (NTRS)
Beach, Tim
1992-01-01
A combination algebraic/elliptic technique is presented for the generation of 3-D grids about turbomachinery blade rows for both axial and radial flow machinery. The technique is build around use of an advanced engineering workstation to construct several 2-D grids interactively on predetermined blade-to-blade surfaces. A 3-D grid is generated by interpolating these surface grids onto an axisymmetric grid. On each blade to blade surface, a grid is created using algebraic techniques near the blade to control orthogonality within the boundary layer region and elliptic techniques in the mid-passage to achieve smoothness. The interactive definition of bezier curves as internal boundaries is the key to simple construction. The approach is adapted for use with the average passage solution technique, although this is not a limitation for most other uses. A variety of examples are presented.
IGB grid: User's manual (A turbomachinery grid generation code)
NASA Technical Reports Server (NTRS)
Beach, T. A.; Hoffman, G.
1992-01-01
A grid generation code called IGB is presented for use in computational investigations of turbomachinery flowfields. It contains a combination of algebraic and elliptic techniques coded for use on an interactive graphics workstation. The instructions for use and a test case are included.
NASA Technical Reports Server (NTRS)
Ives, David
1995-01-01
This paper presents a highly automated hexahedral grid generator based on extensive geometrical and solid modeling operations developed in response to a vision of a designer-driven one day turnaround CFD process which implies a designer-driven one hour grid generation process.
Compactly Generated de Morgan Lattices, Basic Algebras and Effect Algebras
NASA Astrophysics Data System (ADS)
Paseka, Jan; Riečanová, Zdenka
2010-12-01
We prove that a de Morgan lattice is compactly generated if and only if its order topology is compatible with a uniformity on L generated by some separating function family on L. Moreover, if L is complete then L is (o)-topological. Further, if a basic algebra L (hence lattice with sectional antitone involutions) is compactly generated then L is atomic. Thus all non-atomic Boolean algebras as well as non-atomic lattice effect algebras (including non-atomic MV-algebras and orthomodular lattices) are not compactly generated.
Enhanced Elliptic Grid Generation
NASA Technical Reports Server (NTRS)
Kaul, Upender K.
2007-01-01
An enhanced method of elliptic grid generation has been invented. Whereas prior methods require user input of certain grid parameters, this method provides for these parameters to be determined automatically. "Elliptic grid generation" signifies generation of generalized curvilinear coordinate grids through solution of elliptic partial differential equations (PDEs). Usually, such grids are fitted to bounding bodies and used in numerical solution of other PDEs like those of fluid flow, heat flow, and electromagnetics. Such a grid is smooth and has continuous first and second derivatives (and possibly also continuous higher-order derivatives), grid lines are appropriately stretched or clustered, and grid lines are orthogonal or nearly so over most of the grid domain. The source terms in the grid-generating PDEs (hereafter called "defining" PDEs) make it possible for the grid to satisfy requirements for clustering and orthogonality properties in the vicinity of specific surfaces in three dimensions or in the vicinity of specific lines in two dimensions. The grid parameters in question are decay parameters that appear in the source terms of the inhomogeneous defining PDEs. The decay parameters are characteristic lengths in exponential- decay factors that express how the influences of the boundaries decrease with distance from the boundaries. These terms govern the rates at which distance between adjacent grid lines change with distance from nearby boundaries. Heretofore, users have arbitrarily specified decay parameters. However, the characteristic lengths are coupled with the strengths of the source terms, such that arbitrary specification could lead to conflicts among parameter values. Moreover, the manual insertion of decay parameters is cumbersome for static grids and infeasible for dynamically changing grids. In the present method, manual insertion and user specification of decay parameters are neither required nor allowed. Instead, the decay parameters are
Geometric and algebraic multigrid techniques for fluid dynamics problems on unstructured grids
NASA Astrophysics Data System (ADS)
Volkov, K. N.; Emel'yanov, V. N.; Teterina, I. V.
2016-02-01
Issues concerning the implementation and practical application of geometric and algebraic multigrid techniques for solving systems of difference equations generated by the finite volume discretization of the Euler and Navier-Stokes equations on unstructured grids are studied. The construction of prolongation and interpolation operators, as well as grid levels of various resolutions, is discussed. The results of the application of geometric and algebraic multigrid techniques for the simulation of inviscid and viscous compressible fluid flows over an airfoil are compared. Numerical results show that geometric methods ensure faster convergence and weakly depend on the method parameters, while the efficiency of algebraic methods considerably depends on the input parameters.
TIGGERC: Turbomachinery Interactive Grid Generator for 2-D Grid Applications and Users Guide
NASA Technical Reports Server (NTRS)
Miller, David P.
1994-01-01
A two-dimensional multi-block grid generator has been developed for a new design and analysis system for studying multiple blade-row turbomachinery problems. TIGGERC is a mouse driven, interactive grid generation program which can be used to modify boundary coordinates and grid packing and generates surface grids using a hyperbolic tangent or algebraic distribution of grid points on the block boundaries. The interior points of each block grid are distributed using a transfinite interpolation approach. TIGGERC can generate a blocked axisymmetric H-grid, C-grid, I-grid or O-grid for studying turbomachinery flow problems. TIGGERC was developed for operation on Silicon Graphics workstations. Detailed discussion of the grid generation methodology, menu options, operational features and sample grid geometries are presented.
Elliptic surface grid generation on minimal and parametrized surfaces
NASA Technical Reports Server (NTRS)
Spekreijse, S. P.; Nijhuis, G. H.; Boerstoel, J. W.
1995-01-01
An elliptic grid generation method, which generates boundary conforming grids in a two dimensional physical space, is presented. The method is based on the composition of an algebraic and elliptic transformation. The composite mapping obeys the Poisson grid generation system with control functions specified by the algebraic transformation. It is shown that the grid generation on a minimal surface in a three dimensional space is equivalent to the grid generation in a two dimensional domain in physical space. A second elliptic grid generation method, which generates boundary conforming grids on smooth surfaces, is presented. Concerning surface modeling, it is shown that bicubic Hermit interpolation is an excellent method to generate a smooth surface crossing a discrete set of control points.
Interactive surface grid generation
NASA Technical Reports Server (NTRS)
Luh, Raymond Ching-Chung; Pierce, Lawrence E.; Yip, David
1991-01-01
This paper describes a surface grid generation tool called S3D. It is the result of integrating a robust and widely applicable interpolation technique with the latest in workstation technology. Employing the use of a highly efficient and user-friendly graphical interface, S3D permits real-time interactive analyses of surface geometry data and facilitates the construction of surface grids for a wide range of applications in Computational Fluid Dynamics (CFD). The design objectives are for S3D to be stand-alone and easy to use so that CFD analysts can take a hands-on approach toward most if not all of their surface grid generation needs. Representative examples of S3D applications are presented in describing the various elements involved in the process.
OVERGRID: A Unified Overset Grid Generation Graphical Interface
NASA Technical Reports Server (NTRS)
Chan, William M.; Akien, Edwin W. (Technical Monitor)
1999-01-01
This paper presents a unified graphical interface and gridding strategy for performing overset grid generation. The interface called OVERGRID has been specifically designed to follow an efficient overset gridding strategy, and contains general grid manipulation capabilities as well as modules that are specifically suited for overset grids. General grid utilities include functions for grid redistribution, smoothing, concatenation, extraction, extrapolation, projection, and many others. Modules specially tailored for overset grids include a seam curve extractor, hyperbolic and algebraic surface grid generators, a hyperbolic volume grid generator, and a Cartesian box grid generator, Grid visualization is achieved using OpenGL while widgets are constructed with Tcl/Tk. The software is portable between various platforms from UNIX workstations to personal computers.
Hybrid Grid Generation Using NW Grid
Jones-Oliveira, Janet B.; Oliveira, Joseph S.; Trease, Lynn L.; Trease, Harold E.; B.K. Soni, J. Hauser, J.F. Thompson, P.R. Eiseman
2000-09-01
We describe the development and use of a hybrid n-dimensional grid generation system called NWGRID. The Applied Mathematics Group at Pacific Northwest National Laboratory (PNNL) is developing this tool to support the Laboratory's computational science efforts in chemistry, biology, engineering and environmental (subsurface and atmospheric) modeling. NWGRID is the grid generation system, which is designed for multi-scale, multi-material, multi-physics, time-dependent, 3-D, hybrid grids that are either statically adapted or evolved in time. NWGRID'S capabilities include static and dynamic grids, hybrid grids, managing colliding surfaces, and grid optimization[using reconnections, smoothing, and adaptive mesh refinement (AMR) algorithms]. NWGRID'S data structure can manage an arbitrary number of grid objects, each with an arbitrary number of grid attributes. NWGRID uses surface geometry to build volumes by using combinations of Boolean operators and order relations. Point distributions can be input, generated using either ray shooting techniques or defined point-by-point. Connectivity matrices are then generated automatically for all variations of hybrid grids.
NASA Technical Reports Server (NTRS)
Seki, Rycichi
1989-01-01
Because the governing equations in fluid dynamics contain partial differentials and are too difficult in most cases to solve analytically, these differentials are generally replaced by finite difference terms. These terms contain terms in the solution at nearby states. This procedure discretizes the field into a finite number of states. These states, when plotted, form a grid, or mesh, of points. It is at these states, or field points, that the solution is found. The optimum choice of states, the x, y, z coordinate values, minimizes error and computational time. But the process of finding these states is made more difficult by complex boundaries, and by the need to control step size differences between the states, that is, the need to control the spacing of field points. One solution technique uses a different set of state variables, which define a different coordinate system, to generate the grid more easily. A new method, developed by Dr. Joseph Steger, combines elliptic and hyperbolic partial differential equations into a mapping function between the physical and computational coordinate systems. This system of equations offers more control than either equation provides alone. The Steger algorithm was modified in order to allow bodies with stronger concavities to be used, offering the possibility of generating a single grid about multiple bodies. Work was also done on identifying areas where grid breakdown occurs.
Grid generation research at OSU
NASA Technical Reports Server (NTRS)
Nakamura, S.
1992-01-01
In the last two years, effort was concentrated on: (1) surface modeling; (2) surface grid generation; and (3) 3-D flow space grid generation. The surface modeling shares the same objectives as the surface modeling in computer aided design (CAD), so software available in CAD can in principle be used for solid modeling. Unfortunately, however, the CAD software cannot be easily used in practice for grid generation purposes, because they are not designed to provide appropriate data base for grid generation. Therefore, we started developing a generalized surface modeling software from scratch, that provides the data base for the surface grid generation. Generating surface grid is an important step in generating a 3-D space for flow space. To generate a surface grid on a given surface representation, we developed a unique algorithm that works on any non-smooth surfaces. Once the surface grid is generated, a 3-D space can be generated. For this purpose, we also developed a new algorithm, which is a hybrid of the hyperbolic and the elliptic grid generation methods. With this hybrid method, orthogonality of the grid near the solid boundary can be easily achieved without introducing empirical fudge factors. Work to develop 2-D and 3-D grids for turbomachinery blade geometries was performed, and as an extension of this research we are planning to develop an adaptive grid procedure with an interactive grid environment.
TIGGERC: Turbomachinery interactive grid generator energy distributor and restart code
NASA Technical Reports Server (NTRS)
Miller, David P.
1992-01-01
A two dimensional multi-block grid generator was developed for a new design and analysis system for studying multi-blade row turbomachinery problems with an axisymmetric viscous/inviscid 'average passage' through flow code. TIGGERC is a mouse driven, fully interactive grid generation program which can be used to modify boundary coordinates and grid packing. TIGGERC generates grids using a hyperbolic tangent or algebraic distribution of grid points on the block boundaries and the interior points of each block grid are distributed using a transfinite interpolation approach. TIGGERC generates a blocked axisymmetric H grid, C grid, I grid, or O grid for studying turbomachinery flow problems. TIGGERC was developed for operation on small high speed graphic workstations.
Elliptic surface grid generation on minimal and parmetrized surfaces
NASA Technical Reports Server (NTRS)
Spekreijse, S. P.; Nijhuis, G. H.; Boerstoel, J. W.
1995-01-01
An elliptic grid generation method is presented which generates excellent boundary conforming grids in domains in 2D physical space. The method is based on the composition of an algebraic and elliptic transformation. The composite mapping obeys the familiar Poisson grid generation system with control functions specified by the algebraic transformation. New expressions are given for the control functions. Grid orthogonality at the boundary is achieved by modification of the algebraic transformation. It is shown that grid generation on a minimal surface in 3D physical space is in fact equivalent to grid generation in a domain in 2D physical space. A second elliptic grid generation method is presented which generates excellent boundary conforming grids on smooth surfaces. It is assumed that the surfaces are parametrized and that the grid only depends on the shape of the surface and is independent of the parametrization. Concerning surface modeling, it is shown that bicubic Hermite interpolation is an excellent method to generate a smooth surface which is passing through a given discrete set of control points. In contrast to bicubic spline interpolation, there is extra freedom to model the tangent and twist vectors such that spurious oscillations are prevented.
Coarse-grid selection for parallel algebraic multigrid
Cleary, A. J., LLNL
1998-06-01
The need to solve linear systems arising from problems posed on extremely large, unstructured grids has sparked great interest in parallelizing algebraic multigrid (AMG) To date, however, no parallel AMG algorithms exist We introduce a parallel algorithm for the selection of coarse-grid points, a crucial component of AMG, based on modifications of certain paallel independent set algorithms and the application of heuristics designed to insure the quality of the coarse grids A prototype serial version of the algorithm is implemented, and tests are conducted to determine its effect on multigrid convergence, and AMG complexity
Interactive grid generation for turbomachinery flow field simulations
NASA Technical Reports Server (NTRS)
Choo, Yung K.; Reno, Charles; Eiseman, Peter R.
1988-01-01
The control point form of algebraic grid generation presented provides the means that are needed to generate well structured grids of turbomachinery flow simulations. It uses a sparse collection of control points distributed over the flow domain. The shape and position of coordinate curves can be adjusted from these control points while the grid conforms precisely to all boundaries. An interactive program called TURBO, which uses the control point form, is being developed. Basic features of the code are discussed and sample grids are presented. A finite volume LU implicit scheme is used to simulate flow in a turbine cascade on the grid generated by the program.
Interactive grid generation for turbomachinery flow field simulations
NASA Technical Reports Server (NTRS)
Choo, Yung K.; Eiseman, Peter R.; Reno, Charles
1988-01-01
The control point form of algebraic grid generation presented provides the means that are needed to generate well structured grids for turbomachinery flow simulations. It uses a sparse collection of control points distributed over the flow domain. The shape and position of coordinate curves can be adjusted from these control points while the grid conforms precisely to all boundaries. An interactive program called TURBO, which uses the control point form, is being developed. Basic features of the code are discussed and sample grids are presented. A finite volume LU implicit scheme is used to simulate flow in a turbine cascade on the grid generated by the program.
Grid generation for turbomachinery problems
NASA Technical Reports Server (NTRS)
Steinhoff, J.; Reddy, K. C.
1986-01-01
The development of a computer code to generate numerical grids for complex internal flow systems such as the fluid flow inside the space shuttle main engine is outlined. The blending technique for generating a grid for stator-rotor combination at a particular radial section is examined. The computer programs which generate these grids are listed in the Appendices. These codes are capable of generating grids at different cross sections and thus providng three dimensional stator-rotor grids for the turbomachinery of the space shuttle main engine.
Non-Galerkin Coarse Grids for Algebraic Multigrid
Falgout, Robert D.; Schroder, Jacob B.
2014-06-26
Algebraic multigrid (AMG) is a popular and effective solver for systems of linear equations that arise from discretized partial differential equations. And while AMG has been effectively implemented on large scale parallel machines, challenges remain, especially when moving to exascale. Particularly, stencil sizes (the number of nonzeros in a row) tend to increase further down in the coarse grid hierarchy, and this growth leads to more communication. Therefore, as problem size increases and the number of levels in the hierarchy grows, the overall efficiency of the parallel AMG method decreases, sometimes dramatically. This growth in stencil size is due to the standard Galerkin coarse grid operator, $P^T A P$, where $P$ is the prolongation (i.e., interpolation) operator. For example, the coarse grid stencil size for a simple three-dimensional (3D) seven-point finite differencing approximation to diffusion can increase into the thousands on present day machines, causing an associated increase in communication costs. We therefore consider algebraically truncating coarse grid stencils to obtain a non-Galerkin coarse grid. First, the sparsity pattern of the non-Galerkin coarse grid is determined by employing a heuristic minimal “safe” pattern together with strength-of-connection ideas. Second, the nonzero entries are determined by collapsing the stencils in the Galerkin operator using traditional AMG techniques. The result is a reduction in coarse grid stencil size, overall operator complexity, and parallel AMG solve phase times.
TDIGG - TWO-DIMENSIONAL, INTERACTIVE GRID GENERATION CODE
NASA Technical Reports Server (NTRS)
Vu, B. T.
1994-01-01
TDIGG is a fast and versatile program for generating two-dimensional computational grids for use with finite-difference flow-solvers. Both algebraic and elliptic grid generation systems are included. The method for grid generation by algebraic transformation is based on an interpolation algorithm and the elliptic grid generation is established by solving the partial differential equation (PDE). Non-uniform grid distributions are carried out using a hyperbolic tangent stretching function. For algebraic grid systems, interpolations in one direction (univariate) and two directions (bivariate) are considered. These interpolations are associated with linear or cubic Lagrangian/Hermite/Bezier polynomial functions. The algebraic grids can subsequently be smoothed using an elliptic solver. For elliptic grid systems, the PDE can be in the form of Laplace (zero forcing function) or Poisson. The forcing functions in the Poisson equation come from the boundary or the entire domain of the initial algebraic grids. A graphics interface procedure using the Silicon Graphics (GL) Library is included to allow users to visualize the grid variations at each iteration. This will allow users to interactively modify the grid to match their applications. TDIGG is written in FORTRAN 77 for Silicon Graphics IRIS series computers running IRIX. This package requires either MIT's X Window System, Version 11 Revision 4 or SGI (Motif) Window System. A sample executable is provided on the distribution medium. It requires 148K of RAM for execution. The standard distribution medium is a .25 inch streaming magnetic IRIX tape cartridge in UNIX tar format. This program was developed in 1992.
Grid generation strategies for turbomachinery configurations
NASA Astrophysics Data System (ADS)
Lee, K. D.; Henderson, T. L.
1991-01-01
Turbomachinery flow fields involve unique grid generation issues due to their geometrical and physical characteristics. Several strategic approaches are discussed to generate quality grids. The grid quality is further enhanced through blending and adapting. Grid blending smooths the grids locally through averaging and diffusion operators. Grid adaptation redistributes the grid points based on a grid quality assessment. These methods are demonstrated with several examples.
TIGER: Turbomachinery interactive grid generation
NASA Technical Reports Server (NTRS)
Soni, Bharat K.; Shih, Ming-Hsin; Janus, J. Mark
1992-01-01
A three dimensional, interactive grid generation code, TIGER, is being developed for analysis of flows around ducted or unducted propellers. TIGER is a customized grid generator that combines new technology with methods from general grid generation codes. The code generates multiple block, structured grids around multiple blade rows with a hub and shroud for either C grid or H grid topologies. The code is intended for use with a Euler/Navier-Stokes solver also being developed, but is general enough for use with other flow solvers. TIGER features a silicon graphics interactive graphics environment that displays a pop-up window, graphics window, and text window. The geometry is read as a discrete set of points with options for several industrial standard formats and NASA standard formats. Various splines are available for defining the surface geometries. Grid generation is done either interactively or through a batch mode operation using history files from a previously generated grid. The batch mode operation can be done either with a graphical display of the interactive session or with no graphics so that the code can be run on another computer system. Run time can be significantly reduced by running on a Cray-YMP.
Grid generation using classical techniques
NASA Technical Reports Server (NTRS)
Moretti, G.
1980-01-01
A brief historical review of conformal mapping and its applications to problems in fluid mechanics and electromagnetism is presented. The use of conformal mapping as a grid generator is described. The philosophy of the 'closed form' approach and its application to a Neumann problem is discussed. Karman-Trefftz mappings and grids for ablated, three dimensional bodies are also discussed.
Intelligent automated surface grid generation
NASA Technical Reports Server (NTRS)
Yao, Ke-Thia; Gelsey, Andrew
1995-01-01
The goal of our research is to produce a flexible, general grid generator for automated use by other programs, such as numerical optimizers. The current trend in the gridding field is toward interactive gridding. Interactive gridding more readily taps into the spatial reasoning abilities of the human user through the use of a graphical interface with a mouse. However, a sometimes fruitful approach to generating new designs is to apply an optimizer with shape modification operators to improve an initial design. In order for this approach to be useful, the optimizer must be able to automatically grid and evaluate the candidate designs. This paper describes and intelligent gridder that is capable of analyzing the topology of the spatial domain and predicting approximate physical behaviors based on the geometry of the spatial domain to automatically generate grids for computational fluid dynamics simulators. Typically gridding programs are given a partitioning of the spatial domain to assist the gridder. Our gridder is capable of performing this partitioning. This enables the gridder to automatically grid spatial domains of wide range of configurations.
LAPS Grid generation and adaptation
NASA Astrophysics Data System (ADS)
Pagliantini, Cecilia; Delzanno, Gia Luca; Guo, Zehua; Srinivasan, Bhuvana; Tang, Xianzhu; Chacon, Luis
2011-10-01
LAPS uses a common-data framework in which a general purpose grid generation and adaptation package in toroidal and simply connected domains is implemented. The initial focus is on implementing the Winslow/Laplace-Beltrami method for generating non-overlapping block structured grids. This is to be followed by a grid adaptation scheme based on Monge-Kantorovich optimal transport method [Delzanno et al., J. Comput. Phys,227 (2008), 9841-9864], that equidistributes application-specified error. As an initial set of applications, we will lay out grids for an axisymmetric mirror, a field reversed configuration, and an entire poloidal cross section of a tokamak plasma reconstructed from a CMOD experimental shot. These grids will then be used for computing the plasma equilibrium and transport in accompanying presentations. A key issue for Monge-Kantorovich grid optimization is the choice of error or monitor function for equi-distribution. We will compare the Operator Recovery Error Source Detector (ORESD) [Lapenta, Int. J. Num. Meth. Eng,59 (2004) 2065-2087], the Tau method and a strategy based on the grid coarsening [Zhang et al., AIAA J,39 (2001) 1706-1715] to find an ``optimal'' grid. Work supported by DOE OFES.
Elliptic Volume Grid Generation for Viscous CFD Parametric Design Studies
NASA Technical Reports Server (NTRS)
Alter, Stephen J.; Cheatwood, F. McNeil
1996-01-01
This paper presents a robust method for the generation of zonal volume grids of design parametrics for aerodynamic configurations. The process utilizes simple algebraic techniques with parametric splines coupled with elliptic volume grid generation to generate isolated zonal grids for changes in body configuration needed to perform parametric design studies. Speed of the algorithm is maximized through the algebraic methods and reduced number of grid points to be regenerated for each design parametric without sacrificing grid quality and continuity within the volume domain. The method is directly applicable to grid reusability, because it modifies existing ow adapted volume grids and enables the user to restart the CFD solution process with an established flow field. Use of this zonal approach reduces computer usage time to create new volume grids for design parametric studies by an order of magnitude, as compared to current methods which require the regeneration of an entire volume grid. A sample configuration of a proposed Single Stage-to-Orbit Vehicle is used to illustrate an application of this method.
NASA Technical Reports Server (NTRS)
Jameson, Leland
1996-01-01
Wavelets can provide a basis set in which the basis functions are constructed by dilating and translating a fixed function known as the mother wavelet. The mother wavelet can be seen as a high pass filter in the frequency domain. The process of dilating and expanding this high-pass filter can be seen as altering the frequency range that is 'passed' or detected. The process of translation moves this high-pass filter throughout the domain, thereby providing a mechanism to detect the frequencies or scales of information at every location. This is exactly the type of information that is needed for effective grid generation. This paper provides motivation to use wavelets for grid generation in addition to providing the final product: source code for wavelet-based grid generation.
Kim, Joshua; Ionascu, Dan; Zhang, Tiezhi
2013-01-01
Purpose: To accelerate iterative algebraic reconstruction algorithms using a cylindrical image grid. Methods: Tetrahedron beam computed tomography (TBCT) is designed to overcome the scatter and detector problems of cone beam computed tomography (CBCT). Iterative algebraic reconstruction algorithms have been shown to mitigate approximate reconstruction artifacts that appear at large cone angles, but clinical implementation is limited by their high computational cost. In this study, a cylindrical voxelization method on a cylindrical grid is developed in order to take advantage of the symmetries of the cylindrical geometry. The cylindrical geometry is a natural fit for the circular scanning trajectory employed in volumetric CT methods such as CBCT and TBCT. This method was implemented in combination with the simultaneous algebraic reconstruction technique (SART). Both two- and three-dimensional numerical phantoms as well as a patient CT image were utilized to generate the projection sets used for reconstruction. The reconstructed images were compared to the original phantoms using a set of three figures of merit (FOM). Results: The cylindrical voxelization on a cylindrical reconstruction grid was successfully implemented in combination with the SART reconstruction algorithm. The FOM results showed that the cylindrical reconstructions were able to maintain the accuracy of the Cartesian reconstructions. In three dimensions, the cylindrical method provided better accuracy than the Cartesian methods. At the same time, the cylindrical method was able to provide a speedup factor of approximately 40 while also reducing the system matrix storage size by 2 orders of magnitude. Conclusions: TBCT image reconstruction using a cylindrical image grid was able to provide a significant improvement in the reconstruction time and a more compact system matrix for storage on the hard drive and in memory while maintaining the image quality provided by the Cartesian voxelization on a
A paradigm for parallel unstructured grid generation
Gaither, A.; Marcum, D.; Reese, D.
1996-12-31
In this paper, a sequential 2D unstructured grid generator based on iterative point insertion and local reconnection is coupled with a Delauney tessellation domain decomposition scheme to create a scalable parallel unstructured grid generator. The Message Passing Interface (MPI) is used for distributed communication in the parallel grid generator. This work attempts to provide a generic framework to enable the parallelization of fast sequential unstructured grid generators in order to compute grand-challenge scale grids for Computational Field Simulation (CFS). Motivation for moving from sequential to scalable parallel grid generation is presented. Delaunay tessellation and iterative point insertion and local reconnection (advancing front method only) unstructured grid generation techniques are discussed with emphasis on how these techniques can be utilized for parallel unstructured grid generation. Domain decomposition techniques are discussed for both Delauney and advancing front unstructured grid generation with emphasis placed on the differences needed for both grid quality and algorithmic efficiency.
A grid generation system for multi-disciplinary design optimization
NASA Technical Reports Server (NTRS)
Jones, William T.; Samareh-Abolhassani, Jamshid
1995-01-01
A general multi-block three-dimensional volume grid generator is presented which is suitable for Multi-Disciplinary Design Optimization. The code is timely, robust, highly automated, and written in ANSI 'C' for platform independence. Algebraic techniques are used to generate and/or modify block face and volume grids to reflect geometric changes resulting from design optimization. Volume grids are generated/modified in a batch environment and controlled via an ASCII user input deck. This allows the code to be incorporated directly into the design loop. Generated volume grids are presented for a High Speed Civil Transport (HSCT) Wing/Body geometry as well a complex HSCT configuration including horizontal and vertical tails, engine nacelles and pylons, and canard surfaces.
Automatic Overset Grid Generation with Heuristic Feedback Control
NASA Technical Reports Server (NTRS)
Robinson, Peter I.
2001-01-01
An advancing front grid generation system for structured Overset grids is presented which automatically modifies Overset structured surface grids and control lines until user-specified grid qualities are achieved. The system is demonstrated on two examples: the first refines a space shuttle fuselage control line until global truncation error is achieved; the second advances, from control lines, the space shuttle orbiter fuselage top and fuselage side surface grids until proper overlap is achieved. Surface grids are generated in minutes for complex geometries. The system is implemented as a heuristic feedback control (HFC) expert system which iteratively modifies the input specifications for Overset control line and surface grids. It is developed as an extension of modern control theory, production rules systems and subsumption architectures. The methodology provides benefits over the full knowledge lifecycle of an expert system for knowledge acquisition, knowledge representation, and knowledge execution. The vector/matrix framework of modern control theory systematically acquires and represents expert system knowledge. Missing matrix elements imply missing expert knowledge. The execution of the expert system knowledge is performed through symbolic execution of the matrix algebra equations of modern control theory. The dot product operation of matrix algebra is generalized for heuristic symbolic terms. Constant time execution is guaranteed.
Complex Volume Grid Generation Through the Use of Grid Reusability
NASA Technical Reports Server (NTRS)
Alter, Stephen J.
1997-01-01
This paper presents a set of surface and volume grid generation techniques which reuse existing surface and volume grids. These methods use combinations of data manipulations to reduce grid generation time, improve grid characteristics, and increase the capabilities of existing domain discretization software. The manipulation techniques utilize physical and computational domains to produce basis function on which to operate and modify grid character and smooth grids using Trans-Finite Interpolation, a vector interpolation method and parametric re-mapping technique. With these new techniques, inviscid grids can be converted to viscous grids, multiple zone grid adaption can be performed to improve CFD solver efficiency, and topological changes to improve modeling of flow fields can be done simply and quickly. Examples of these capabilities are illustrated as applied to various configurations.
Tuned grid generation with ICEM CFD
NASA Technical Reports Server (NTRS)
Wulf, Armin; Akdag, Vedat
1995-01-01
ICEM CFD is a CAD based grid generation package that supports multiblock structured, unstructured tetrahedral and unstructured hexahedral grids. Major development efforts have been spent to extend ICEM CFD's multiblock structured and hexahedral unstructured grid generation capabilities. The modules added are: a parametric grid generation module and a semi-automatic hexahedral grid generation module. A fully automatic version of the hexahedral grid generation module for around a set of predefined objects in rectilinear enclosures has been developed. These modules will be presented and the procedures used will be described, and examples will be discussed.
Grid-coordinate generation program
Cosner, Oliver J.; Horwich, Esther
1974-01-01
This program description of the grid-coordinate generation program is written for computer users who are familiar with digital aquifer models. The program computes the coordinates for a variable grid -used in the 'Pinder Model' (a finite-difference aquifer simulator), for input to the CalComp GPCP (general purpose contouring program). The program adjusts the y-value by a user-supplied constant in order to transpose the origin of the model grid from the upper left-hand corner to the lower left-hand corner of the grid. The user has the options of, (1.) choosing the boundaries of the plot; (2.) adjusting the z-values (altitudes) by a constant; (3.) deleting superfluous z-values and (4.) subtracting the simulated surfaces from each other to obtain the decline. Output of this program includes the fixed format CNTL data cards and the other data cards required for input to GPCP. The output from GPCP then is used to produce a potentiometric map or a decline map by means of the CalComp plotter.
Survey of Volumetric Grid Generators
NASA Technical Reports Server (NTRS)
Woo, Alex; Volakis, John; Hulbert, Greg; Case, Jeff; Presley, Leroy L. (Technical Monitor)
1994-01-01
This document is the result of an Internet Survey of Volumetric grid generators. As such we have included information from only the responses which were sent to us. After the initial publication and posting of this survey, we would encourage authors and users of grid generators to send further information. Here is the initial query posted to SIGGRID@nas and the USENET group sci.physics.computational.fluid-dynamics. Date: Sun, 30 Jan 94 11:37:52 -0800 From: woo (Alex Woo x6010 227-6 rm 315) Subject: Info Sought for Survey of Grid Generators I am collecting information and reviews of both government sponsored and commercial mesh generators for large scientific calculations, both block structured and unstructured. If you send me a review of a mesh generator, please indicate its availability and cost. If you are a commercial concern with information on a product, please also include references for possible reviewers. Please email to woo@ra-next.arc.nasa.gov. I will post a summary and probably write a short note for the IEEE Antennas and Propagation Magazine. Alex Woo, MS 227-6 woo@ames.arc.nasa.gov NASA Ames Research Center NASAMAIL ACWOO Moffett Field, CA 94035-1000 SPANET 24582::W00 (415) 604-6010 (FAX) 604-4357 fhplabs,decwrl,uunet)!ames!woo Disclaimer: These are not official statements of NASA or EMCC. We did not include all the submitted text here. Instead we have created a database entry in the freely available and widely used BIBTeX format which has an Uniform Resource Locator (URL) field pointing to more details. The BIBTeX database is modeled after those available from the BIBNET project at University of Utah.
Multiblock grid generation for jet engine configurations
NASA Technical Reports Server (NTRS)
Stewart, Mark E. M.
1992-01-01
The goal was to create methods for generating grids with minimal human intervention that are applicable to a wide range of problems and compatible with existing numerical methods and with existing and proposed computers. The following topics that are related to multiblock grid generation are briefly covered in viewgraph form: finding a domain decomposition, dimensioning grids, grid smoothing, manipulating grids and decompositions, and some specializations for jet engine configurations.
Grid generation for the solution of partial differential equations
NASA Technical Reports Server (NTRS)
Eiseman, Peter R.; Erlebacher, Gordon
1987-01-01
A general survey of grid generators is presented with a concern for understanding why grids are necessary, how they are applied, and how they are generated. After an examination of the need for meshes, the overall applications setting is established with a categorization of the various connectivity patterns. This is split between structured grids and unstructured meshes. Altogether, the categorization establishes the foundation upon which grid generation techniques are developed. The two primary categories are algebraic techniques and partial differential equation techniques. These are each split into basic parts, and accordingly are individually examined in some detail. In the process, the interrelations between the various parts are accented. From the established background in the primary techniques, consideration is shifted to the topic of interactive grid generation and then to adaptive meshes. The setting for adaptivity is established with a suitable means to monitor severe solution behavior. Adaptive grids are considered first and are followed by adaptive triangular meshes. Then the consideration shifts to the temporal coupling between grid generators and PDE-solvers. To conclude, a reflection upon the discussion, herein, is given.
Grid generation for the solution of partial differential equations
NASA Technical Reports Server (NTRS)
Eiseman, Peter R.; Erlebacher, Gordon
1989-01-01
A general survey of grid generators is presented with a concern for understanding why grids are necessary, how they are applied, and how they are generated. After an examination of the need for meshes, the overall applications setting is established with a categorization of the various connectivity patterns. This is split between structured grids and unstructured meshes. Altogether, the categorization establishes the foundation upon which grid generation techniques are developed. The two primary categories are algebraic techniques and partial differential equation techniques. These are each split into basic parts, and accordingly are individually examined in some detail. In the process, the interrelations between the various parts are accented. From the established background in the primary techniques, consideration is shifted to the topic of interactive grid generation and then to adaptive meshes. The setting for adaptivity is established with a suitable means to monitor severe solution behavior. Adaptive grids are considered first and are followed by adaptive triangular meshes. Then the consideration shifts to the temporal coupling between grid generators and PDE-solvers. To conclude, a reflection upon the discussion, herein, is given.
Best Practices In Overset Grid Generation
NASA Technical Reports Server (NTRS)
Chan, William M.; Gomez, Reynaldo J., III; Rogers, Stuart E.; Buning, Pieter G.; Kwak, Dochan (Technical Monitor)
2002-01-01
Grid generation for overset grids on complex geometry can be divided into four main steps: geometry processing, surface grid generation, volume grid generation and domain connectivity. For each of these steps, the procedures currently practiced by experienced users are described. Typical problems encountered are also highlighted and discussed. Most of the guidelines are derived from experience on a variety of problems including space launch and return vehicles, subsonic transports with propulsion and high lift devices, supersonic vehicles, rotorcraft vehicles, and turbomachinery.
GridTool: A surface modeling and grid generation tool
NASA Technical Reports Server (NTRS)
Samareh-Abolhassani, Jamshid
1995-01-01
GridTool is designed around the concept that the surface grids are generated on a set of bi-linear patches. This type of grid generation is quite easy to implement, and it avoids the problems associated with complex CAD surface representations and associated surface parameterizations. However, the resulting surface grids are close to but not on the original CAD surfaces. This problem can be alleviated by projecting the resulting surface grids onto the original CAD surfaces. GridTool is designed primary for unstructured grid generation systems. Currently, GridTool supports VGRID and FELISA systems, and it can be easily extended to support other unstructured grid generation systems. The data in GridTool is stored parametrically so that once the problem is set up, one can modify the surfaces and the entire set of points, curves and patches will be updated automatically. This is very useful in a multidisciplinary design and optimization process. GridTool is written entirely in ANSI 'C', the interface is based on the FORMS library, and the graphics is based on the GL library. The code has been tested successfully on IRIS workstations running IRIX4.0 and above. The memory is allocated dynamically, therefore, memory size will depend on the complexity of geometry/grid. GridTool data structure is based on a link-list structure which allows the required memory to expand and contract dynamically according to the user's data size and action. Data structure contains several types of objects such as points, curves, patches, sources and surfaces. At any given time, there is always an active object which is drawn in magenta, or in their highlighted colors as defined by the resource file which will be discussed later.
Parallel grid generation algorithm for distributed memory computers
NASA Technical Reports Server (NTRS)
Moitra, Stuti; Moitra, Anutosh
1994-01-01
A parallel grid-generation algorithm and its implementation on the Intel iPSC/860 computer are described. The grid-generation scheme is based on an algebraic formulation of homotopic relations. Methods for utilizing the inherent parallelism of the grid-generation scheme are described, and implementation of multiple levELs of parallelism on multiple instruction multiple data machines are indicated. The algorithm is capable of providing near orthogonality and spacing control at solid boundaries while requiring minimal interprocessor communications. Results obtained on the Intel hypercube for a blended wing-body configuration are used to demonstrate the effectiveness of the algorithm. Fortran implementations bAsed on the native programming model of the iPSC/860 computer and the Express system of software tools are reported. Computational gains in execution time speed-up ratios are given.
Progress in Grid Generation: From Chimera to DRAGON Grids
NASA Technical Reports Server (NTRS)
Liou, Meng-Sing; Kao, Kai-Hsiung
1994-01-01
Hybrid grids, composed of structured and unstructured grids, combines the best features of both. The chimera method is a major stepstone toward a hybrid grid from which the present approach is evolved. The chimera grid composes a set of overlapped structured grids which are independently generated and body-fitted, yielding a high quality grid readily accessible for efficient solution schemes. The chimera method has been shown to be efficient to generate a grid about complex geometries and has been demonstrated to deliver accurate aerodynamic prediction of complex flows. While its geometrical flexibility is attractive, interpolation of data in the overlapped regions - which in today's practice in 3D is done in a nonconservative fashion, is not. In the present paper we propose a hybrid grid scheme that maximizes the advantages of the chimera scheme and adapts the strengths of the unstructured grid while at the same time keeps its weaknesses minimal. Like the chimera method, we first divide up the physical domain by a set of structured body-fitted grids which are separately generated and overlaid throughout a complex configuration. To eliminate any pure data manipulation which does not necessarily follow governing equations, we use non-structured grids only to directly replace the region of the arbitrarily overlapped grids. This new adaptation to the chimera thinking is coined the DRAGON grid. The nonstructured grid region sandwiched between the structured grids is limited in size, resulting in only a small increase in memory and computational effort. The DRAGON method has three important advantages: (1) preserving strengths of the chimera grid; (2) eliminating difficulties sometimes encountered in the chimera scheme, such as the orphan points and bad quality of interpolation stencils; and (3) making grid communication in a fully conservative and consistent manner insofar as the governing equations are concerned. To demonstrate its use, the governing equations are
Generating Three-Dimensional Grids About Anything
NASA Technical Reports Server (NTRS)
Sorenson, Reese L.
1991-01-01
Three-Dimensional Grids About Anything by Poisson's Equation (3DGRAPE) computer program designed to make computational grids in or about almost any shape. Generated by solution of Poisson's differential equations in three dimensions. Program automatically finds its own values for inhomogeneous terms giving near-orthogonality and controlled grid-cell height at boundaries. Grids generated applied to both viscous and inviscid aerodynamic problems, and to problems in other areas of fluid dynamics. Written in 100 percent FORTRAN 77.
Generating Composite Overlapping Grids on CAD Geometries
Henshaw, W.D.
2002-02-07
We describe some algorithms and tools that have been developed to generate composite overlapping grids on geometries that have been defined with computer aided design (CAD) programs. This process consists of five main steps. Starting from a description of the surfaces defining the computational domain we (1) correct errors in the CAD representation, (2) determine topology of the patched-surface, (3) build a global triangulation of the surface, (4) construct structured surface and volume grids using hyperbolic grid generation, and (5) generate the overlapping grid by determining the holes and the interpolation points. The overlapping grid generator which is used for the final step also supports the rapid generation of grids for block-structured adaptive mesh refinement and for moving grids. These algorithms have been implemented as part of the Overture object-oriented framework.
Geometry modeling and multi-block grid generation for turbomachinery configurations
NASA Technical Reports Server (NTRS)
Shih, Ming H.; Soni, Bharat K.
1992-01-01
An interactive 3D grid generation code, Turbomachinery Interactive Grid genERation (TIGER), was developed for general turbomachinery configurations. TIGER features the automatic generation of multi-block structured grids around multiple blade rows for either internal, external, or internal-external turbomachinery flow fields. Utilization of the Bezier's curves achieves a smooth grid and better orthogonality. TIGER generates the algebraic grid automatically based on geometric information provided by its built-in pseudo-AI algorithm. However, due to the large variation of turbomachinery configurations, this initial grid may not always be as good as desired. TIGER therefore provides graphical user interactions during the process which allow the user to design, modify, as well as manipulate the grid, including the capability of elliptic surface grid generation.
Grid generation for 3D turbomachinery configurations
NASA Technical Reports Server (NTRS)
Shih, Ming-Hsin; Soni, Bharat K.
1992-01-01
A numerical grid generation algorithm associated with the flow field about turbomachinery geometries is presented. Graphical user interface is developed with the FORMS Library to create an interactive, user-friendly working environment. This customized algorithm reduces the man-hours required to generate a grid associated with turbomachinery geometry, as compared to those required by general-purpose grid generation softwares. Bezier curves are utilized both interactively and automatically to accomplish grid line smoothness and orthogonality. Graphical user interactions are provided in the algorithm and allow the user to design and manipulate the grid lines with a mouse.
Grid Generation Techniques Utilizing the Volume Grid Manipulator
NASA Technical Reports Server (NTRS)
Alter, Stephen J.
1998-01-01
This paper presents grid generation techniques available in the Volume Grid Manipulation (VGM) code. The VGM code is designed to manipulate existing line, surface and volume grids to improve the quality of the data. It embodies an easy to read rich language of commands that enables such alterations as topology changes, grid adaption and smoothing. Additionally, the VGM code can be used to construct simplified straight lines, splines, and conic sections which are common curves used in the generation and manipulation of points, lines, surfaces and volumes (i.e., grid data). These simple geometric curves are essential in the construction of domain discretizations for computational fluid dynamic simulations. By comparison to previously established methods of generating these curves interactively, the VGM code provides control of slope continuity and grid point-to-point stretchings as well as quick changes in the controlling parameters. The VGM code offers the capability to couple the generation of these geometries with an extensive manipulation methodology in a scripting language. The scripting language allows parametric studies of a vehicle geometry to be efficiently performed to evaluate favorable trends in the design process. As examples of the powerful capabilities of the VGM code, a wake flow field domain will be appended to an existing X33 Venturestar volume grid; negative volumes resulting from grid expansions to enable flow field capture on a simple geometry, will be corrected; and geometrical changes to a vehicle component of the X33 Venturestar will be shown.
Workshop on Grid Generation and Related Areas
NASA Technical Reports Server (NTRS)
1992-01-01
A collection of papers given at the Workshop on Grid Generation and Related Areas is presented. The purpose of this workshop was to assemble engineers and scientists who are currently working on grid generation for computational fluid dynamics (CFD), surface modeling, and related areas. The objectives were to provide an informal forum on grid generation and related topics, to assess user experience, to identify needs, and to help promote synergy among engineers and scientists working in this area. The workshop consisted of four sessions representative of grid generation and surface modeling research and application within NASA LeRC. Each session contained presentations and an open discussion period.
TURBOGRID - Turbomachinery applications of grid generation
NASA Astrophysics Data System (ADS)
Soni, Bharat K.; Shih, Ming-Hsin
1990-07-01
Numerical grid generation algorithm associated with the field region about turbomachinery systems is presented. The algorithm is incorporated as a module, TIGER (Turbomachinery Interactive Grid genERation) of the modular general purpose computer code GENIE. Interactive definitions of the mathematical description of blades, hub and shroud with minimal user interactions, adaption of the weighted transfinite interpolation technique for efficient generation of grid blocks/zones, automatic construction of the Bezier curves to accomplish slope continuity, and efficient utilization of IRIS-graphics capabilities are the salient features of this algorithm which results in a significant time savings for a given turbomachinery geometry-grid application.
NASA Technical Reports Server (NTRS)
Golik, W. L.
1996-01-01
A robust solver for the elliptic grid generation equations is sought via a numerical study. The system of PDEs is discretized with finite differences, and multigrid methods are applied to the resulting nonlinear algebraic equations. Multigrid iterations are compared with respect to the robustness and efficiency. Different smoothers are tried to improve the convergence of iterations. The methods are applied to four 2D grid generation problems over a wide range of grid distortions. The results of the study help to select smoothing schemes and the overall multigrid procedures for elliptic grid generation.
Getting a Grip on Grid Generation
NASA Technical Reports Server (NTRS)
2002-01-01
GridPro is an automatic, object-oriented, multi-block grid generator that provides ease of use, high quality, rapid production, and parametric design. When paired with a 3-D graphic user interface called az- Manager, GridPro presents users with an extremely efficient, interactive capability to build topology, edit surfaces, set computational fluid dynamics (CFD) boundary conditions, and view multi-block grids. The origins of the GridPro technology date back to a 1989 SBIR contract with NASA's Glenn Research Center, in which Glenn was seeking a multi-block grid generation program that would run automatically upon identifying a pattern of grid blocks supplied by a user. The technology is currently used in many engineering fields, including aerospace, turbo- machinery, automotive, and chemical industries.
Grid generation: A view from the trenches
NASA Technical Reports Server (NTRS)
Ives, David; Miller, Robert; Siddons, William; Vandyke, Kevin
1995-01-01
This paper presents 'A view from the trenches' on CFD grid generation from a Pratt & Whitney perspective. We anticipate that other organizations have similar views. We focus on customer expectations and the consequent requirements. We enunciate a vision for grid generation, discuss issues that developers must recognize.
VGRIDSG: An unstructured surface grid generation program
NASA Technical Reports Server (NTRS)
Bockelie, Michael J.
1993-01-01
This report contains an overview of the VGRIDSG unstructured surface grid generation program. The VGRIDSG program was created from the VGRID3D unstructured grid generation program developed by Vigyan, Inc. The purpose of this report is to document the changes from the original VGRID3D program and to describe the capabilities of the new program.
NASA Technical Reports Server (NTRS)
Shih, T. I.-P.; Bailey, R. T.; Nguyen, H. L.; Roelke, R. J.
1990-01-01
An efficient computer program, called GRID2D/3D was developed to generate single and composite grid systems within geometrically complex two- and three-dimensional (2- and 3-D) spatial domains that can deform with time. GRID2D/3D generates single grid systems by using algebraic grid generation methods based on transfinite interpolation in which the distribution of grid points within the spatial domain is controlled by stretching functions. All single grid systems generated by GRID2D/3D can have grid lines that are continuous and differentiable everywhere up to the second-order. Also, grid lines can intersect boundaries of the spatial domain orthogonally. GRID2D/3D generates composite grid systems by patching together two or more single grid systems. The patching can be discontinuous or continuous. For continuous composite grid systems, the grid lines are continuous and differentiable everywhere up to the second-order except at interfaces where different single grid systems meet. At interfaces where different single grid systems meet, the grid lines are only differentiable up to the first-order. For 2-D spatial domains, the boundary curves are described by using either cubic or tension spline interpolation. For 3-D spatial domains, the boundary surfaces are described by using either linear Coon's interpolation, bi-hyperbolic spline interpolation, or a new technique referred to as 3-D bi-directional Hermite interpolation. Since grid systems generated by algebraic methods can have grid lines that overlap one another, GRID2D/3D contains a graphics package for evaluating the grid systems generated. With the graphics package, the user can generate grid systems in an interactive manner with the grid generation part of GRID2D/3D. GRID2D/3D is written in FORTRAN 77 and can be run on any IBM PC, XT, or AT compatible computer. In order to use GRID2D/3D on workstations or mainframe computers, some minor modifications must be made in the graphics part of the program; no
Unstructured grid generation using the distance function
NASA Technical Reports Server (NTRS)
Bihari, Barna L.; Chakravarthy, Sukumar R.
1991-01-01
A new class of methods for obtaining level sets to generate unstructured grids is presented. The consecutive grid levels are computed using the distance functions, which corresponds to solving the Hamilton-Jacobi equations representing the equations of motion of fronts propagating with curvature-dependent speed. The relationship between the distance function and the governing equations will be discussed as well as its application to generating grids. Multi-ply connected domains and complex geometries are handled naturally, with a straightforward generalization to several space dimensions. The grid points for the unstructured grid are obtained simultaneously with the grid levels. The search involved in checking for overlapping triangles is minimized by triangulating the entire domain one level at a time.
Modeling and Grid Generation of Iced Airfoils
NASA Technical Reports Server (NTRS)
Vickerman, Mary B.; Baez, Marivell; Braun, Donald C.; Hackenberg, Anthony W.; Pennline, James A.; Schilling, Herbert W.
2007-01-01
SmaggIce Version 2.0 is a software toolkit for geometric modeling and grid generation for two-dimensional, singleand multi-element, clean and iced airfoils. A previous version of SmaggIce was described in Preparing and Analyzing Iced Airfoils, NASA Tech Briefs, Vol. 28, No. 8 (August 2004), page 32. To recapitulate: Ice shapes make it difficult to generate quality grids around airfoils, yet these grids are essential for predicting ice-induced complex flow. This software efficiently creates high-quality structured grids with tools that are uniquely tailored for various ice shapes. SmaggIce Version 2.0 significantly enhances the previous version primarily by adding the capability to generate grids for multi-element airfoils. This version of the software is an important step in streamlining the aeronautical analysis of ice airfoils using computational fluid dynamics (CFD) tools. The user may prepare the ice shape, define the flow domain, decompose it into blocks, generate grids, modify/divide/merge blocks, and control grid density and smoothness. All these steps may be performed efficiently even for the difficult glaze and rime ice shapes. Providing the means to generate highly controlled grids near rough ice, the software includes the creation of a wrap-around block (called the "viscous sublayer block"), which is a thin, C-type block around the wake line and iced airfoil. For multi-element airfoils, the software makes use of grids that wrap around and fill in the areas between the viscous sub-layer blocks for all elements that make up the airfoil. A scripting feature records the history of interactive steps, which can be edited and replayed later to produce other grids. Using this version of SmaggIce, ice shape handling and grid generation can become a practical engineering process, rather than a laborious research effort.
NASA Technical Reports Server (NTRS)
Rostand, Philippe
1988-01-01
The incorporation of algebraic turbulence models in a solver for the 2-D compressible Navier-Stokes equations using triangular grids is described. A practical way to use the Cebeci Smith model, and to modify it in separated regions is proposed. The ability of the model to predict high speed, perfect gas boundary layers is investigated from a numerical point of view.
Algebraic grid adaptation method using non-uniform rational B-spline surface modeling
NASA Technical Reports Server (NTRS)
Yang, Jiann-Cherng; Soni, B. K.
1992-01-01
An algebraic adaptive grid system based on equidistribution law and utilized by the Non-Uniform Rational B-Spline (NURBS) surface for redistribution is presented. A weight function, utilizing a properly weighted boolean sum of various flow field characteristics is developed. Computational examples are presented to demonstrate the success of this technique.
Unstructured Grid Generation Techniques and Software
NASA Technical Reports Server (NTRS)
Posenau, Mary-Anne K. (Editor)
1993-01-01
The Workshop on Unstructured Grid Generation Techniques and Software was conducted for NASA to assess its unstructured grid activities, improve the coordination among NASA centers, and promote technology transfer to industry. The proceedings represent contributions from Ames, Langley, and Lewis Research Centers, and the Johnson and Marshall Space Flight Centers. This report is a compilation of the presentations made at the workshop.
Towards classical spectrum generating algebras for f-deformations
NASA Astrophysics Data System (ADS)
Kullock, Ricardo; Latini, Danilo
2016-01-01
In this paper we revise the classical analog of f-oscillators, a generalization of q-oscillators given in Man'ko et al. (1997) [8], in the framework of classical spectrum generating algebras (SGA) introduced in Kuru and Negro (2008) [9]. We write down the deformed Poisson algebra characterizing the entire family of non-linear oscillators and construct its general solution algebraically. The latter, covering the full range of f-deformations, shows an energy dependence both in the amplitude and the frequency of the motion.
A mathematical basis for automated structured grid generation with close coupling to the flow solver
Barnette, D.W.
1998-02-01
The first two truncation error terms resulting from finite differencing the convection terms in the two-dimensional Navier-Stokes equations are examined for the purpose of constructing two-dimensional grid generation schemes. These schemes are constructed such that the resulting grid distributions drive the error terms to zero. Two sets of equations result, one for each error term, that show promise in generating grids that provide more accurate flow solutions and possibly faster convergence. One set results in an algebraic scheme that drives the first truncation term to zero, and the other a hyperbolic scheme that drives the second term to zero. Also discussed is the possibility of using the schemes in sequentially constructing a grid in an iterative algorithm involving the flow solver. In essence, the process is envisioned to generate not only a flow field solution but the grid as well, rendering the approach a hands-off method for grid generation
NURBS evaluation and utilization for grid generation
Yu, Tzu-Yi; Soni, B.K.
1996-12-31
In the last few years, Non-Uniform Rational BSpline (NURBS) has evolved as an essential tool for a semi-analytical representation of geometrical entities encountered in Computational Field Simulation (CFS). The grid generation techniques based on NURBS have been developed and reported in the literature by various researchers. However, the evaluation of NURBS for surface/volume grid point generation is time consuming and the representation of widely utilized aerodynamic shapes into NURBS is not trivial. This paper addressed these issues. An enhanced algorithm for NURBS evaluation based on the proper utilization of the basis functions is presented. An accurate representation of the widely utilized transition duct designed by using superellipse equation is developed. An example of the NURBS surface definition to a 3D volume and its utilization in grid adaptation by combing NURBS with elliptic generation system is presented. The computational example involving a flow field around a generic missile configuration is presented for demonstrating grid adaptation.
Rigel: An interactive structured grid generation system
Hachfeld, W.D.; Khamayseh, A.K.; Hansen, G.A.
1998-02-01
An interactive structured grid generation application that facilitates the construction of complex, discretized, simulation models directly from the original CAD geometry specifications is presented. The application, named Rigel, reads physical model descriptions generated by modern CAD packages. Rigel includes a suite of interactive geometry editing functions to assist the user in the construction of a topologically correct geometry from the original CAD specification. Once a topologically correct geometry is created, an interactively steered grid generation capability is provided to facilitate the construction of an appropriate discretization for the simulation. Grid quality enhancement is supported with the application of user-directed elliptic smoothing, refinement, and coarsening operators. After a grid is completed, various output filters are supplied to write an input file for the target simulation code. This paper is intended to provide an overview of the mechanics of this process and to highlight some of the novel algorithms and techniques employed.
Elliptic generation of composite three-dimensional grids about realistic aircraft
NASA Technical Reports Server (NTRS)
Sorenson, Reese L.
1986-01-01
An elliptic method for generating composite grids about realistic aircraft is presented. A body-conforming grid is first generated about the entire aircraft by the solution of Poisson's differential equation. This grid has relatively coarse spacing, and it covers the entire physical domain. At boundary surfaces, cell size is controlled and cell skewness is nearly eliminated by inhomogeneous terms, which are found automatically by the program. Certain regions of the grid in which high gradients are expected, and which map into rectangular solids in the computational domain, are then designated for zonal refinement. Spacing in the zonal grids is reduced by adding points with a simple, algebraic scheme. Details of the grid-generation method are presented along with results of the present application, a wing/body configuration based on the F-16 fighter aircraft.
Elliptic generation of composite three-dimensional grids about realistic aircraft
NASA Technical Reports Server (NTRS)
Sorenson, R. L.
1986-01-01
An elliptic method for generating composite grids about realistic aircraft is presented. A body-conforming grid is first generated about the entire aircraft by the solution of Poisson's differential equation. This grid has relatively coarse spacing, and it covers the entire physical domain. At boundary surfaces, cell size is controlled and cell skewness is nearly eliminated by inhomogeneous terms, which are found automatically by the program. Certain regions of the grid in which high gradients are expected, and which map into rectangular solids in the computational domain, are then designated for zonal refinement. Spacing in the zonal grids is reduced by adding points with a simple, algebraic scheme. Details of the grid generation method are presented along with results of the present application, a wing-body configuration based on the F-16 fighter aircraft.
NASA Technical Reports Server (NTRS)
Steinthorsson, E.; Shih, T. I-P.; Roelke, R. J.
1991-01-01
In order to generate good quality systems for complicated three-dimensional spatial domains, the grid-generation method used must be able to exert rather precise controls over grid-point distributions. Several techniques are presented that enhance control of grid-point distribution for a class of algebraic grid-generation methods known as the two-, four-, and six-boundary methods. These techniques include variable stretching functions from bilinear interpolation, interpolating functions based on tension splines, and normalized K-factors. The techniques developed in this study were incorporated into a new version of GRID3D called GRID3D-v2. The usefulness of GRID3D-v2 was demonstrated by using it to generate a three-dimensional grid system in the coolent passage of a radial turbine blade with serpentine channels and pin fins.
Multiblock grid generation with automatic zoning
NASA Technical Reports Server (NTRS)
Eiseman, Peter R.
1995-01-01
An overview will be given for multiblock grid generation with automatic zoning. We shall explore the many advantages and benefits of this exciting technology and will also see how to apply it to a number of interesting cases. The technology is available in the form of a commercial code, GridPro(registered trademark)/az3000. This code takes surface geometry definitions and patterns of points as its primary input and produces high quality grids as its output. Before we embark upon our exploration, we shall first give a brief background of the environment in which this technology fits.
Introduction to grid generation systems in turbomachinery
NASA Astrophysics Data System (ADS)
Camarero, R.; Ozell, B.; Reggio, M.; Caron, A.
Body-fitted curvilinear grid generation for the numerical simulation of three dimensional flow in turbomachines is introduced. The grids yield coordinate curves aligned with the domain boundaries. The numerical scheme for the governing equations is carried out on a rectangular mesh, giving a simpler and more accurate algorithm since bondaries coincide with coordinate grids, and no interpolation is required. The geometric complexity, through the transformation, is imbedded into the coefficients of the governing equations, affording the possibility of writing generalized codes applicable to a variety of geometries. This results in a great saving in the code development effort.
Computer Program For Generation Of Surface Grids
NASA Technical Reports Server (NTRS)
Ching, Raymond; Pierce, Lawrence
1993-01-01
S3D is useful computer program for generation of grids on surfaces of bodies having complicated shapes. Product of integration of robust and widely applicable interpolation technique with latest in computer-workstation technology. Incorporates highly efficient and easy-to-use graphical-interface software, enables real-time and interactive analyses of surface-geometry data and facilitates construction of surface grids.
Spectral Topography Generation for Arbitrary Grids
NASA Astrophysics Data System (ADS)
Oh, T. J.
2015-12-01
A new topography generation tool utilizing spectral transformation technique for both structured and unstructured grids is presented. For the source global digital elevation data, the NASA Shuttle Radar Topography Mission (SRTM) 15 arc-second dataset (gap-filling by Jonathan de Ferranti) is used and for land/water mask source, the NASA Moderate Resolution Imaging Spectroradiometer (MODIS) 30 arc-second land water mask dataset v5 is used. The original source data is coarsened to a intermediate global 2 minute lat-lon mesh. Then, spectral transformation to the wave space and inverse transformation with wavenumber truncation is performed for isotropic topography smoothness control. Target grid topography mapping is done by bivariate cubic spline interpolation from the truncated 2 minute lat-lon topography. Gibbs phenomenon in the water region can be removed by overwriting ocean masked target coordinate grids with interpolated values from the intermediate 2 minute grid. Finally, a weak smoothing operator is applied on the target grid to minimize the land/water surface height discontinuity that might have been introduced by the Gibbs oscillation removal procedure. Overall, the new topography generation approach provides spectrally-derived, smooth topography with isotropic resolution and minimum damping, enabling realistic topography forcing in the numerical model. Topography is generated for the cubed-sphere grid and tested on the KIAPS Integrated Model (KIM).
The 3D Euler solutions using automated Cartesian grid generation
NASA Technical Reports Server (NTRS)
Melton, John E.; Enomoto, Francis Y.; Berger, Marsha J.
1993-01-01
Viewgraphs on 3-dimensional Euler solutions using automated Cartesian grid generation are presented. Topics covered include: computational fluid dynamics (CFD) and the design cycle; Cartesian grid strategy; structured body fit; grid generation; prolate spheroid; and ONERA M6 wing.
Three-dimensional surface grid generation for calculation of thermal radiation shape factors
NASA Technical Reports Server (NTRS)
Aly, Hany M.
1992-01-01
A technique is described to generate three dimensional surface grids suitable for calculating shape factors for thermal radiative heat transfer. The surface under consideration is approximated by finite triangular elements generated in a special manner. The grid is generated by dividing the surface into a two dimensional array of nodes. Each node is defined by its coordinates. Each set of four adjacent nodes is used to construct two triangular elements. Each triangular element is characterized by the vector representation of its vertices. Vector algebra is used to calculate all desired geometric properties of grid elements. The properties are used to determine the shape factor between the element and an area element in space. The grid generation can be graphically displayed using any software with three dimensional features. DISSPLA was used to view the grids.
IGES transformer and NURBS in grid generation
NASA Technical Reports Server (NTRS)
Yu, Tzu-Yi; Soni, Bharat K.
1993-01-01
In the field of Grid Generation and the CAD/CAM, there are numerous geometry output formats which require the designer to spend a great deal of time manipulating geometrical entities in order to achieve a useful sculptured geometrical description for grid generation. Also in this process, there is a danger of losing fidelity of the geometry under consideration. This stresses the importance of a standard geometry definition for the communication link between varying CAD/CAM and grid system. The IGES (Initial Graphics Exchange Specification) file is a widely used communication between CAD/CAM and the analysis tools. The scientists at NASA Research Centers - including NASA Ames, NASA Langley, NASA Lewis, NASA Marshall - have recognized this importance and, therefore, in 1992 they formed the committee of the 'NASA-IGES' which is the subset of the standard IGES. This committee stresses the importance and encourages the CFD community to use the standard IGES file for the interface between the CAD/CAM and CFD analysis. Also, two of the IGES entities -- the NURBS Curve (Entity 126) and NURBS Surface (Entity 128) -- which have many useful geometric properties -- like the convex hull property, local control property and affine invariance, also widely utilized analytical geometries can be accurately represented using NURBS. This is important in today grid generation tools because of the emphasis of the interactive design. To satisfy the geometry transformation between the CAD/CAM system and Grid Generation field, the CAGI (Computer Aided Geometry Design) developed, which include the Geometry Transformation, Geometry Manipulation and Geometry Generation as well as the user interface. This paper will present the successful development IGES file transformer and application of NURBS definition in the grid generation.
Batch mode grid generation: An endangered species
NASA Technical Reports Server (NTRS)
Schuster, David M.
1992-01-01
Non-interactive grid generation schemes should thrive as emphasis shifts from development of numerical analysis and design methods to application of these tools to real engineering problems. A strong case is presented for the continued development and application of non-interactive geometry modeling methods. Guidelines, strategies, and techniques for developing and implementing these tools are presented using current non-interactive grid generation methods as examples. These schemes play an important role in the development of multidisciplinary analysis methods and some of these applications are also discussed.
A three-dimensional grid generation method for gas-turbine combustor flow computations
NASA Astrophysics Data System (ADS)
Shyy, Wei; Braaten, Mark E.; Sober, Janet S.
1987-02-01
A special-purpose code suitable for generating a curvilinear nonorthogonal grid system for gas-turbine combustor flow computations has been produced. The code is capable of handling an arbitrary number of dilution holes with any radii as well as film-cooling slots on the top and bottom surfaces. A zonal approach has been developed to handle the fast length scale variations imposed by the geometric constraints and to minimize the overall computational efforts needed to generate the grids. The code combines partial differential equation and algebraic interpolation methods to generate the grid system. The salient features of the grid characteristics are discussed. Also included are sample results of a 3-D turbulent combusting flow field calculated on the grid system produced by this methodology.
NASA Technical Reports Server (NTRS)
Smith, R. E.; Everton, E. L.; Weilmuenster, K. J.; Weise, M. R.; Farr, N.
1990-01-01
The surface definition and grid generation about an Assured Crew Return Vehicle (ACRV) for the Space Station Freedom are described. The purpose of the surface definition and grid generation is to provide the necessary geometry information for CFD calculations about the vehicle. There are two salient features in this description. The first is that the numerical model representing the ACRV configuration is obtained from the measurement of an existing wind tunnel model. The method for smoothing the measured data and obtaining the numerical model is described. The second feature is the description of the algebraic grid generation method and software to compute volume grids about the ACRV. The methods and software allow rapid computation of volume grids for a wide range of flow conditions.
Katz, Jessica; Cochran, Jaquelin
2015-05-27
Greening the Grid provides technical assistance to energy system planners, regulators, and grid operators to overcome challenges associated with integrating variable renewable energy into the grid. This document, part of a Greening the Grid toolkit, provides power system planners with tips to help secure and sustain investment in new renewable energy generation by aligning renewable energy policy targets and incentives with grid integration considerations.
Generation Of Surface Grids From Data Points
NASA Technical Reports Server (NTRS)
Luh, Raymond Ching-Chung
1991-01-01
Computational procedure generates grids on complicated three-dimensional surfaces from sets of data points that lie on and specify those surfaces. Starting with grouping of possibly sparse surface points into lines and/or patches, procedure involves interpolation within and blending of lines and/or patches and possibly redistribution and reassembly of patches to obtain finished system of zonal patch grids that match at boundaries between them. Procedure semiautomated via computer program that performs all steps except selection of patches and interpolation points, left to discretion of user.
Integrated geometry and grid generation system for complex configurations
NASA Technical Reports Server (NTRS)
Akdag, Vedat; Wulf, Armin
1992-01-01
A grid generation system was developed that enables grid generation for complex configurations. The system called ICEM/CFD is described and its role in computational fluid dynamics (CFD) applications is presented. The capabilities of the system include full computer aided design (CAD), grid generation on the actual CAD geometry definition using robust surface projection algorithms, interfacing easily with known CAD packages through common file formats for geometry transfer, grid quality evaluation of the volume grid, coupling boundary condition set-up for block faces with grid topology generation, multi-block grid generation with or without point continuity and block to block interface requirement, and generating grid files directly compatible with known flow solvers. The interactive and integrated approach to the problem of computational grid generation not only substantially reduces manpower time but also increases the flexibility of later grid modifications and enhancements which is required in an environment where CFD is integrated into a product design cycle.
Three-dimensional elliptic grid generation with fully automatic boundary constraints
NASA Astrophysics Data System (ADS)
Kaul, Upender K.
2010-08-01
A new procedure for generating smooth uniformly clustered three-dimensional structured elliptic grids is presented here which formulates three-dimensional boundary constraints by extending the two-dimensional counterpart presented by the author earlier. This fully automatic procedure obviates the need for manual specification of decay parameters over the six bounding surfaces of a given volume grid. The procedure has been demonstrated here for the Mars Science Laboratory (MSL) geometries such as aeroshell and canopy, as well as the Inflatable Aerodynamic Decelerator (IAD) geometry and a 3D analytically defined geometry. The new procedure also enables generation of single-block grids for such geometries because the automatic boundary constraints permit the decay parameters to evolve as part of the solution to the elliptic grid system of equations. These decay parameters are no longer just constants, as specified in the conventional approach, but functions of generalized coordinate variables over a given bounding surface. Since these decay functions vary over a given boundary, orthogonal grids around any arbitrary simply-connected boundary can be clustered automatically without having to break up the boundaries and the corresponding interior or exterior domains into various blocks for grid generation. The new boundary constraints are not limited to the simply-connected regions only, but can also be formulated around multiply-connected and isolated regions in the interior. The proposed method is superior to other methods of grid generation such as algebraic and hyperbolic techniques in that the grids obtained here are C2 continuous, whereas simple elliptic smoothing of algebraic or hyperbolic grids to enforce C2 continuity destroys the grid clustering near the boundaries. US patent 7231329.
An interactive grid generation procedure for axial and radial flow turbomachinery
NASA Technical Reports Server (NTRS)
Beach, Timothy A.
1989-01-01
A combination algebraic/elliptic technique is presented for the generation of three dimensional grids about turbo-machinery blade rows for both axial and radial flow machinery. The technique is built around use of an advanced engineering workstation to construct several two dimensional grids interactively on predetermined blade-to-blade surfaces. A three dimensional grid is generated by interpolating these surface grids onto an axisymmetric grid. On each blade-to-blade surface, a grid is created using algebraic techniques near the blade to control orthogonality within the boundary layer region and elliptic techniques in the mid-passage to achieve smoothness. The interactive definition of bezier curves as internal boundaries is the key to simple construction. This procedure lends itself well to zonal grid construction, an important example being the tip clearance region. Calculations done to date include a space shuttle main engine turbopump blade, a radial inflow turbine blade, and the first stator of the United Technologies Research Center large scale rotating rig. A finite Navier-Stokes solver was used in each case.
An interactive grid generation procedure for axial and radial flow turbomachinery
NASA Astrophysics Data System (ADS)
Beach, T. A.
1990-01-01
A combination algebraic/elliptic technique is presented for the generation of three dimensional grids about turbo-machinery blade rows for both axial and radial flow machinery. The technique is built around use of an advanced engineering workstation to construct several two dimensional grids interactively on predetermined blade-to-blade surfaces. A three dimensional grid is generated by interpolating these surface grids onto an axisymmetric grid. On each blade-to-blade surface, a grid is created using algebraic techniques near the blade to control orthogonality within the boundary layer region and elliptic techniques in the mid-passage to achieve smoothness. The interactive definition of bezier curves as internal boundaries is the key to simple construction. This procedure lends itself well to zonal grid construction, an important example being the tip clearance region. Calculations done to date include a space shuttle main engine turbopump blade, a radial inflow turbine blade, and the first stator of the United Technologies Research Center large scale rotating rig. A finite Navier-Stokes solver was used in each case.
Criteria for evaluation of grid generation systems
NASA Technical Reports Server (NTRS)
Ascoli, Edward P.; Barson, Steven L.; Decroix, Michele E.; Hsu, Wayne W.
1993-01-01
Many CFD grid generation systems are in use nationally, but few comparative studies have been performed to quantify their relative merits. A study was undertaken to systematically evaluate and select the best CFD grid generation codes available. Detailed evaluation criteria were established as the basis for the evaluation conducted. Descriptions of thirty-four separate criteria, grouped into eight general categories are provided. Benchmark test cases, developed to test basic features of selected codes, are described in detail. Scoring guidelines were generated to establish standards for measuring code capabilities, ensuring uniformity of ratings, and minimizing personal bias among the three code evaluators. Ten candidate codes were identified from government, industry, universities, and commercial software companies. A three phase evaluation was conducted. In Phase 1, ten codes identified were screened through conversations with code authors and other industry experts. Seven codes were carried forward into a Phase 2 evaluation in which all codes were scored according to the predefined criteria. Two codes emerged as being significantly better than the others: RAGGS and GRIDGEN. Finally, these two codes were carried forward into a Phase 3 evaluation in which complex 3-D multizone grids were generated to verify capability.
Grid generation and flow computation about a Martian entry vehicle
NASA Technical Reports Server (NTRS)
Stewart, J. E.; Tiwari, S. N.
1990-01-01
A number of vehicles are currently being proposed for a manned mission to Mars. One of these vehicles has a modified blunt-nosed cone configuration. Experimental results were obtained for this vehicle in 1968. They show lift-over-drag ratios comparable to those needed for Mars entry. Computations are performed to verify the earlier results and to further describe the flight characteristics of this vehicle. An analytical method is used to define the surface of this vehicle. A single-block volume grid is generated around the vehicle using the algebraic Two-Boundary Grid Generation algorithm (TBGG) and transfinite interpolation. Euler solutions are then obtained from a Langley Aerodynamic Upward Relaxation Algorithm (LAURA) at Mach 6.0 and angles of attack of 0, 6, and 12 deg. The lift coefficient determined from the LAURA code agree very well with the experimental results. The drag and pitching moment coefficients, however, are underestimated by the code since viscous effects are not considered. Contour plots of the flowfield show no evidence of separation for angles of attack up to 12 deg.
Automatic structured grid generation using Gridgen (some restrictions apply)
NASA Technical Reports Server (NTRS)
Chawner, John R.; Steinbrenner, John P.
1995-01-01
The authors have noticed in the recent grid generation literature an emphasis on the automation of structured grid generation. The motivation behind such work is clear; grid generation is easily the most despised task in the grid-analyze-visualize triad of computational analysis (CA). However, because grid generation is closely coupled to both the design and analysis software and because quantitative measures of grid quality are lacking, 'push button' grid generation usually results in a compromise between speed, control, and quality. Overt emphasis on automation obscures the substantive issues of providing users with flexible tools for generating and modifying high quality grids in a design environment. In support of this paper's tongue-in-cheek title, many features of the Gridgen software are described. Gridgen is by no stretch of the imagination an automatic grid generator. Despite this fact, the code does utilize many automation techniques that permit interesting regenerative features.
Flames in fractal grid generated turbulence
NASA Astrophysics Data System (ADS)
Goh, K. H. H.; Geipel, P.; Hampp, F.; Lindstedt, R. P.
2013-12-01
Twin premixed turbulent opposed jet flames were stabilized for lean mixtures of air with methane and propane in fractal grid generated turbulence. A density segregation method was applied alongside particle image velocimetry to obtain velocity and scalar statistics. It is shown that the current fractal grids increase the turbulence levels by around a factor of 2. Proper orthogonal decomposition (POD) was applied to show that the fractal grids produce slightly larger turbulent structures that decay at a slower rate as compared to conventional perforated plates. Conditional POD (CPOD) was also implemented using the density segregation technique and the results show that CPOD is essential to segregate the relative structures and turbulent kinetic energy distributions in each stream. The Kolmogorov length scales were also estimated providing values ∼0.1 and ∼0.5 mm in the reactants and products, respectively. Resolved profiles of flame surface density indicate that a thin flame assumption leading to bimodal statistics is not perfectly valid under the current conditions and it is expected that the data obtained will be of significant value to the development of computational methods that can provide information on the conditional structure of turbulence. It is concluded that the increase in the turbulent Reynolds number is without any negative impact on other parameters and that fractal grids provide a route towards removing the classical problem of a relatively low ratio of turbulent to bulk strain associated with the opposed jet configuration.
Advancing-layers method for generation of unstructured viscous grids
NASA Technical Reports Server (NTRS)
Pirzadeh, Shahyar
1993-01-01
A novel approach for generating highly stretched grids which is based on a modified advancing-front technique and benefits from the generality, flexibility, and grid quality of the conventional advancing-front-based Euler grid generators is presented. The method is self-sufficient for the insertion of grid points in the boundary layer and beyond. Since it is based on a totally unstructured grid strategy, the method alleviates the difficulties stemming from the structural limitations of the prismatic techniques.
NASA Technical Reports Server (NTRS)
Bailey, R. T.; Shih, T. I.-P.; Nguyen, H. L.; Roelke, R. J.
1990-01-01
An efficient computer program, called GRID2D/3D, was developed to generate single and composite grid systems within geometrically complex two- and three-dimensional (2- and 3-D) spatial domains that can deform with time. GRID2D/3D generates single grid systems by using algebraic grid generation methods based on transfinite interpolation in which the distribution of grid points within the spatial domain is controlled by stretching functions. All single grid systems generated by GRID2D/3D can have grid lines that are continuous and differentiable everywhere up to the second-order. Also, grid lines can intersect boundaries of the spatial domain orthogonally. GRID2D/3D generates composite grid systems by patching together two or more single grid systems. The patching can be discontinuous or continuous. For continuous composite grid systems, the grid lines are continuous and differentiable everywhere up to the second-order except at interfaces where different single grid systems meet. At interfaces where different single grid systems meet, the grid lines are only differentiable up to the first-order. For 2-D spatial domains, the boundary curves are described by using either cubic or tension spline interpolation. For 3-D spatial domains, the boundary surfaces are described by using either linear Coon's interpolation, bi-hyperbolic spline interpolation, or a new technique referred to as 3-D bi-directional Hermite interpolation. Since grid systems generated by algebraic methods can have grid lines that overlap one another, GRID2D/3D contains a graphics package for evaluating the grid systems generated. With the graphics package, the user can generate grid systems in an interactive manner with the grid generation part of GRID2D/3D. GRID2D/3D is written in FORTRAN 77 and can be run on any IBM PC, XT, or AT compatible computer. In order to use GRID2D/3D on workstations or mainframe computers, some minor modifications must be made in the graphics part of the program; no
Hyperbolic Prismatic Grid Generation and Solution of Euler Equations on Prismatic Grids
NASA Technical Reports Server (NTRS)
Pandya, S. A.; Chattot, JJ; Hafez, M. M.; Kutler, Paul (Technical Monitor)
1994-01-01
A hyperbolic grid generation method is used to generate prismatic grids and an approach using prismatic grids to solve the Euler equations is presented. The theory of the stability and feasibility of the hyperbolic grid generation method is presented. The hyperbolic grid generation method of Steger et al for structured grids is applied to a three dimensional triangularized surface definition to generate a grid that is unstructured on each successive layer. The grid, however, retains structure in the body-normal direction and has a computational cell shaped like a triangular prism. In order to take advantage of the structure in the normal direction, a finite-volume scheme that treats the unknowns along the normal direction implicitly is introduced and the flow over a sphere is simulated.
Three-dimensional elliptic grid generation for an F-16
NASA Technical Reports Server (NTRS)
Sorenson, Reese L.
1988-01-01
A case history depicting the effort to generate a computational grid for the simulation of transonic flow about an F-16 aircraft at realistic flight conditions is presented. The flow solver for which this grid is designed is a zonal one, using the Reynolds averaged Navier-Stokes equations near the surface of the aircraft, and the Euler equations in regions removed from the aircraft. A body conforming global grid, suitable for the Euler equation, is first generated using 3-D Poisson equations having inhomogeneous terms modeled after the 2-D GRAPE code. Regions of the global grid are then designated for zonal refinement as appropriate to accurately model the flow physics. Grid spacing suitable for solution of the Navier-Stokes equations is generated in the refinement zones by simple subdivision of the given coarse grid intervals. That grid generation project is described, with particular emphasis on the global coarse grid.
Unstructured viscous grid generation by advancing-front method
NASA Technical Reports Server (NTRS)
Pirzadeh, Shahyar
1993-01-01
A new method of generating unstructured triangular/tetrahedral grids with high-aspect-ratio cells is proposed. The method is based on new grid-marching strategy referred to as 'advancing-layers' for construction of highly stretched cells in the boundary layer and the conventional advancing-front technique for generation of regular, equilateral cells in the inviscid-flow region. Unlike the existing semi-structured viscous grid generation techniques, the new procedure relies on a totally unstructured advancing-front grid strategy resulting in a substantially enhanced grid flexibility and efficiency. The method is conceptually simple but powerful, capable of producing high quality viscous grids for complex configurations with ease. A number of two-dimensional, triangular grids are presented to demonstrate the methodology. The basic elements of the method, however, have been primarily designed with three-dimensional problems in mind, making it extendible for tetrahedral, viscous grid generation.
Software Surface Modeling and Grid Generation Steering Committee
NASA Technical Reports Server (NTRS)
Smith, Robert E. (Editor)
1992-01-01
It is a NASA objective to promote improvements in the capability and efficiency of computational fluid dynamics. Grid generation, the creation of a discrete representation of the solution domain, is an essential part of computational fluid dynamics. However, grid generation about complex boundaries requires sophisticated surface-model descriptions of the boundaries. The surface modeling and the associated computation of surface grids consume an extremely large percentage of the total time required for volume grid generation. Efficient and user friendly software systems for surface modeling and grid generation are critical for computational fluid dynamics to reach its potential. The papers presented here represent the state-of-the-art in software systems for surface modeling and grid generation. Several papers describe improved techniques for grid generation.
NASA Technical Reports Server (NTRS)
Rostand, Philippe
1989-01-01
The incorporation of algebraic turbulence models in a solver for the 2-D compressible Navier-Stokes equations using triangular grids is described. A practial way to use the Cebeci Smith model, and to modify it in separated regions is proposed. The ability of the model to predict high speed, perfect gas boundary layers is investigated from a numerical point of view.
An algebra for spatio-temporal information generation
NASA Astrophysics Data System (ADS)
Pebesma, Edzer; Scheider, Simon; Gräler, Benedikt; Stasch, Christoph; Hinz, Matthias
2016-04-01
When we accept the premises of James Frew's laws of metadata (Frew's first law: scientists don't write metadata; Frew's second law: any scientist can be forced to write bad metadata), but also assume that scientists try to maximise the impact of their research findings, can we develop our information infrastructures such that useful metadata is generated automatically? Currently, sharing of data and software to completely reproduce research findings is becoming standard, e.g. in the Journal of Statistical Software [1]. The reproduction (e.g. R) scripts however convey correct syntax, but still limited semantics. We propose [2] a new, platform-neutral way to algebraically describe how data is generated, e.g. by observation, and how data is derived, e.g. by processing observations. It starts with forming functions composed of four reference system types (space, time, quality, entity), which express for instance continuity of objects over time, and continuity of fields over space and time. Data, which is discrete by definition, is generated by evaluating such functions at discrete space and time instances, or by evaluating a convolution (aggregation) over them. Derived data is obtained by inputting data to data derivation functions, which for instance interpolate, estimate, aggregate, or convert fields into objects and vice versa. As opposed to the traditional when, where and what semantics of data sets, our algebra focuses on describing how a data set was generated. We argue that it can be used to discover data sets that were derived from a particular source x, or derived by a particular procedure y. It may also form the basis for inferring meaningfulness of derivation procedures [3]. Current research focuses on automatically generating provenance documentation from R scripts. [1] http://www.jstatsoft.org/ (open access) [2] http://www.meaningfulspatialstatistics.org has the full paper (in review) [3] Stasch, C., S. Scheider, E. Pebesma, W. Kuhn, 2014. Meaningful
Asymptotics of bivariate generating functions with algebraic singularities
NASA Astrophysics Data System (ADS)
Greenwood, Torin
Flajolet and Odlyzko (1990) derived asymptotic formulae the coefficients of a class of uni- variate generating functions with algebraic singularities. Gao and Richmond (1992) and Hwang (1996, 1998) extended these results to classes of multivariate generating functions, in both cases by reducing to the univariate case. Pemantle and Wilson (2013) outlined new multivariate ana- lytic techniques and used them to analyze the coefficients of rational generating functions. After overviewing these methods, we use them to find asymptotic formulae for the coefficients of a broad class of bivariate generating functions with algebraic singularities. Beginning with the Cauchy integral formula, we explicity deform the contour of integration so that it hugs a set of critical points. The asymptotic contribution to the integral comes from analyzing the integrand near these points, leading to explicit asymptotic formulae. Next, we use this formula to analyze an example from current research. In the following chapter, we apply multivariate analytic techniques to quan- tum walks. Bressler and Pemantle (2007) found a (d + 1)-dimensional rational generating function whose coefficients described the amplitude of a particle at a position in the integer lattice after n steps. Here, the minimal critical points form a curve on the (d + 1)-dimensional unit torus. We find asymptotic formulae for the amplitude of a particle in a given position, normalized by the number of steps n, as n approaches infinity. Each critical point contributes to the asymptotics for a specific normalized position. Using Groebner bases in Maple again, we compute the explicit locations of peak amplitudes. In a scaling window of size the square root of n near the peaks, each amplitude is asymptotic to an Airy function.
Computing Aerodynamic Performance of a 2D Iced Airfoil: Blocking Topology and Grid Generation
NASA Technical Reports Server (NTRS)
Chi, X.; Zhu, B.; Shih, T. I.-P.; Slater, J. W.; Addy, H. E.; Choo, Yung K.; Lee, Chi-Ming (Technical Monitor)
2002-01-01
The ice accrued on airfoils can have enormously complicated shapes with multiple protruded horns and feathers. In this paper, several blocking topologies are proposed and evaluated on their ability to produce high-quality structured multi-block grid systems. A transition layer grid is introduced to ensure that jaggedness on the ice-surface geometry do not to propagate into the domain. This is important for grid-generation methods based on hyperbolic PDEs (Partial Differential Equations) and algebraic transfinite interpolation. A 'thick' wrap-around grid is introduced to ensure that grid lines clustered next to solid walls do not propagate as streaks of tightly packed grid lines into the interior of the domain along block boundaries. For ice shapes that are not too complicated, a method is presented for generating high-quality single-block grids. To demonstrate the usefulness of the methods developed, grids and CFD solutions were generated for two iced airfoils: the NLF0414 airfoil with and without the 623-ice shape and the B575/767 airfoil with and without the 145m-ice shape. To validate the computations, the computed lift coefficients as a function of angle of attack were compared with available experimental data. The ice shapes and the blocking topologies were prepared by NASA Glenn's SmaggIce software. The grid systems were generated by using a four-boundary method based on Hermite interpolation with controls on clustering, orthogonality next to walls, and C continuity across block boundaries. The flow was modeled by the ensemble-averaged compressible Navier-Stokes equations, closed by the shear-stress transport turbulence model in which the integration is to the wall. All solutions were generated by using the NPARC WIND code.
Interactive grid generation program for CAP-TSD
NASA Technical Reports Server (NTRS)
Bland, Samuel R.
1990-01-01
A grid generation program for use with the CAP-TSD transonic small disturbance code is described. The program runs interactively in FORTRAN on the Sun Workstation. A fifth-degree polynomial is used to map the grid index onto the computational coordinate. The grid is plotted to aid in the assessment of its quality and may be saved on file in NAMELIST format.
NASA Technical Reports Server (NTRS)
Chan, William M.; Akien, Edwin (Technical Monitor)
2002-01-01
For many years, generation of overset grids for complex configurations has required the use of a number of different independently developed software utilities. Results created by each step were then visualized using a separate visualization tool before moving on to the next. A new software tool called OVERGRID was developed which allows the user to perform all the grid generation steps and visualization under one environment. OVERGRID provides grid diagnostic functions such as surface tangent and normal checks as well as grid manipulation functions such as extraction, extrapolation, concatenation, redistribution, smoothing, and projection. Moreover, it also contains hyperbolic surface and volume grid generation modules that are specifically suited for overset grid generation. It is the first time that such a unified interface existed for the creation of overset grids for complex geometries. New concepts on automatic overset surface grid generation around surface discontinuities will also be briefly presented. Special control curves on the surface such as intersection curves, sharp edges, open boundaries, are called seam curves. The seam curves are first automatically extracted from a multiple panel network description of the surface. Points where three or more seam curves meet are automatically identified and are called seam corners. Seam corner surface grids are automatically generated using a singular axis topology. Hyperbolic surface grids are then grown from the seam curves that are automatically trimmed away from the seam corners.
Evaluation of the Dornier Gmbh interactive grid generation system
NASA Technical Reports Server (NTRS)
Brown, Robert L.
1989-01-01
An interactive grid generation program, INGRID, is investigated and evaluated. A description of the task and work performed, a description and evaluation of INGRID, and a discussion of the possibilities for bringing INGRID into the NASA and Numerical Aerodynamic Simulator (NAS) computing environments is included. The interactive grid generation program was found to be a viable approach for grid generation and determined that it could be converted to work in the NAS environment but that INGRID does not solve the fundamentally hard problems associated with grid generation, specifically, domain decomposition.
DRAGON Grid: A Three-Dimensional Hybrid Grid Generation Code Developed
NASA Technical Reports Server (NTRS)
Liou, Meng-Sing
2000-01-01
Because grid generation can consume 70 percent of the total analysis time for a typical three-dimensional viscous flow simulation for a practical engineering device, payoffs from research and development could reduce costs and increase throughputs considerably. In this study, researchers at the NASA Glenn Research Center at Lewis Field developed a new hybrid grid approach with the advantages of flexibility, high-quality grids suitable for an accurate resolution of viscous regions, and a low memory requirement. These advantages will, in turn, reduce analysis time and increase accuracy. They result from an innovative combination of structured and unstructured grids to represent the geometry and the computation domain. The present approach makes use of the respective strengths of both the structured and unstructured grid methods, while minimizing their weaknesses. First, the Chimera grid generates high-quality, mostly orthogonal meshes around individual components. This process is flexible and can be done easily. Normally, these individual grids are required overlap each other so that the solution on one grid can communicate with another. However, when this communication is carried out via a nonconservative interpolation procedure, a spurious solution can result. Current research is aimed at entirely eliminating this undesired interpolation by directly replacing arbitrary grid overlapping with a nonstructured grid called a DRAGON grid, which uses the same set of conservation laws over the entire region, thus ensuring conservation everywhere. The DRAGON grid is shown for a typical film-cooled turbine vane with 33 holes and 3 plenum compartments. There are structured grids around each geometrical entity and unstructured grids connecting them. In fiscal year 1999, Glenn researchers developed and tested the three-dimensional DRAGON grid-generation tools. A flow solver suitable for the DRAGON grid has been developed, and a series of validation tests are underway.
NASA Technical Reports Server (NTRS)
Eriksson, L. E.
1980-01-01
A direct algebraic method was developed and applied to generate three dimensional grids around wing-body configurations. The method used is a generalized transfinite interpolation method which generates the desired coordinate transformation using geometric data only on the boundaries of the domain of interest. The geometric data that can be specified includes not only coordinates on the boundaries but also out-of-surface parametric derivatives that give a very precise control over the transformation in the vicinity of the surface. In addition to this, the method gives good control over the stretching of the mesh between different boundaries.
Structured background grids for generation of unstructured grids by advancing front method
NASA Technical Reports Server (NTRS)
Pirzadeh, Shahyar
1991-01-01
A new method of background grid construction is introduced for generation of unstructured tetrahedral grids using the advancing-front technique. Unlike the conventional triangular/tetrahedral background grids which are difficult to construct and usually inadequate in performance, the new method exploits the simplicity of uniform Cartesian meshes and provides grids of better quality. The approach is analogous to solving a steady-state heat conduction problem with discrete heat sources. The spacing parameters of grid points are distributed over the nodes of a Cartesian background grid by interpolating from a few prescribed sources and solving a Poisson equation. To increase the control over the grid point distribution, a directional clustering approach is used. The new method is convenient to use and provides better grid quality and flexibility. Sample results are presented to demonstrate the power of the method.
Generating functions and multiplicity formulas: The case of rank two simple Lie algebras
NASA Astrophysics Data System (ADS)
Fernández Núñez, José; García Fuertes, Wifredo; Perelomov, Askold M.
2015-09-01
A procedure is described that makes use of the generating function of characters to obtain a new generating function H giving the multiplicities of each weight in all the representations of a simple Lie algebra. The way to extract from H explicit multiplicity formulas for particular weights is explained and the results corresponding to rank two simple Lie algebras are shown.
Surface grid generation for wing-fuselage bodies
NASA Technical Reports Server (NTRS)
Smith, R. E.; Kudlinski, R. A.; Pitts, J. I.
1984-01-01
In the application of finite-difference methods to obtain numerical solutions of viscous compressible fluid flow about wing-fuselage bodies, it is advantageous to transform the governing equations to an idealized boundary-fitted coordinate system. The advantages are reduced computational complexity and added accuracy in the application of boundary conditions. The solution process requires that a grid be superimposed on the physical solution domain which corresponds to a uniform grid on a rectangular computational domain (uniform rectangular parallel-epiped). Grid generation is the determination of a one to one relationship between grid points in the physical domain and grid points in the computational domain. A technique for computing wing-fuselage surface grids using the Harris geometry and software for smooth-surface representation is described. Grid spacing control concepts which govern the relationship between the wing-fuselage surface and the computational grid are also presented.
Advanced Unstructured Grid Generation for Complex Aerodynamic Applications
NASA Technical Reports Server (NTRS)
Pirzadeh, Shahyar Z.
2008-01-01
A new approach for distribution of grid points on the surface and in the volume has been developed and implemented in the NASA unstructured grid generation code VGRID. In addition to the point and line sources of prior work, the new approach utilizes surface and volume sources for automatic curvature-based grid sizing and convenient point distribution in the volume. A new exponential growth function produces smoother and more efficient grids and provides superior control over distribution of grid points in the field. All types of sources support anisotropic grid stretching which not only improves the grid economy but also provides more accurate solutions for certain aerodynamic applications. The new approach does not require a three-dimensional background grid as in the previous methods. Instead, it makes use of an efficient bounding-box auxiliary medium for storing grid parameters defined by surface sources. The new approach is less memory-intensive and more efficient computationally. The grids generated with the new method either eliminate the need for adaptive grid refinement for certain class of problems or provide high quality initial grids that would enhance the performance of many adaptation methods.
NASA Technical Reports Server (NTRS)
Warsi, Saif A.
1989-01-01
A detailed operating manual is presented for a grid generating program that produces 3-D meshes for advanced turboprops. The code uses both algebraic and elliptic partial differential equation methods to generate single rotation and counterrotation, H or C type meshes for the z - r planes and H type for the z - theta planes. The code allows easy specification of geometrical constraints (such as blade angle, location of bounding surfaces, etc.), mesh control parameters (point distribution near blades and nacelle, number of grid points desired, etc.), and it has good runtime diagnostics. An overview is provided of the mesh generation procedure, sample input dataset with detailed explanation of all input, and example meshes.
MESH2D GRID GENERATOR DESIGN AND USE
Flach, G.; Smith, F.
2012-01-20
Mesh2d is a Fortran90 program designed to generate two-dimensional structured grids of the form [x(i),y(i,j)] where [x,y] are grid coordinates identified by indices (i,j). The x(i) coordinates alone can be used to specify a one-dimensional grid. Because the x-coordinates vary only with the i index, a two-dimensional grid is composed in part of straight vertical lines. However, the nominally horizontal y(i,j{sub 0}) coordinates along index i are permitted to undulate or otherwise vary. Mesh2d also assigns an integer material type to each grid cell, mtyp(i,j), in a user-specified manner. The complete grid is specified through three separate input files defining the x(i), y(i,j), and mtyp(i,j) variations. The overall mesh is constructed from grid zones that are typically then subdivided into a collection of smaller grid cells. The grid zones usually correspond to distinct materials or larger-scale geometric shapes. The structured grid zones are identified through uppercase indices (I,J). Subdivision of zonal regions into grid cells can be done uniformly, or nonuniformly using either a polynomial or geometric skewing algorithm. Grid cells may be concentrated backward, forward, or toward both ends. Figure 1 illustrates the above concepts in the context of a simple four zone grid.
Surface and Volume Grid Generation in Parametric Form
NASA Technical Reports Server (NTRS)
Yu, Tzuyi; Soni, Bharat K.; Benjamin, Ted; Williams, Robert
1996-01-01
The algorithm for surface modeling and volume grid generation using parametric Non-Uniform Rational B-splines (NURBS) geometric representation are presented. The enhanced re-parameterization algorithm which can yield a desired physical distribution on the curve, surface, and volume is also presented. This approach bridges the gap between computer aided design surface/volume definition and surface/volume grid generation.
Grid generation on trimmed Bezier and NURBS quilted surfaces
NASA Technical Reports Server (NTRS)
Woan, Chung-Jin; Clever, Willard C.; Tam, Clement K.
1995-01-01
This paper presents some recently added capabilities to RAGGS, Rockwell Automated Grid Generation System. Included are the trimmed surface handling and display capability and structures and unstructured grid generation on trimmed Bezier and NURBS (non-uniform rational B-spline surfaces) quilted surfaces. Samples are given to demonstrate the new capabilities.
S3D: An interactive surface grid generation tool
NASA Technical Reports Server (NTRS)
Luh, Raymond Ching-Chung; Pierce, Lawrence E.; Yip, David
1992-01-01
S3D, an interactive software tool for surface grid generation, is described. S3D provides the means with which a geometry definition based either on a discretized curve set or a rectangular set can be quickly processed towards the generation of a surface grid for computational fluid dynamics (CFD) applications. This is made possible as a result of implementing commonly encountered surface gridding tasks in an environment with a highly efficient and user friendly graphical interface. Some of the more advanced features of S3D include surface-surface intersections, optimized surface domain decomposition and recomposition, and automated propagation of edge distributions to surrounding grids.
TCGRID: A three dimensional C-grid generator for turbomachinery
NASA Technical Reports Server (NTRS)
Chima, Rodrick V.
1992-01-01
A fast 3-D grid code for turbomachinery was developed. The code, TCGRID (Turbomachinery C-GRID), can generate either C or H type grids for fairly arbitrary axial or radical turbomachinery geometries. The code also has limited blocked grid capability and can generate an axisymmetric H type grid upstream of the blade row or an O type grid within the tip clearance region. Hub and tip geometries are input as a simple list of pairs. All geometric data is handled using parametric splines so that geometries that turn 90 degrees can be handled without difficulty. Blade input is in standard MERIDL or Lewis compressor design code format. TCGRID adds leading and trailing edge circles to MERIDL geometries and intersects the blade with the hub and tip if necessary using a novel intersection algorithm. The procedure used to generate the grid is given. Output is in PLOT3D format, which can also be read by the RVC3D (Rotor Viscous Code 3-D) Navier-Stokes code for turbomachinery. Intermediate 2-D or 3-D grids useful for debug and other purposes can also be output using a convenient output flag. A grid generated figure is given.
Three-dimensional hybrid grid generation using advancing front techniques
NASA Technical Reports Server (NTRS)
Steinbrenner, John P.; Noack, Ralph W.
1995-01-01
A new 3-dimensional hybrid grid generation technique has been developed, based on ideas of advancing fronts for both structured and unstructured grids. In this approach, structured grids are first generate independently around individual components of the geometry. Fronts are initialized on these structure grids, and advanced outward so that new cells are extracted directly from the structured grids. Employing typical advancing front techniques, cells are rejected if they intersect the existing front or fail other criteria When no more viable structured cells exist further cells are advanced in an unstructured manner to close off the overall domain, resulting in a grid of 'hybrid' form. There are two primary advantages to the hybrid formulation. First, generating blocks with limited regard to topology eliminates the bottleneck encountered when a multiple block system is used to fully encapsulate a domain. Individual blocks may be generated free of external constraints, which will significantly reduce the generation time. Secondly, grid points near the body (presumably with high aspect ratio) will still maintain a structured (non-triangular or tetrahedral) character, thereby maximizing grid quality and solution accuracy near the surface.
Advanced Unstructured Grid Generation for Complex Aerodynamic Applications
NASA Technical Reports Server (NTRS)
Pirzadeh, Shahyar
2010-01-01
A new approach for distribution of grid points on the surface and in the volume has been developed. In addition to the point and line sources of prior work, the new approach utilizes surface and volume sources for automatic curvature-based grid sizing and convenient point distribution in the volume. A new exponential growth function produces smoother and more efficient grids and provides superior control over distribution of grid points in the field. All types of sources support anisotropic grid stretching which not only improves the grid economy but also provides more accurate solutions for certain aerodynamic applications. The new approach does not require a three-dimensional background grid as in the previous methods. Instead, it makes use of an efficient bounding-box auxiliary medium for storing grid parameters defined by surface sources. The new approach is less memory-intensive and more efficient computationally. The grids generated with the new method either eliminate the need for adaptive grid refinement for certain class of problems or provide high quality initial grids that would enhance the performance of many adaptation methods.
An interactive grid generator for TOUGH family code
Energy Science and Technology Software Center (ESTSC)
2004-01-09
WinGridder has been developed for designing, generating, and visualizing (at various spatial scales) numerical grids used in reservoir simulations and groundwater modeling studies. It can save mesh files for TOUGH family codes and output additional grid information for various purposes in either graphic format or plain text format, many important features, such as inclined faults and offset, layering structure, local refinements, and embedded engineering structures, can be represented in the grid. The main advantages ofmore » this grid-generation software are its user friendly graphical interfaces, flexible grid design capabilities, efficient grid generation, and powerful searching and post-processing capability, especially for large size grid (e.g., a grid of million grid cells). The main improvements of the version 2.0 are (1) to add a capability of handling a repository with multiple sub-regions and specified drifts, (2) to use an interpolation method, instead of picking the nearest point, in calculating the geological data from the given digital geological model, and (3) enhanced searching and other capability.« less
NASA Technical Reports Server (NTRS)
Choo, Yung K.; Soh, Woo-Yung; Yoon, Seokkwan
1989-01-01
A finite-volume lower-upper (LU) implicit scheme is used to simulate an inviscid flow in a turbine cascade. This approximate factorization scheme requires only the inversion of sparse lower and upper triangular matrices, which can be done efficiently without extensive storage. As an implicit scheme it allows a large time step to reach the steady state. An interactive grid generation program (TURBO), which is being developed, is used to generate grids. This program uses the control point form of algebraic grid generation which uses a sparse collection of control points from which the shape and position of coordinate curves can be adjusted. A distinct advantage of TURBO compared with other grid generation programs is that it allows the easy change of local mesh structure without affecting the grid outside the domain of dependence. Sample grids are generated by TURBO for a compressor rotor blade and a turbine cascade. The turbine cascade flow is simulated by using the LU implicit scheme on the grid generated by TURBO.
NASA Technical Reports Server (NTRS)
Choo, Yung K.; Soh, Woo-Yung; Yoon, Seokkwan
1989-01-01
A finite-volume lower-upper (LU) implicit scheme is used to simulate an inviscid flow in a tubine cascade. This approximate factorization scheme requires only the inversion of sparse lower and upper triangular matrices, which can be done efficiently without extensive storage. As an implicit scheme it allows a large time step to reach the steady state. An interactive grid generation program (TURBO), which is being developed, is used to generate grids. This program uses the control point form of algebraic grid generation which uses a sparse collection of control points from which the shape and position of coordinate curves can be adjusted. A distinct advantage of TURBO compared with other grid generation programs is that it allows the easy change of local mesh structure without affecting the grid outside the domain of independence. Sample grids are generated by TURBO for a compressor rotor blade and a turbine cascade. The turbine cascade flow is simulated by using the LU implicit scheme on the grid generated by TURBO.
A generalized scheme for three-dimensional hyperbolic grid generation
NASA Technical Reports Server (NTRS)
Chan, William M.; Steger, Joseph L.
1991-01-01
A hyperbolic grid generation scheme formulated from grid orthogonality and cell volume specification is generalized such that high quality three-dimensional grids can be obtained for a wide variety of geometries. The speed of the scheme is one to two orders of magnitude faster than typical elliptic grid generation methods. The robustness of the scheme is significantly enhanced by several new techniques. By using a spatially variable smoothing coefficient, orthogonality and smoothness of the grid are maintained around complex concave and convex surface topologies. A metric correction procedure is employed to guarantee that the grid marches out of a corner by bisecting the angles subtended by the neighboring points. Extra robustness at severe convex corners is achieved by special local treatments. Different extrapolation methods are used to provide smoothness at floating edges and axis regions. The versatility of the new hyperbolic grid generation scheme is demonstrated by three-dimensional grids generated for external components of the intergrated Space Shuttle vehicle and the SOFIA telescope.
Methods for prismatic/tetrahedral grid generation and adaptation
NASA Astrophysics Data System (ADS)
Kallinderis, Y.
1995-10-01
The present work involves generation of hybrid prismatic/tetrahedral grids for complex 3-D geometries including multi-body domains. The prisms cover the region close to each body's surface, while tetrahedra are created elsewhere. Two developments are presented for hybrid grid generation around complex 3-D geometries. The first is a new octree/advancing front type of method for generation of the tetrahedra of the hybrid mesh. The main feature of the present advancing front tetrahedra generator that is different from previous such methods is that it does not require the creation of a background mesh by the user for the determination of the grid-spacing and stretching parameters. These are determined via an automatically generated octree. The second development is a method for treating the narrow gaps in between different bodies in a multiply-connected domain. This method is applied to a two-element wing case. A High Speed Civil Transport (HSCT) type of aircraft geometry is considered. The generated hybrid grid required only 170 K tetrahedra instead of an estimated two million had a tetrahedral mesh been used in the prisms region as well. A solution adaptive scheme for viscous computations on hybrid grids is also presented. A hybrid grid adaptation scheme that employs both h-refinement and redistribution strategies is developed to provide optimum meshes for viscous flow computations. Grid refinement is a dual adaptation scheme that couples 3-D, isotropic division of tetrahedra and 2-D, directional division of prisms.
Best Practices in Overset Grid Generation
NASA Technical Reports Server (NTRS)
Gomez, Reynaldo J., III
2002-01-01
Accurate geometry + high quality grids are necessary for an accurate solution. Other requirements include a) Verified/validated solver with appropriate physics b) Convergence criteria consistent with application: 1) Aerodynamics - forces and moments; 2) Heat transfer - maximum and minimum heat transfer coefficients.
3D Structured Grid Generation Codes for Turbomachinery
NASA Technical Reports Server (NTRS)
Loellbach, James; Tsung, Fu-Lin
1999-01-01
This report describes the research tasks during the past year. The research was mainly in the area of computational grid generation in support of CFD analyses of turbomachinery components. In addition to the grid generation work, a numerical simulation was obtained for the flow through a centrifugal gas compressor using an unstructured Navier-Stokes solver. Other tasks involved many different turbomachinery component analyses. These analyses were performed for NASA projects or for industrial applications. The work includes both centrifugal and axial machines, single and multiple blade rows, and steady and unsteady analyses. Over the past five years, a set of structured grid generation codes were developed that allow grids to be obtained fairly quickly for the large majority of configurations we encounter. These codes do not comprise a generalized grid generation package; they are noninteractive codes specifically designed for turbomachinery blade row geometries. But because of this limited scope, the codes are small, fast, and portable, and they can be run in the batch mode on small workstations. During the past year, these programs were used to generate computational grids were modified for a wide variety of configurations. In particular, the codes or wrote supplementary codes to improve our grid generation capabilities for multiple blade row configurations. This involves generating separate grids for each blade row, and then making them match and overlap by a few grid points at their common interface so that fluid properties are communicated across the interface. Unsteady rotor/stator analyses were performed for an axial turbine, a centrifugal compressor, and a centrifugal pump. Steady-state single-blade-row analyses were made for a study of blade sweep in transonic compressors. There was also cooperation on the application of an unstructured Navier-Stokes solver for turbomachinery flow simulations. In particular, the unstructured solver was used to analyze the
Incompressible and anelastic flow simulations on numerically generated grids
NASA Technical Reports Server (NTRS)
Sharman, R. D.; Keller, T. L.; Wurtele, M. G.
1988-01-01
In the numerical simulation of incompressible and anelastic flows, it is necessary to solve an elliptic equation at each time step. When the boundaries of such flows are nonrectangular, it may be advantageous to solve the equations on a new, numerically generated coordinate grid, in which the property of orthogonality has been preserved. Flow equations in general curvilinear coordinates maintaining the conservative form are given for both anelastic models using the momentum equations, and for incompressible models, using the vorticity equation. The general problem of grid-generation in two dimensions is presented, and a quasi-conformal transformation technique is discussed in detail. Some examples of grids generated by this technique are exhibited. Three examples of the flow of a stratified fluid over obstacles are presented, in which the grid-generation permits some new results to be obtained.
Grid generation and inviscid flow computation about aircraft geometries
NASA Technical Reports Server (NTRS)
Smith, Robert E.
1989-01-01
Grid generation and Euler flow about fighter aircraft are described. A fighter aircraft geometry is specified by an area ruled fuselage with an internal duct, cranked delta wing or strake/wing combinations, canard and/or horizontal tail surfaces, and vertical tail surfaces. The initial step before grid generation and flow computation is the determination of a suitable grid topology. The external grid topology that has been applied is called a dual-block topology which is a patched C (exp 1) continuous multiple-block system where inner blocks cover the highly-swept part of a cranked wing or strake, rearward inner-part of the wing, and tail components. Outer-blocks cover the remainder of the fuselage, outer-part of the wing, canards and extend to the far field boundaries. The grid generation is based on transfinite interpolation with Lagrangian blending functions. This procedure has been applied to the Langley experimental fighter configuration and a modified F-18 configuration. Supersonic flow between Mach 1.3 and 2.5 and angles of attack between 0 degrees and 10 degrees have been computed with associated Euler solvers based on the finite-volume approach. When coupling geometric details such as boundary layer diverter regions, duct regions with inlets and outlets, or slots with the general external grid, imposing C (exp 1) continuity can be extremely tedious. The approach taken here is to patch blocks together at common interfaces where there is no grid continuity, but enforce conservation in the finite-volume solution. The key to this technique is how to obtain the information required for a conservative interface. The Ramshaw technique which automates the computation of proportional areas of two overlapping grids on a planar surface and is suitable for coding was used. Researchers generated internal duct grids for the Langley experimental fighter configuration independent of the external grid topology, with a conservative interface at the inlet and outlet.
Surface modeling and grid generation for aeropropulsion CFD
NASA Technical Reports Server (NTRS)
Choo, Yung K.; Slater, John W.; Loellbach, James; Lee, Jinho
1995-01-01
The efforts in geometry modeling and grid generation at the NASA Lewis Research Center, as applied to the computational fluid dynamic (CFD) analysis of aeropropulsion systems, are presented. The efforts are mainly characterized by a focus on the analysis of components of an aeropropulsion system, which involve turbulent viscous flow with heat transfer and chemistry. Thus, this discussion will follow that characterization and will sequence through the components of typical propulsion systems consisting of inlets, compressors, combustors, turbines, and nozzles. For each component, some applications of CFD analysis will be presented to show how CFD is used to compute the desired performance information, how geometry modeling and grid generation are performed, and what issues have developed related to geometry modeling and grid generation. The discussion will illustrate the following needs related to geometry modeling and grid generation as observed in aeropropulsion analysis: (1) accurate and efficient resolution of turbulent viscous and chemically-reacting flowfields; (2) easy-to-use interfaces with CAD data for automated grid generation about complex geometries; and (3) automated batch grid generation software for use with design and optimization software.
Some effects of vortex shedding in grid-generated turbulence
NASA Astrophysics Data System (ADS)
Melina, Gianfrancesco; Bruce, Paul J. K.; Vassilicos, John Christos
2015-11-01
We perform hot-wire measurements in a wind tunnel downstream of different types of turbulence-generating grids: a regular grid (RG60), a fractal square grid (FSG17) and a single square grid (SSG). We characterize the flow highlighting similarities and differences between the grids and between the production and the decay regions of turbulence. We focus on the effects of vortex shedding from the bars of the grids. For this purpose we design a novel 3D configuration formed by the SSG and a set of four splitter plates detached from the grid. We show that, by placing the splitter plates, the peak of turbulence intensity on the centerline is reduced and its location is moved downstream. We compare data from the different turbulence generators and find that a reduction of vortex shedding energy correlates with an increase in the magnitudes of the skewness and flatness of the turbulent velocity fluctuations in the production region. The authors acknowledge support form the EU through the FP7 Marie Curie MULTISOLVE project (grant agreement No. 317269).
Marshall Space Flight Center surface modeling and grid generation applications
NASA Technical Reports Server (NTRS)
Williams, Robert W.; Benjamin, Theodore G.; Cornelison, Joni W.
1995-01-01
The Solid Rocket Motors (SRM) used by NASA to propel the Space Shuttle employ gimballing nozzles as a means for vehicular guidance during launch and ascent. Gimballing a nozzle renders the pressure field of the exhaust gases nonaxisymmetric. This has two effects: (1) it exerts a torque and side load on the nozzle; and (2) the exhaust gases flow circumferentially in the aft-dome region, thermally loading the flexible boot, case-to-nozzle joint, and casing insulation. The use of CFD models to simulate such flows is imperative in order to assess SRM design. The grids for these problems were constructed by obtaining information from drawings and tabulated coordinates. The 2D axisymmetric grids were designed and generated using the EZ-Surf and GEN2D surface and grid generation codes. These 2D grids were solved using codes such as FDNS, GASP, and MINT. These axisymmetric grids were rotated around the center-line to form 3D nongimballed grids. These were then gimballed around the pivot point and the gaps or overlaps resurfaced to obtain the final domains, which contained approximately 366,000 grid points. The 2D solutions were then rotated and manipulated as appropriate for geometry and used as initial guesses in the final solution. The analyses were used in answering questions about flight criteria.
Marshall Space Flight Center surface modeling and grid generation applications
NASA Astrophysics Data System (ADS)
Williams, Robert W.; Benjamin, Theodore G.; Cornelison, Joni W.
1995-03-01
The Solid Rocket Motors (SRM) used by NASA to propel the Space Shuttle employ gimballing nozzles as a means for vehicular guidance during launch and ascent. Gimballing a nozzle renders the pressure field of the exhaust gases nonaxisymmetric. This has two effects: (1) it exerts a torque and side load on the nozzle; and (2) the exhaust gases flow circumferentially in the aft-dome region, thermally loading the flexible boot, case-to-nozzle joint, and casing insulation. The use of CFD models to simulate such flows is imperative in order to assess SRM design. The grids for these problems were constructed by obtaining information from drawings and tabulated coordinates. The 2D axisymmetric grids were designed and generated using the EZ-Surf and GEN2D surface and grid generation codes. These 2D grids were solved using codes such as FDNS, GASP, and MINT. These axisymmetric grids were rotated around the center-line to form 3D nongimballed grids. These were then gimballed around the pivot point and the gaps or overlaps resurfaced to obtain the final domains, which contained approximately 366,000 grid points. The 2D solutions were then rotated and manipulated as appropriate for geometry and used as initial guesses in the final solution. The analyses were used in answering questions about flight criteria.
Ray tracing for point distribution in unstructured grid generation
Khamayseh, A.; Ortega, F.; Trease, H.
1995-12-31
We present a procedure by which grid points are generated on surfaces or within three-dimensional volumes to produce high quality unstructed grids for complex geometries. The virtue of this method is based on ray-tracing approach for curved polyhedra whose faces may lie on natural quadrics (planes, cylinders, cones, or spheres) or triangular faceted surfaces. We also present an efficient point location algorithm for identifying points relative to various regions with classification of inside/on/outside.
Triangle geometry processing for surface modeling and cartesian grid generation
Aftosmis, Michael J [San Mateo, CA; Melton, John E [Hollister, CA; Berger, Marsha J [New York, NY
2002-09-03
Cartesian mesh generation is accomplished for component based geometries, by intersecting components subject to mesh generation to extract wetted surfaces with a geometry engine using adaptive precision arithmetic in a system which automatically breaks ties with respect to geometric degeneracies. During volume mesh generation, intersected surface triangulations are received to enable mesh generation with cell division of an initially coarse grid. The hexagonal cells are resolved, preserving the ability to directionally divide cells which are locally well aligned.
Triangle Geometry Processing for Surface Modeling and Cartesian Grid Generation
NASA Technical Reports Server (NTRS)
Aftosmis, Michael J. (Inventor); Melton, John E. (Inventor); Berger, Marsha J. (Inventor)
2002-01-01
Cartesian mesh generation is accomplished for component based geometries, by intersecting components subject to mesh generation to extract wetted surfaces with a geometry engine using adaptive precision arithmetic in a system which automatically breaks ties with respect to geometric degeneracies. During volume mesh generation, intersected surface triangulations are received to enable mesh generation with cell division of an initially coarse grid. The hexagonal cells are resolved, preserving the ability to directionally divide cells which are locally well aligned.
Geometry definition and grid generation for a complete fighter aircraft
NASA Technical Reports Server (NTRS)
Edwards, T. A.
1986-01-01
Recent advances in computing power and numerical solution procedures have enabled computational fluid dynamicists to attempt increasingly difficult problems. In particular, efforts are focusing on computations of complex three-dimensional flow fields about realistic aerodynamic bodies. To perform such computations, a very accurate and detailed description of the surface geometry must be provided, and a three-dimensional grid must be generated in the space around the body. The geometry must be supplied in a format compatible with the grid generation requirements, and must be verified to be free of inconsistencies. This paper presents a procedure for performing the geometry definition of a fighter aircraft that makes use of a commercial computer-aided design/computer-aided manufacturing system. Furthermore, visual representations of the geometry are generated using a computer graphics system for verification of the body definition. Finally, the three-dimensional grids for fighter-like aircraft are generated by means of an efficient new parabolic grid generation method. This method exhibits good control of grid quality.
A Richer Understanding of Algebra
ERIC Educational Resources Information Center
Foy, Michelle
2008-01-01
Algebra is one of those hard-to-teach topics where pupils seem to struggle to see it as more than a set of rules to learn, but this author recently used the software "Grid Algebra" from ATM, which engaged her Year 7 pupils in exploring algebraic concepts for themselves. "Grid Algebra" allows pupils to experience number, pre-algebra, and algebra…
Grid generation and flow solution method for Euler equations on unstructured grids
NASA Technical Reports Server (NTRS)
Anderson, W. Kyle
1992-01-01
A grid generation and flow solution algorithm for the Euler equations on unstructured grids is presented. The grid generation scheme, which uses Delaunay triangulation, generates the field points for the mesh based on cell aspect ratios and allows clustering of grid points near solid surfaces. The flow solution method is an implicit algorithm in which the linear set of equations arising at each time step is solved using a Gauss-Seidel procedure that is completely vectorizable. Also, a study is conducted to examine the number of subiterations required for good convergence of the overall algorithm. Grid generation results are shown in two dimensions for an NACA 0012 airfoil as well as a two element configuration. Flow solution results are shown for a two dimensional flow over the NACA 0012 airfoil and for a two element configuration in which the solution was obtained through an adaptation procedure and compared with an exact solution. Preliminary three dimensional results also are shown in which the subsonic flow over a business jet is computed.
Variational method for adaptive grid generation
Brackbill, J.U.
1983-01-01
A variational method for generating adaptive meshes is described. Functionals measuring smoothness, skewness, orientation, and the Jacobian are minimized to generate a mapping from a rectilinear domain in natural coordinate to an arbitrary domain in physical coordinates. From the mapping, a mesh is easily constructed. In using the method to adaptively zone computational problems, as few as one third the number of mesh points are required in each coordinate direction compared with a uniformly zoned mesh.
NASA Technical Reports Server (NTRS)
Smith, R. E.
1981-01-01
A grid generation technique called the two boundary technique is developed and applied for the solution of the three dimensional Navier-Stokes equations. The Navier-Stokes equations are transformed from a cartesian coordinate system to a computational coordinate system, and the grid generation technique provides the Jacobian matrix describing the transformation. The two boundary technique is based on algebraically defining two distinct boundaries of a flow domain and the distribution of the grid is achieved by applying functions to the uniform computational grid which redistribute the computational independent variables and consequently concentrate or disperse the grid points in the physical domain. The Navier-Stokes equations are solved using a MacCormack time-split technique. Grids and supersonic laminar flow solutions are obtained for a family of three dimensional corners and two spike-nosed bodies.
NASA Technical Reports Server (NTRS)
Dulikravich, D. S.
1982-01-01
A fast computer program, GRID3C, was developed for accurately generating periodic, boundary conforming, three dimensional, consecutively refined computational grids applicable to realistic axial turbomachinery geometries. The method is based on using two functions to generate two dimensional grids on a number of coaxial axisymmetric surfaces positioned between the centerbody and the outer radial boundary. These boundary fitted grids are of the C type and are characterized by quasi-orthogonality and geometric periodicity. The built in nonorthogonal coordinate stretchings and shearings cause the grid clustering in the regions of interest. The stretching parameters are part of the input to GRID3C. In its present version GRID3C can generate and store a maximum of four consecutively refined three dimensional grids. The output grid coordinates can be calculated either in the Cartesian or in the cylindrical coordinate system.
Enhanced Product Generation at NASA Data Centers Through Grid Technology
NASA Technical Reports Server (NTRS)
Barkstrom, Bruce R.; Hinke, Thomas H.; Gavali, Shradha; Seufzer, William J.
2003-01-01
This paper describes how grid technology can support the ability of NASA data centers to provide customized data products. A combination of grid technology and commodity processors are proposed to provide the bandwidth necessary to perform customized processing of data, with customized data subsetting providing the initial example. This customized subsetting engine can be used to support a new type of subsetting, called phenomena-based subsetting, where data is subsetted based on its association with some phenomena, such as mesoscale convective systems or hurricanes. This concept is expanded to allow the phenomena to be detected in one type of data, with the subsetting requirements transmitted to the subsetting engine to subset a different type of data. The subsetting requirements are generated by a data mining system and transmitted to the subsetter in the form of an XML feature index that describes the spatial and temporal extent of the phenomena. For this work, a grid-based mining system called the Grid Miner is used to identify the phenomena and generate the feature index. This paper discusses the value of grid technology in facilitating the development of a high performance customized product processing and the coupling of a grid mining system to support phenomena-based subsetting.
Mixed Element Type Unstructured Grid Generation for Viscous Flow Applications
NASA Technical Reports Server (NTRS)
Marcum, David L.; Gaither, J. Adam
2000-01-01
A procedure is presented for efficient generation of high-quality unstructured grids suitable for CFD simulation of high Reynolds number viscous flow fields. Layers of anisotropic elements are generated by advancing along prescribed normals from solid boundaries. The points are generated such that either pentahedral or tetrahedral elements with an implied connectivity can be be directly recovered. As points are generated they are temporarily attached to a volume triangulation of the boundary points. This triangulation allows efficient local search algorithms to be used when checking merging layers, The existing advancing-front/local-reconnection procedure is used to generate isotropic elements outside of the anisotropic region. Results are presented for a variety of applications. The results demonstrate that high-quality anisotropic unstructured grids can be efficiently and consistently generated for complex configurations.
Recent enhancements to the GRIDGEN structured grid generation system
NASA Technical Reports Server (NTRS)
Steinbrenner, John P.; Chawner, John R.
1992-01-01
Significant enhancements are being implemented into the GRIDGEN3D, multiple block, structured grid generation software. Automatic, point-to-point, interblock connectivity will be possible through the addition of the domain entity to GRIDBLOCK's block construction process. Also, the unification of GRIDGEN2D and GRIDBLOCK has begun with the addition of edge grid point distribution capability to GRIDBLOCK. The geometric accuracy of surface grids and the ease with which databases may be obtained is being improved by adding support for standard computer-aided design formats (e.g., PATRAN Neutral and IGES files). Finally, volume grid quality was improved through addition of new SOR algorithm features and the new hybrid control function type to GRIDGEN3D.
NASA Astrophysics Data System (ADS)
Schertzer, Daniel; Tchiguirinskaia, Ioulia
2014-05-01
A complex key feature of turbulence is that the velocity is a vector field, whereas intermittency, another key feature, has been mostly understood, analysed and simulated in scalar frameworks. This gap has prevented many developments. Some years ago, the general framework of 'Lie cascades' was introduced (Schertzer and Lovejoy, 1993) to deal with both features by considering cascades generated by stochastic Lie algebra. However, the theoretical efforts were mostly concentrated on the decomposition of this algebra into its radical and a semi-simple algebra and faced too many degrees of freedom. In this communication, we show that the class of Clifford algebra is already wide enough, very convenient and physically meaningful to understand, analyse and simulate intermittent vector fields.
Grid generation and surface modeling for CFD
NASA Technical Reports Server (NTRS)
Connell, Stuart D.; Sober, Janet S.; Lamson, Scott H.
1995-01-01
When computing the flow around complex three dimensional configurations, the generation of the mesh is the most time consuming part of any calculation. With some meshing technologies this can take of the order of a man month or more. The requirement for a number of design iterations coupled with ever decreasing time allocated for design leads to the need for a significant acceleration of this process. Of the two competing approaches, block-structured and unstructured, only the unstructured approach will allow fully automatic mesh generation directly from a CAD model. Using this approach coupled with the techniques described in this paper, it is possible to reduce the mesh generation time from man months to a few hours on a workstation. The desire to closely couple a CFD code with a design or optimization algorithm requires that the changes to the geometry be performed quickly and in a smooth manner. This need for smoothness necessitates the use of Bezier polynomials in place of the more usual NURBS or cubic splines. A two dimensional Bezier polynomial based design system is described.
NASA Technical Reports Server (NTRS)
Houston, Johnny L.
1989-01-01
Program EAGLE (Eglin Arbitrary Geometry Implicit Euler) Numerical Grid Generation System is a composite (multi-block) algebraic or elliptic grid generation system designed to discretize the domain in and/or around any arbitrarily shaped three dimensional regions. This system combines a boundary conforming surface generation scheme and includes plotting routines designed to take full advantage of the DISSPLA Graphics Package (Version 9.0). Program EAGLE is written to compile and execute efficiently on any Cray machine with or without solid state disk (SSD) devices. Also, the code uses namelist inputs which are supported by all Cray machines using the FORTRAN compiler CFT77. The namelist inputs makes it easier for the user to understand the inputs and operation of Program EAGLE. EAGLE's numerical grid generator is constructed in the following form: main program, EGG (executive routine); subroutine SURFAC (surface generation routine); subroutine GRID (grid generation routine); and subroutine GRDPLOT (grid plotting routines). The EAGLE code was modified to use on the NASA-LaRC SNS computer (Cray 2S) system. During the modification a conversion program was developed for the output data of EAGLE's subroutine GRID to permit the data to be graphically displayed by IRIS workstations, using Plot3D. The code of program EAGLE was modified to make operational subroutine GRDPLOT (using DI-3000 Graphics Software Packages) on the NASA-LaRC SNS Computer System. How to implement graphically, the output data of subroutine GRID was determined on any NASA-LaRC graphics terminal that has access to the SNS Computer System DI-300 Graphics Software Packages. A Quick Reference User Guide was developed for the use of program EAGLE on the NASA-LaRC SNS Computer System. One or more application program(s) was illustrated using program EAGLE on the NASA LaRC SNS Computer System, with emphasis on graphics illustrations.
A grid generation and flow solution method for the Euler equations on unstructured grids
NASA Technical Reports Server (NTRS)
Anderson, W. Kyle
1994-01-01
A grid generation and flow solution algorithm for the Euler equations on unstructured grids is presented. The grid generation scheme utilizes Delaunay triangulation and self-generates the field points for the mesh based on cell aspect ratios and allows for clustering near solid surfaces. The flow solution method is an implicit algorithm in which the linear set of equations arising at each time step is solved using a Gauss Seidel procedure which is completely vectorizable. In addition, a study is conducted to examine the number of subiterations required for good convergence of the overall algorithm. Grid generation results are shown in two dimensions for a National Advisory Committee for Aeronautics (NACA) 0012 airfoil as well as a two-element configuration. Flow solution results are shown for two-dimensional flow over the NACA 0012 airfoil and for a two-element configuration in which the solution has been obtained through an adaptation procedure and compared to an exact solution. Preliminary three-dimensional results are also shown in which subsonic flow over a business jet is computed.
A grid generation and flow solution method for the Euler equations on unstructured grids
Anderson, W.K. )
1994-01-01
A grid generation and flow solution algorithm for the Euler equations on unstructured grids is presented. The grid generation scheme utilizes Delaunay triangulation and self-generates the field points for the mesh based on cell aspect ratios and allows for clustering near solid surfaces. The flow solution method is an implicit algorithm in which the linear set or equations arising at each time step is solved using a Gauss Seidel procedure which is completely vectorizable. In addition, a study is conducted to examine the number of subiterations required for good convergence of the overall algorithm. Grid generation results are shown in two dimensions for a NACA 0012 airfoil as well as two-element configuration. Flow solution results are shown for two-dimensional flow over the NACA 0012 airfoil and for a two-element configuration in which the solution has been obtained through an adaptation procedure and compared to an exact solution. Preliminary three-dimensional results are also shown in which subsonic flow over a business jet is computed. 31 refs. 30 figs.
Quantum entanglement in states generated by bilocal group algebras
Hamma, Alioscia; Ionicioiu, Radu; Zanardi, Paolo
2005-07-15
Given a finite group G with a bilocal representation, we investigate the bipartite entanglement in the state constructed from the group algebra of G acting on a separable reference state. We find an upper bound for the von Neumann entropy for a bipartition (A,B) of a quantum system and conditions to saturate it. We show that these states can be interpreted as ground states of generic Hamiltonians or as the physical states in a quantum gauge theory and that under specific conditions their geometric entropy satisfies the entropic area law. If G is a group of spin flips acting on a set of qubits, these states are locally equivalent to 2-colorable (i.e., bipartite) graph states and they include Greenberger-Horne-Zeilinger, cluster states, etc. Examples include an application to qudits and a calculation of the n-tangle for 2-colorable graph states.
Feynman graph generation and calculations in the Hopf algebra of Feynman graphs
NASA Astrophysics Data System (ADS)
Borinsky, Michael
2014-12-01
Two programs for the computation of perturbative expansions of quantum field theory amplitudes are provided. feyngen can be used to generate Feynman graphs for Yang-Mills, QED and φk theories. Using dedicated graph theoretic tools feyngen can generate graphs of comparatively high loop orders. feyncop implements the Hopf algebra of those Feynman graphs which incorporates the renormalization procedure necessary to calculate finite results in perturbation theory of the underlying quantum field theory. feyngen is validated by comparison to explicit calculations of zero dimensional quantum field theories and feyncop is validated using a combinatorial identity on the Hopf algebra of graphs.
GridMan: A grid manipulation system
NASA Technical Reports Server (NTRS)
Eiseman, Peter R.; Wang, Zhu
1992-01-01
GridMan is an interactive grid manipulation system. It operates on grids to produce new grids which conform to user demands. The input grids are not constrained to come from any particular source. They may be generated by algebraic methods, elliptic methods, hyperbolic methods, parabolic methods, or some combination of methods. The methods are included in the various available structured grid generation codes. These codes perform the basic assembly function for the various elements of the initial grid. For block structured grids, the assembly can be quite complex due to a large number of clock corners, edges, and faces for which various connections and orientations must be properly identified. The grid generation codes are distinguished among themselves by their balance between interactive and automatic actions and by their modest variations in control. The basic form of GridMan provides a much more substantial level of grid control and will take its input from any of the structured grid generation codes. The communication link to the outside codes is a data file which contains the grid or section of grid.
Surface Modeling and Grid Generation of Orbital Sciences X34 Vehicle. Phase 1
NASA Technical Reports Server (NTRS)
Alter, Stephen J.
1997-01-01
The surface modeling and grid generation requirements, motivations, and methods used to develop Computational Fluid Dynamic volume grids for the X34-Phase 1 are presented. The requirements set forth by the Aerothermodynamics Branch at the NASA Langley Research Center serve as the basis for the final techniques used in the construction of all volume grids, including grids for parametric studies of the X34. The Integrated Computer Engineering and Manufacturing code for Computational Fluid Dynamics (ICEM/CFD), the Grid Generation code (GRIDGEN), the Three-Dimensional Multi-block Advanced Grid Generation System (3DMAGGS) code, and Volume Grid Manipulator (VGM) code are used to enable the necessary surface modeling, surface grid generation, volume grid generation, and grid alterations, respectively. All volume grids generated for the X34, as outlined in this paper, were used for CFD simulations within the Aerothermodynamics Branch.
A method for generating volumetric fault zone grids for pillar gridded reservoir models
NASA Astrophysics Data System (ADS)
Qu, Dongfang; Røe, Per; Tveranger, Jan
2015-08-01
The internal structure and petrophysical property distribution of fault zones are commonly exceedingly complex compared to the surrounding host rock from which they are derived. This in turn produces highly complex fluid flow patterns which affect petroleum migration and trapping as well as reservoir behavior during production and injection. Detailed rendering and forecasting of fluid flow inside fault zones require high-resolution, explicit models of fault zone structure and properties. A fundamental requirement for achieving this is the ability to create volumetric grids in which modeling of fault zone structures and properties can be performed. Answering this need, a method for generating volumetric fault zone grids which can be seamlessly integrated into existing standard reservoir modeling tools is presented. The algorithm has been tested on a wide range of fault configurations of varying complexity, providing flexible modeling grids which in turn can be populated with fault zone structures and properties.
Automatic code generation in SPARK: Applications of computer algebra and compiler-compilers
Nataf, J.M.; Winkelmann, F.
1992-09-01
We show how computer algebra and compiler-compilers are used for automatic code generation in the Simulation Problem Analysis and Research Kernel (SPARK), an object oriented environment for modeling complex physical systems that can be described by differential-algebraic equations. After a brief overview of SPARK, we describe the use of computer algebra in SPARK's symbolic interface, which generates solution code for equations that are entered in symbolic form. We also describe how the Lex/Yacc compiler-compiler is used to achieve important extensions to the SPARK simulation language, including parametrized macro objects and steady-state resetting of a dynamic simulation. The application of these methods to solving the partial differential equations for two-dimensional heat flow is illustrated.
Automatic code generation in SPARK: Applications of computer algebra and compiler-compilers
Nataf, J.M.; Winkelmann, F.
1992-09-01
We show how computer algebra and compiler-compilers are used for automatic code generation in the Simulation Problem Analysis and Research Kernel (SPARK), an object oriented environment for modeling complex physical systems that can be described by differential-algebraic equations. After a brief overview of SPARK, we describe the use of computer algebra in SPARK`s symbolic interface, which generates solution code for equations that are entered in symbolic form. We also describe how the Lex/Yacc compiler-compiler is used to achieve important extensions to the SPARK simulation language, including parametrized macro objects and steady-state resetting of a dynamic simulation. The application of these methods to solving the partial differential equations for two-dimensional heat flow is illustrated.
A novel hyperbolic grid generation procedure with inherent adaptive dissipation
Tai, C.H.; Yin, S.L.; Soong, C.Y.
1995-01-01
This paper reports a novel hyperbolic grid-generation with an inherent adaptive dissipation (HGAD), which is capable of improving the oscillation and overlapping of grid lines. In the present work upwinding differencing is applied to discretize the hyperbolic system and, thereby, to develop the adaptive dissipation coefficient. Complex configurations with the features of geometric discontinuity, exceptional concavity and convexity are used as the test cases for comparison of the present HGAD procedure with the conventional hyerbolic and elliptic ones. The results reveal that the HGAD method is superior in orthogonality and smoothness of the grid system. In addition, the computational efficiency of the flow solver may be improved by using the present HGAD procedure. 15 refs., 8 figs.
On Generating Discrete Integrable Systems via Lie Algebras and Commutator Equations
NASA Astrophysics Data System (ADS)
Zhang, Yu-Feng; Honwah, Tam
2016-03-01
In the paper, we introduce the Lie algebras and the commutator equations to rewrite the Tu-d scheme for generating discrete integrable systems regularly. By the approach the various loop algebras of the Lie algebra A1 are defined so that the well-known Toda hierarchy and a novel discrete integrable system are obtained, respectively. A reduction of the later hierarchy is just right the famous Ablowitz-Ladik hierarchy. Finally, via two different enlarging Lie algebras of the Lie algebra A1, we derive two resulting differential-difference integrable couplings of the Toda hierarchy, of course, they are all various discrete expanding integrable models of the Toda hierarchy. When the introduced spectral matrices are higher degrees, the way presented in the paper is more convenient to generate discrete integrable equations than the Tu-d scheme by using the software Maple. Supported by the National Natural Science Foundation of China under Grant No. 11371361, the Innovation Team of Jiangsu Province hosted by China University of Mining and Technology (2014), and Hong Kong Research Grant Council under Grant No. HKBU202512, as well as the Natural Science Foundation of Shandong Province under Grant No. ZR2013AL016
On Generating Discrete Integrable Systems via Lie Algebras and Commutator Equations
NASA Astrophysics Data System (ADS)
Zhang, Yu-Feng; Tam, Honwah
2016-03-01
In the paper, we introduce the Lie algebras and the commutator equations to rewrite the Tu-d scheme for generating discrete integrable systems regularly. By the approach the various loop algebras of the Lie algebra A1 are defined so that the well-known Toda hierarchy and a novel discrete integrable system are obtained, respectively. A reduction of the later hierarchy is just right the famous Ablowitz–Ladik hierarchy. Finally, via two different enlarging Lie algebras of the Lie algebra A1, we derive two resulting differential-difference integrable couplings of the Toda hierarchy, of course, they are all various discrete expanding integrable models of the Toda hierarchy. When the introduced spectral matrices are higher degrees, the way presented in the paper is more convenient to generate discrete integrable equations than the Tu-d scheme by using the software Maple. Supported by the National Natural Science Foundation of China under Grant No. 11371361, the Innovation Team of Jiangsu Province hosted by China University of Mining and Technology (2014), and Hong Kong Research Grant Council under Grant No. HKBU202512, as well as the Natural Science Foundation of Shandong Province under Grant No. ZR2013AL016
Grid generation about complex three-dimensional aircraft configurations
NASA Technical Reports Server (NTRS)
Klopfer, Goetz H.
1991-01-01
The problem of obtaining three dimensional grids with sufficient resolution to resolve all the flow or other physical features of interest is addressed. The generation of a computational grid involves a series of compromises to resolve several conflicting requirements. On one hand, one would like the grid to be fine enough and not too skewed to reduce the numerical errors and to adequately resolve the pertinent physical features of the flow field about the aircraft. On the other hand, the capabilities of present or even future supercomputers are finite and the number of mesh points must be limited to a reasonable number: one which is usually much less than desired for numerical accuracy. One technique to overcome this limitation is the 'zonal' grid approach. In this method, the overall field is subdivided into smaller zones or blocks in each of which an independent grid is generated with enough grid density to resolve the flow features in that zone. The zonal boundaries or interfaces require special boundary conditions such that the conservation properties of the governing equations are observed. Much work was done in 3-D zonal approaches with nonconservative zonal interfaces. A 3-D zonal conservative interfacing method that is efficient and easy to implement was developed during the past year. During the course of the work, it became apparent that it would be much more feasible to do the conservative interfacing with cell-centered finite volume codes instead of the originally planned finite difference codes. Accordingly, the CNS code was converted to finite volume form. This new version of the code is named CNSFV. The original multi-zonal interfacing capability of the CNS code was enhanced by generalizing the procedure to allow for completely arbitrarily shaped zones with no mesh continuity between the zones. While this zoning capability works well for most flow situations, it is, however, still nonconservative. The conservative interface algorithm was also
Grid Generation Issues and CFD Simulation Accuracy for the X33 Aerothermal Simulations
NASA Technical Reports Server (NTRS)
Polsky, Susan; Papadopoulos, Periklis; Davies, Carol; Loomis, Mark; Prabhu, Dinesh; Langhoff, Stephen R. (Technical Monitor)
1997-01-01
Grid generation issues relating to the simulation of the X33 aerothermal environment using the GASP code are explored. Required grid densities and normal grid stretching are discussed with regards to predicting the fluid dynamic and heating environments with the desired accuracy. The generation of volume grids is explored and includes discussions of structured grid generation packages such as GRIDGEN, GRIDPRO and HYPGEN. Volume grid manipulation techniques for obtaining desired outer boundary and grid clustering using the OUTBOUND code are examined. The generation of the surface grid with the required surface grid with the required surface grid topology is also discussed. Utilizing grids without singular axes is explored as a method of avoiding numerical difficulties at the singular line.
Algebras Generated by Geometric Scalar Forms and their Applications in Physics and Social Sciences
Keller, Jaime
2008-09-17
The present paper analyzes the consequences of defining that the geometric scalar form is not necessarily quadratic, but in general K-atic, that is obtained from the K{sup th} power of the linear form, requiring {l_brace}e{sub i};i = 1,...,N;(e{sub i}){sup K} = 1{r_brace} and d-vector {sigma}{sub i}x{sub i}e{sub i}. We consider the algebras which are thus generated, for positive integer K, a generalization of the geometric algebras we know under the names of Clifford or Grassmann algebras. We then obtain a set of geometric K-algebras. We also consider the generalization of special functions of geometry which corresponds to the K-order scalar forms (as trigonometric functions and other related geometric functions which are based on the use of quadratic forms). We present an overview of the use of quadratic forms in physics as in our general theory, we have called START. And, in order to give an introduction to the use of the more general K-algebras and to the possible application to sciences other than physics, the application to social sciences is considered.For the applications to physics we show that quadratic spaces are a fundamental clue to understand the structure of theoretical physics (see, for example, Keller in ICNAAM 2005 and 2006)
Vortex shedding effects in grid-generated turbulence
NASA Astrophysics Data System (ADS)
Melina, G.; Bruce, P. J. K.; Vassilicos, J. C.
2016-08-01
The flow on the centerline of grid-generated turbulence is characterized via hot-wire anemometry for three grids with different geometry: a regular grid (RG60), a fractal grid (FSG17), and a single-square grid (SSG). Due to a higher value of the thickness t0 of its bars, SSG produces greater values of turbulence intensity Tu than FSG17, despite SSG having a smaller blockage ratio. However, the higher Tu for SSG is mainly due to a more pronounced vortex shedding contribution. The effects of vortex shedding suppression along the streamwise direction x are studied by testing a three-dimensional configuration, formed by SSG and a set of four splitter plates detached from the grid (SSG+SP). When vortex shedding is damped, the centerline location of the peak of turbulence intensity xpeak moves downstream and Tu considerably decreases in the production region. For FSG17 the vortex shedding is less intense and it disappears more quickly, in terms of x /xpeak , when compared to all the other configurations. When vortex shedding is attenuated, the integral length scale Lu grows more slowly in the streamwise direction, this being verified both for FSG17 and for SSG+SP. In the production region, there is a correlation between the vortex shedding energy and the skewness and the flatness of the velocity fluctuations. When vortex shedding is not significant, the skewness is highly negative and the flatness is much larger than 3. On the opposite side, when vortex shedding is prominent, the non-Gaussian behavior of the velocity fluctuations becomes masked.
Hydrogen ionic plasma generated using Al plasma grid
NASA Astrophysics Data System (ADS)
Oohara, W.; Anegawa, N.; Egawa, M.; Kawata, K.; Kamikawa, T.
2016-08-01
Negative hydrogen ions are produced in the apertures of a plasma grid made of aluminum under the irradiation of positive ions, generating an ionic plasma consisting of positive and negative ions. The saturation current ratio obtained using a Langmuir probe reflects the existence ratio of electrons and is found to increase in connection with the diffusion of the ionic plasma. The local increment of the current ratio suggests the collapse of negative ions and the replacement of detached electrons.
A finite volume method for numerical grid generation
NASA Astrophysics Data System (ADS)
Beale, S. B.
1999-07-01
A novel method to generate body-fitted grids based on the direct solution for three scalar functions is derived. The solution for scalar variables , and is obtained with a conventional finite volume method based on a physical space formulation. The grid is adapted or re-zoned to eliminate the residual error between the current solution and the desired solution, by means of an implicit grid-correction procedure. The scalar variables are re-mapped and the process is reiterated until convergence is obtained. Calculations are performed for a variety of problems by assuming combined Dirichlet-Neumann and pure Dirichlet boundary conditions involving the use of transcendental control functions, as well as functions designed to effect grid control automatically on the basis of boundary values. The use of dimensional analysis to build stable exponential functions and other control functions is demonstrated. Automatic procedures are implemented: one based on a finite difference approximation to the Cristoffel terms assuming local-boundary orthogonality, and another designed to procure boundary orthogonality. The performance of the new scheme is shown to be comparable with that of conventional inverse methods when calculations are performed on benchmark problems through the application of point-by-point and whole-field solution schemes. Advantages and disadvantages of the present method are critically appraised. Copyright
Multilevel elliptic smoothing of large three-dimensional grids
NASA Technical Reports Server (NTRS)
Mastin, C. Wayne
1995-01-01
Elliptic grid generation methods have been used for many years to smooth and improve grids generated by algebraic interpolation schemes. However, the elliptic system that must be solved is nonlinear and convergence is generally very slow for large grids. In an attempt to make elliptic methods practical for large three-dimensional grids, a two-stage implementation is developed where the overall grid point locations are set using a coarse grid generated by the elliptic system. The coarse grid is then interpolated to generate a finer grid which is smoothed using only a few iterations of the elliptic system.
Geometry Modeling and Grid Generation for Design and Optimization
NASA Technical Reports Server (NTRS)
Samareh, Jamshid A.
1998-01-01
Geometry modeling and grid generation (GMGG) have played and will continue to play an important role in computational aerosciences. During the past two decades, tremendous progress has occurred in GMGG; however, GMGG is still the biggest bottleneck to routine applications for complicated Computational Fluid Dynamics (CFD) and Computational Structures Mechanics (CSM) models for analysis, design, and optimization. We are still far from incorporating GMGG tools in a design and optimization environment for complicated configurations. It is still a challenging task to parameterize an existing model in today's Computer-Aided Design (CAD) systems, and the models created are not always good enough for automatic grid generation tools. Designers may believe their models are complete and accurate, but unseen imperfections (e.g., gaps, unwanted wiggles, free edges, slivers, and transition cracks) often cause problems in gridding for CSM and CFD. Despite many advances in grid generation, the process is still the most labor-intensive and time-consuming part of the computational aerosciences for analysis, design, and optimization. In an ideal design environment, a design engineer would use a parametric model to evaluate alternative designs effortlessly and optimize an existing design for a new set of design objectives and constraints. For this ideal environment to be realized, the GMGG tools must have the following characteristics: (1) be automated, (2) provide consistent geometry across all disciplines, (3) be parametric, and (4) provide sensitivity derivatives. This paper will review the status of GMGG for analysis, design, and optimization processes, and it will focus on some emerging ideas that will advance the GMGG toward the ideal design environment.
Chemical image generation with a grid-gate device
NASA Astrophysics Data System (ADS)
Filippini, D.; Gunnarsson, J.; Lundström, I.
2004-12-01
Scanning light pulse technique generating distinctive chemical images of diverse gases is demonstrated using a sensing arrangement that allows unrestricted choice of sensing materials, disregarding its conductivity or morphology. The present device, a metal oxide semiconductor structure, disentangles biasing from chemical functions by providing an inert grid as a gate that supplies the proper biasing, while functional materials even in the form of disconnected clusters can be used for sensing. The reading of conductimetric chemical responses of clustered materials, in nominal operating conditions, is demonstrated by the generation of chemical images acquired for inversion biasing conditions.
NASA Technical Reports Server (NTRS)
Samareh, Jamshid A.
2000-01-01
The purpose of this paper is to discuss grid generation issues and to challenge the grid generation community to develop tools suitable for automated multidisciplinary analysis and design optimization of aerospace vehicles. Special attention is given to the grid generation issues of computational fluid dynamics and computational structural mechanics disciplines.
A geometry-based adaptive unstructured grid generation algorithm for complex geological media
NASA Astrophysics Data System (ADS)
Bahrainian, Seyed Saied; Dezfuli, Alireza Daneh
2014-07-01
In this paper a novel unstructured grid generation algorithm is presented that considers the effect of geological features and well locations in grid resolution. The proposed grid generation algorithm presents a strategy for definition and construction of an initial grid based on the geological model, geometry adaptation of geological features, and grid resolution control. The algorithm is applied to seismotectonic map of the Masjed-i-Soleiman reservoir. Comparison of grid results with the “Triangle” program shows a more suitable permeability contrast. Immiscible two-phase flow solutions are presented for a fractured porous media test case using different grid resolutions. Adapted grid on the fracture geometry gave identical results with that of a fine grid. The adapted grid employed 88.2% less CPU time when compared to the solutions obtained by the fine grid.
An automatic, unstructured grid-generation system for geologically complex reservoirs
Kocberber, S.
1995-10-01
This paper presents an automatic, 3D, locally unstructured hybrid-grid generation system for sloping faults. This gridding system replaces a portion of an existing finite-difference grid around sloping faults with a finite-element grid made of tetrahedrons. This innovative approach retains the finite-difference character of the grid and minimizes the decrease in computational efficiency. This paper discusses the details of the gridding techniques used and provides several example grids that demonstrate that locally unstructured grids can accurately represent geologically complex reservoirs.
NASA Technical Reports Server (NTRS)
Choo, Yung K.; Slater, John W.; Henderson, Todd L.; Bidwell, Colin S.; Braun, Donald C.; Chung, Joongkee
1998-01-01
TURBO-GRD is a software system for interactive two-dimensional boundary/field grid generation. modification, and refinement. Its features allow users to explicitly control grid quality locally and globally. The grid control can be achieved interactively by using control points that the user picks and moves on the workstation monitor or by direct stretching and refining. The techniques used in the code are the control point form of algebraic grid generation, a damped cubic spline for edge meshing and parametric mapping between physical and computational domains. It also performs elliptic grid smoothing and free-form boundary control for boundary geometry manipulation. Internal block boundaries are constructed and shaped by using Bezier curve. Because TURBO-GRD is a highly interactive code, users can read in an initial solution, display its solution contour in the background of the grid and control net, and exercise grid modification using the solution contour as a guide. This process can be called an interactive solution-adaptive grid generation.
Three-dimensional grid generation about a submarine
NASA Technical Reports Server (NTRS)
Abolhassani, Jamshid Samareh; Smith, Robert E.
1988-01-01
A systematic multiple-block grid method has been developed to compute grids about submarines. Several topologies are proposed, and an oscillatory transfinite interpolation is used in the grid construction.
Spectrum generating algebra for the continuous spectrum of a free particle in Lobachevski space
Gadella, M.; Negro, J.; Santander, M.; Pronko, G. P.
2013-02-15
In this paper, we construct a Spectrum Generating Algebra (SGA) for a quantum system with purely continuous spectrum: the quantum free particle in a Lobachevski space with constant negative curvature. The SGA contains the geometrical symmetry algebra of the system plus a subalgebra of operators that give the spectrum of the system and connects the eigenfunctions of the Hamiltonian among themselves. In our case, the geometrical symmetry algebra is so(3,1) and the SGA is so(4,2). We start with a representation of so(4,2) by functions on a realization of the Lobachevski space given by a two-sheeted hyperboloid, where the Lie algebra commutators are the usual Poisson-Dirac brackets. Then, we introduce a quantized version of the representation in which functions are replaced by operators on a Hilbert space and Poisson-Dirac brackets by commutators. Eigenfunctions of the Hamiltonian are given and 'naive' ladder operators are identified. The previously defined 'naive' ladder operators shift the eigenvalues by a complex number so that an alternative approach is necessary. This is obtained by a non-self-adjoint function of a linear combination of the ladder operators, which gives the correct relation among the eigenfunctions of the Hamiltonian. We give an eigenfunction expansion of functions over the upper sheet of a two-sheeted hyperboloid in terms of the eigenfunctions of the Hamiltonian.
Development of an Automatic Grid Generator for Multi-Element High-Lift Wings
NASA Technical Reports Server (NTRS)
Eberhardt, Scott; Wibowo, Pratomo; Tu, Eugene
1996-01-01
The procedure to generate the grid around a complex wing configuration is presented in this report. The automatic grid generation utilizes the Modified Advancing Front Method as a predictor and an elliptic scheme as a corrector. The scheme will advance the surface grid one cell outward and the newly obtained grid is corrected using the Laplace equation. The predictor-corrector step ensures that the grid produced will be smooth for every configuration. The predictor-corrector scheme is extended for a complex wing configuration. A new technique is developed to deal with the grid generation in the wing-gaps and on the flaps. It will create the grids that fill the gap on the wing surface and the gap created by the flaps. The scheme recognizes these configurations automatically so that minimal user input is required. By utilizing an appropriate sequence in advancing the grid points on a wing surface, the automatic grid generation for complex wing configurations is achieved.
Application of the multigrid method to grid generation
NASA Technical Reports Server (NTRS)
Ohring, S.
1980-01-01
The multigrid method (MGM), used to numerically solve the pair of nonlinear elliptic equations commonly used to generate two dimensional boundary-fitted coordinate systems is discussed. Two different geometries are considered: one involving a coordinate system fitted about a circle and the other selected for an impinging jet flow problem. Two different relaxation schemes are tried: one is successive point overrelaxation and the other is a four-color scheme vectorizeable to take advantage of a parallel processor computer for greater computational speed. Results using MGM are compared with those using SOR (doing successive overrelaxations with the corresponding relaxation scheme on the fine grid only). It is found that MGM becomes significantly more effective than SOR as more accuracy is demanded and as more corrective grids, or more grid points, are used. For the accuracy required, it is found that MGM is two to three times faster than SOR in computing time. With the four-color relaxation scheme as applied to the impinging jet problem, the advantage of MGM over SOR is not as great. This may be due to the effect of a poor initial guess on MGM for this problem.
Automated, Parametric Geometry Modeling and Grid Generation for Turbomachinery Applications
NASA Technical Reports Server (NTRS)
Harrand, Vincent J.; Uchitel, Vadim G.; Whitmire, John B.
2000-01-01
The objective of this Phase I project is to develop a highly automated software system for rapid geometry modeling and grid generation for turbomachinery applications. The proposed system features a graphical user interface for interactive control, a direct interface to commercial CAD/PDM systems, support for IGES geometry output, and a scripting capability for obtaining a high level of automation and end-user customization of the tool. The developed system is fully parametric and highly automated, and, therefore, significantly reduces the turnaround time for 3D geometry modeling, grid generation and model setup. This facilitates design environments in which a large number of cases need to be generated, such as for parametric analysis and design optimization of turbomachinery equipment. In Phase I we have successfully demonstrated the feasibility of the approach. The system has been tested on a wide variety of turbomachinery geometries, including several impellers and a multi stage rotor-stator combination. In Phase II, we plan to integrate the developed system with turbomachinery design software and with commercial CAD/PDM software.
Anisotropic Solution Adaptive Unstructured Grid Generation Using AFLR
NASA Technical Reports Server (NTRS)
Marcum, David L.
2007-01-01
An existing volume grid generation procedure, AFLR3, was successfully modified to generate anisotropic tetrahedral elements using a directional metric transformation defined at source nodes. The procedure can be coupled with a solver and an error estimator as part of an overall anisotropic solution adaptation methodology. It is suitable for use with an error estimator based on an adjoint, optimization, sensitivity derivative, or related approach. This offers many advantages, including more efficient point placement along with robust and efficient error estimation. It also serves as a framework for true grid optimization wherein error estimation and computational resources can be used as cost functions to determine the optimal point distribution. Within AFLR3 the metric transformation is implemented using a set of transformation vectors and associated aspect ratios. The modified overall procedure is presented along with details of the anisotropic transformation implementation. Multiple two-and three-dimensional examples are also presented that demonstrate the capability of the modified AFLR procedure to generate anisotropic elements using a set of source nodes with anisotropic transformation metrics. The example cases presented use moderate levels of anisotropy and result in usable element quality. Future testing with various flow solvers and methods for obtaining transformation metric information is needed to determine practical limits and evaluate the efficacy of the overall approach.
SUSY QM, symmetries and spectrum generating algebras for two-dimensional systems
Martinez, D. Mota, R.D.
2008-04-15
We show in a systematic and clear way how factorization methods can be used to construct the generators for hidden and dynamical symmetries. This is shown by studying the 2D problems of hydrogen atom, the isotropic harmonic oscillator and the radial potential A{rho}{sup 2{zeta}}{sup -2} - B{rho}{sup {zeta}}{sup -2}. We show that in these cases the non-compact (compact) algebra corresponds to so(2, 1) (su(2))
Noniterative three-dimensional grid generation using parabolic partial differential equations
NASA Technical Reports Server (NTRS)
Edwards, T. A.
1985-01-01
A new algorithm for generating three-dimensional grids has been developed and implemented which numerically solves a parabolic partial differential equation (PDE). The solution procedure marches outward in two coordinate directions, and requires inversion of a scalar tridiagonal system in the third. Source terms have been introduced to control the spacing and angle of grid lines near the grid boundaries, and to control the outer boundary point distribution. The method has been found to generate grids about 100 times faster than comparable grids generated via solution of elliptic PDEs, and produces smooth grids for finite-difference flow calculations.
NASA Technical Reports Server (NTRS)
Steger, Joseph L.
1989-01-01
Hyperbolic grid generation procedures are described which have been used in external flow simulations about complex configurations. For many practical applications a single well-ordered (i.e., structured) grid can be used to mesh an entire configuration, in other problems, composite or unstructured grid procedures are needed. Although the hyperbolic partial differential equation grid generation procedure has mainly been utilized to generate structured grids, an extension of the procedure to semiunstructured grids is briefly described. Extensions of the methodology are also described using two-dimensional equations.
Grid-generated isotropic homogeneous turbulence at high Reynolds numbers
NASA Technical Reports Server (NTRS)
Rosen, G.
1981-01-01
Consideration is given to an empirical formula for the longitudinal correlation function for grid-generated incompressible fluid turbulence at Reynolds numbers above 12,800. The formula, which relates the longitudinal correlation function to the inverse cube of a dimensionless geometrical ratio, is shown to minimize the global correlation integrals into which the two-point velocity correlation tensor has been substituted subject to a global constraint on the Sobolev concomitent of the longitudinal correlation function. Furthermore, the energy spectrum function associated with the empirical formula is shown to satisfy a tertiary Helmholtz-type linear condition throughout the initial period of decay.
Parallel and Streaming Generation of Ghost Data for Structured Grids
Isenburg, M; Lindstrom, P; Childs, H
2008-04-15
Parallel simulations decompose large domains into many blocks. A fundamental requirement for subsequent parallel analysis and visualization is the presence of ghost data that supplements each block with a layer of adjacent data elements from neighboring blocks. The standard approach for generating ghost data requires all blocks to be in memory at once. This becomes impractical when there are fewer processors - and thus less aggregate memory - available for analysis than for simulation. We describe an algorithm for generating ghost data for structured grids that uses many fewer processors than previously possible. Our algorithm stores as little as one block per processor in memory and can run on as few processors as are available (possibly just one). The key idea is to slightly change the size of the original blocks by declaring parts of them to be ghost data, and by later padding adjacent blocks with this data.
NASA Astrophysics Data System (ADS)
Korf, Lisa A.; Schroeck, Franklin E.
2015-12-01
We consider an effect algebra of phase space localization operators for a quantum mechanical Hilbert space that contains no non-trivial projections, and the C*-algebra generated by it. This C∗-algebra forms an informationally complete set in the original Hilbert space. Its elements are shown to have singular-value-based decompositions that permit their characterization in terms of limits of linear combinations of products of pairs of the phase space fuzzy localization operators. Through these results, it is shown that the informational completeness of the C*-algebra can be greatly reduced to the informational completeness of the set of products of pairs formed from the elements of the effect algebra.
NASA Astrophysics Data System (ADS)
Chen, Hsian-Yang; Lam, Ching Hung
2014-06-01
In this paper, we construct explicitly certain moonshine type vertex operator algebras generated by a set of Ising vectors I such that (1) for any e ≠ f ∈ I, the subVOA VOA(e, f) generated by e and f is isomorphic to either U2B or U3C; and (2) the subgroup generated by the corresponding Miyamoto involutions {τe | e ∈ I} is isomorphic to the Weyl group of a root system of type An, Dn, E6, E7 or E8. The structures of the corresponding vertex operator algebras and their Griess algebras are also studied. In particular, the central charge of these vertex operator algebras are determined.
Direct numerical simulation of turbulent mixing in grid-generated turbulence
NASA Astrophysics Data System (ADS)
Nagata, Kouji; Suzuki, Hiroki; Sakai, Yasuhiko; Hayase, Toshiyuki; Kubo, Takashi
2008-12-01
Turbulent mixing of passive scalar (heat) in grid-generated turbulence (GGT) is simulated by means of direct numerical simulation (DNS). A turbulence-generating grid, on which the velocity components are set to zero, is located downstream of the channel entrance, and it is numerically constructed on the staggered mesh arrangement using the immersed boundary method. The grid types constructed are: (a) square-mesh biplane grid, (b) square-mesh single-plane grid, (c) composite grid consisting of parallel square-bars and (d) fractal grid. Two fluids with different temperatures are provided separately in the upper and lower streams upstream of the turbulence-generating grids, generating the thermal mixing layer behind the grids. For the grid (a), simulations for two different Prandtl numbers of 0.71 and 7.1, corresponding to air and water flows, are conducted to investigate the effect of the Prandtl number. The results show that the typical grid turbulence and shearless mixing layer are generated downstream of the grids. The results of the scalar field show that a typical thermal mixing layer is generated as well, and the effects of the Prandtl numbers on turbulent heat transfer are observed.
Numerical grid generation and flow simulation in SSME thrust chamber
Gross, K.W.; Daley, P.L.; Przekwas, A.J.
1987-01-01
The development of liquid and solid rocket engines for future space projects demands a detailed optimization process for highly efficient performance and cost reasons. Also, testing of full size engines may not be feasible when the large size requires test facilities which are cost prohibitive or if vacuum operation cannot be acquired. For such situations only scaling from small test scale measurements or accurate analytical predictions will provide the performance prior to actually flying the mission. A rigorous approach for simulating the combustion processes in liquid rocket engines by employing a direct solution of Navier-Stokes equations within the entire volume of the thrust chambers is presented. This method is illustrated in the solution of reactive flow in the Space Shuttle Main Engine (SSME) thrust chamber. The objective is to review recent improvements in the mathematical model and to present the grid generation methodology suitable for rocket thrust chamber geometries.
Knowledge-based zonal grid generation for computational fluid dynamics
NASA Technical Reports Server (NTRS)
Andrews, Alison E.
1988-01-01
Automation of flow field zoning in two dimensions is an important step towards reducing the difficulty of three-dimensional grid generation in computational fluid dynamics. Using a knowledge-based approach makes sense, but problems arise which are caused by aspects of zoning involving perception, lack of expert consensus, and design processes. These obstacles are overcome by means of a simple shape and configuration language, a tunable zoning archetype, and a method of assembling plans from selected, predefined subplans. A demonstration system for knowledge-based two-dimensional flow field zoning has been successfully implemented and tested on representative aerodynamic configurations. The results show that this approach can produce flow field zonings that are acceptable to experts with differing evaluation criteria.
Unstructured Grid Generation for Complex 3D High-Lift Configurations
NASA Technical Reports Server (NTRS)
Pirzadeh, Shahyar Z.
1999-01-01
The application of an unstructured grid methodology on a three-dimensional high-lift configuration is presented. The focus of this paper is on the grid generation aspect of an integrated effort for the development of an unstructured-grid computational fluid dynamics (CFD) capability at the NASA Langley Research Center. The meshing approach is based on tetrahedral grids generated by the advancing-front and the advancing-layers procedures. The capability of the method for solving high-lift problems is demonstrated on an aircraft model referred to as the energy efficient transport configuration. The grid generation issues, including the pros and cons of the present approach, are discussed in relation to the high-lift problems. Limited viscous flow results are presented to demonstrate the viability of the generated grids. A corresponding Navier-Stokes solution capability, along with further computations on the present grid, is presented in a companion SAE paper.
Bgridi - Interactive three-dimensional turbomachinery grid generation system with applications
Shoemaker, J.M.; Hah, C. NASA, Lewis Research Center, Cleveland, OH )
1993-01-01
An interactive, graphics-based grid generation system for 3D turbomachinery geometries has been developed. The system consists of separate modules for geometry modeling and grid generation. The grid generation method generates a series of 2D grids in the blade-to-blade passage to build up the 3D grid. A Poisson equation with forcing functions selected to control orthogonality and spacing on all boundaries is solved to generate the grid. Interactive definition of Bezier curves and surfaces as internal boundaries is used to improve control of grid quality. A multi-block data structure simpifies the creation of structured H-grids about complex turbomachinery geometries. The multi-block strategy facilitates the creation of a grid in the tip flow region, which is an important contributor to losses within the passage. The grid generation system is applied to several complex geometries including a simple radial impeller, a conventional turbine rotor, the SSME LOX turbine rotor with and without a tip flow grid, a multi-passage inducer-impeller, and a tip-flow cascade. In addition, a calculation of the tip-flow cascade flow field is shown. 17 refs.
Bgridi - Interactive three-dimensional turbomachinery grid generation system with applications
NASA Technical Reports Server (NTRS)
Shoemaker, J. M.; Hah, Chunill
1993-01-01
An interactive, graphics-based grid generation system for 3D turbomachinery geometries has been developed. The system consists of separate modules for geometry modeling and grid generation. The grid generation method generates a series of 2D grids in the blade-to-blade passage to build up the 3D grid. A Poisson equation with forcing functions selected to control orthogonality and spacing on all boundaries is solved to generate the grid. Interactive definition of Bezier curves and surfaces as internal boundaries is used to improve control of grid quality. A multi-block data structure simpifies the creation of structured H-grids about complex turbomachinery geometries. The multi-block strategy facilitates the creation of a grid in the tip flow region, which is an important contributor to losses within the passage. The grid generation system is applied to several complex geometries including a simple radial impeller, a conventional turbine rotor, the SSME LOX turbine rotor with and without a tip flow grid, a multi-passage inducer-impeller, and a tip-flow cascade. In addition, a calculation of the tip-flow cascade flow field is shown.
NASA Technical Reports Server (NTRS)
Spekreijse, S. P.; Boerstoel, J. W.; Vitagliano, P. L.; Kuyvenhoven, J. L.
1992-01-01
About five years ago, a joint development was started of a flow simulation system for engine-airframe integration studies on propeller as well as jet aircraft. The initial system was based on the Euler equations and made operational for industrial aerodynamic design work. The system consists of three major components: a domain modeller, for the graphical interactive subdivision of flow domains into an unstructured collection of blocks; a grid generator, for the graphical interactive computation of structured grids in blocks; and a flow solver, for the computation of flows on multi-block grids. The industrial partners of the collaboration and NLR have demonstrated that the domain modeller, grid generator and flow solver can be applied to simulate Euler flows around complete aircraft, including propulsion system simulation. Extension to Navier-Stokes flows is in progress. Delft Hydraulics has shown that both the domain modeller and grid generator can also be applied successfully for hydrodynamic configurations. An overview is given about the main aspects of both domain modelling and grid generation.
Specialized CFD Grid Generation Methods for Near-Field Sonic Boom Prediction
NASA Technical Reports Server (NTRS)
Park, Michael A.; Campbell, Richard L.; Elmiligui, Alaa; Cliff, Susan E.; Nayani, Sudheer N.
2014-01-01
Ongoing interest in analysis and design of low sonic boom supersonic transports re- quires accurate and ecient Computational Fluid Dynamics (CFD) tools. Specialized grid generation techniques are employed to predict near- eld acoustic signatures of these con- gurations. A fundamental examination of grid properties is performed including grid alignment with ow characteristics and element type. The issues a ecting the robustness of cylindrical surface extrusion are illustrated. This study will compare three methods in the extrusion family of grid generation methods that produce grids aligned with the freestream Mach angle. These methods are applied to con gurations from the First AIAA Sonic Boom Prediction Workshop.
NGP: Defining a grid generation paradigm based on NURBS and solid modeling topology
Gaither, A.; Jean, B.; Remotigue, M.; Whitmire, J.
1996-12-31
A grid generation paradigm is presented that allows a user to build both structured and unstructured grids within the same environment. It provides the user with a flexible, efficient and accurate way to generate these grids. The paradigm utilizes a Boundary Representation (B-rep) radial edge non-manifold solid modeling topology data structure for all geometric and grid interrogations. Non-Uniform Rational B-Splines (NURBS) are utilized as the geometric representation to ensure accuracy and provide generality for both geometric and grid manipulations.
Three-dimensional adaptive grid generation for body-fitted coordinate system
NASA Astrophysics Data System (ADS)
Chen, S. C.
1988-08-01
This report describes a numerical method for generating 3-D grids for general configurations. The basic method involves the solution of a set of quasi-linear elliptic partial differential equations via pointwise relaxation with a local relaxation factor. It allows specification of the grid spacing off the boundary surfaces and the grid orthogonality at the boundary surfaces. It includes adaptive mechanisms to improve smoothness, orthogonality, and flow resolution in the grid interior.
Three-dimensional adaptive grid generation for body-fitted coordinate system
NASA Astrophysics Data System (ADS)
Chen, S. C.
This report describes a numerical method for generating 3-D grids for general configurations. The basic method involves the solution of a set of quasi-linear elliptic partial differential equations via pointwise relaxation with a local relaxation factor. It allows specification of the grid spacing off the boundary surfaces and the grid orthogonality at the boundary surfaces. It includes adaptive mechanisms to improve smoothness, orthogonality, and flow resolution in the grid interior.
Domain decomposition by the advancing-partition method for parallel unstructured grid generation
NASA Technical Reports Server (NTRS)
Pirzadeh, Shahyar Z. (Inventor); Banihashemi, legal representative, Soheila (Inventor)
2012-01-01
In a method for domain decomposition for generating unstructured grids, a surface mesh is generated for a spatial domain. A location of a partition plane dividing the domain into two sections is determined. Triangular faces on the surface mesh that intersect the partition plane are identified. A partition grid of tetrahedral cells, dividing the domain into two sub-domains, is generated using a marching process in which a front comprises only faces of new cells which intersect the partition plane. The partition grid is generated until no active faces remain on the front. Triangular faces on each side of the partition plane are collected into two separate subsets. Each subset of triangular faces is renumbered locally and a local/global mapping is created for each sub-domain. A volume grid is generated for each sub-domain. The partition grid and volume grids are then merged using the local-global mapping.
WinGridder - An interactive grid generator for TOUGH - A user's manual (Version 1.0)
Pan, Lehua; Hinds, Jennifer; Haukwa, Charles; Wu, Yu-Shu; Bodvarsson, Gudmundur
2001-07-18
WinGridder is a Windows-based software package for designing, generating, and visualizing at various spatial scales numerical grids used in reservoir simulations and groundwater modeling studies. Development of this software was motivated by the requirements of the TOUGH (Transport of Unsaturated Groundwater and Heat) family of codes (Pruess 1987, 1991) for simulating subsurface processes related to high-level nuclear waste isolation in partially saturated geological media. Although the TOUGH family of codes has great flexibility in handling the variety of grid information required to describe complex objects, designing and generating a suitable irregular grid can be a tedious and error-prone process, even with the help of existing grid generating programs. This is especially true when the number of cells and connections is very large. The processes of inspecting the quality of the grid or extracting sub-grids or other specific grid information are also complex. The mesh maker embedded within TOUGH2 generates only uniform numerical grids and handles only one set of uniform fracture and matrix properties throughout the model domain. This is not suitable for grid generation in complex flow and transport simulations (such as those of Yucca Mountain, which have heterogeneity in both fracture and matrix media). As a result, the software program Amesh (Haukwa 2000) was developed to generate irregular, effective-continuum (ECM) grids.
ON 3D, AUTOMATED, SELF-CONTAINED GRID GENERATION WITHIN THE RAGE CAMR HYDROCODE
Oakes, W.R.; Henning, P.J.; Gittings, M.L.; Weaver, R.P.
2000-06-01
We discuss using the inherent grid manipulation capability within a Continuously Adaptive Mesh Refinement hydrodynamics code, RAGE, to implement parallel, automated, self-contained grid generation. We show how arbitrarily complex 3D geometries specified in any unambiguous form can be used. The RAGE computational environment is any of several massively parallel computers being developed under the Department Of Energy's Accelerated Strategic Computing Initiative. A typical 3D RAGE analysis may contain 100 million cells and occupy 2000 processors for several weeks. RAGE grid generation is embarrassingly parallel. The RAGE computational grid is an octree decomposition of the model space. The problem domain is subdivided into as many subdomains as the number of processors assigned to the problem. The grid for each subdomain is then generated independently, except for occasional adjustments. Geometry used for initial grid generation includes CSG combinations of NURBS-based boundary representation models, stereo lithography (STL) files, implicit surfaces, and functionally perturbed surfaces.
Structured grid generation using a CAD solid model for an aero-gas turbine combustion system
Eccles, N.C.; Manners, A.P.
1996-12-31
An aero-gas turbine combustion system was used to demonstrate the problems of creating a single block structured grid suitable for CFD predictions from a designer`s parametric solid model. The solid model had to be filtered of sub-grid detail and computational fluid volumes generated from the solid model of the metal. Alternative methods of transferring the geometry from the CAD package to the grid generator were considered. The type and method of grid generation was found to influence all stages in manipulating the geometry.
Generation and adaptation of 3-D unstructured grids for transient problems
NASA Technical Reports Server (NTRS)
Loehner, Rainald
1990-01-01
Grid generation and adaptive refinement techniques suitable for the simulation of strongly unsteady flows past geometrically complex bodies in 3-D are described. The grids are generated using the advancing front technique. Emphasis is placed not to generate elements that are too small, as this would severely increase the cost of simulations with explicit flow solvers. The grids are adapted to an evolving flowfield using simple h-refinement. A grid change is performed every 5 to 10 timesteps, and only one level of refinement/coarsening is allowed per mesh change.
Automated grid generation from models of complex geologic structure and stratigraphy
Gable, C.; Trease, H.; Cherry, T.
1996-04-01
The construction of computational grids which accurately reflect complex geologic structure and stratigraphy for flow and transport models poses a formidable task. With an understanding of stratigraphy, material properties and boundary and initial conditions, the task of incorporating this data into a numerical model can be difficult and time consuming. Most GIS tools for representing complex geologic volumes and surfaces are not designed for producing optimal grids for flow and transport computation. We have developed a tool, GEOMESH, for generating finite element grids that maintain the geometric integrity of input volumes, surfaces, and geologic data and produce an optimal (Delaunay) tetrahedral grid that can be used for flow and transport computations. GEOMESH also satisfies the constraint that the geometric coupling coefficients of the grid are positive for all elements. GEOMESH generates grids for two dimensional cross sections, three dimensional regional models, represents faults and fractures, and has the capability of including finer grids representing tunnels and well bores into grids. GEOMESH also permits adaptive grid refinement in three dimensions. The tools to glue, merge and insert grids together demonstrate how complex grids can be built from simpler pieces. The resulting grid can be utilized by unstructured finite element or integrated finite difference computational physics codes.
Domain Decomposition By the Advancing-Partition Method for Parallel Unstructured Grid Generation
NASA Technical Reports Server (NTRS)
Pirzadeh, Shahyar Z.; Zagaris, George
2009-01-01
A new method of domain decomposition has been developed for generating unstructured grids in subdomains either sequentially or using multiple computers in parallel. Domain decomposition is a crucial and challenging step for parallel grid generation. Prior methods are generally based on auxiliary, complex, and computationally intensive operations for defining partition interfaces and usually produce grids of lower quality than those generated in single domains. The new technique, referred to as "Advancing Partition," is based on the Advancing-Front method, which partitions a domain as part of the volume mesh generation in a consistent and "natural" way. The benefits of this approach are: 1) the process of domain decomposition is highly automated, 2) partitioning of domain does not compromise the quality of the generated grids, and 3) the computational overhead for domain decomposition is minimal. The new method has been implemented in NASA's unstructured grid generation code VGRID.
Geometry modeling and grid generation using 3D NURBS control volume
NASA Technical Reports Server (NTRS)
Yu, Tzu-Yi; Soni, Bharat K.; Shih, Ming-Hsin
1995-01-01
The algorithms for volume grid generation using NURBS geometric representation are presented. The parameterization algorithm is enhanced to yield a desired physical distribution on the curve, surface and volume. This approach bridges the gap between CAD surface/volume definition and surface/volume grid generation. Computational examples associated with practical configurations have shown the utilization of these algorithms.
Gable, C.W.; Trease, H.E.; Cherry, T.A.
1996-04-01
The construction of grids that accurately reflect geologic structure and stratigraphy for computational flow and transport models poses a formidable task. Even with a complete understanding of stratigraphy, material properties, boundary and initial conditions, the task of incorporating data into a numerical model can be difficult and time consuming. Furthermore, most tools available for representing complex geologic surfaces and volumes are not designed for producing optimal grids for flow and transport computation. We have developed a modeling tool, GEOMESH, for automating finite element grid generation that maintains the geometric integrity of geologic structure and stratigraphy. The method produces an optimal (Delaunay) tetrahedral grid that can be used for flow and transport computations. The process of developing a flow and transport model can be divided into three parts: (1) Developing accurate conceptual models inclusive of geologic interpretation, material characterization and construction of a stratigraphic and hydrostratigraphic framework model, (2) Building and initializing computational frameworks; grid generation, boundary and initial conditions, (3) Computational physics models of flow and transport. Process (1) and (3) have received considerable attention whereas (2) has not. This work concentrates on grid generation and its connections to geologic characterization and process modeling. Applications of GEOMESH illustrate grid generation for two dimensional cross sections, three dimensional regional models, and adaptive grid refinement in three dimensions. Examples of grid representation of wells and tunnels with GEOMESH can be found in Cherry et al. The resulting grid can be utilized by unstructured finite element or integrated finite difference models.
Adaptive grid generation in a patient-specific cerebral aneurysm.
Hodis, Simona; Kallmes, David F; Dragomir-Daescu, Dan
2013-11-01
Adapting grid density to flow behavior provides the advantage of increasing solution accuracy while decreasing the number of grid elements in the simulation domain, therefore reducing the computational time. One method for grid adaptation requires successive refinement of grid density based on observed solution behavior until the numerical errors between successive grids are negligible. However, such an approach is time consuming and it is often neglected by the researchers. We present a technique to calculate the grid size distribution of an adaptive grid for computational fluid dynamics (CFD) simulations in a complex cerebral aneurysm geometry based on the kinematic curvature and torsion calculated from the velocity field. The relationship between the kinematic characteristics of the flow and the element size of the adaptive grid leads to a mathematical equation to calculate the grid size in different regions of the flow. The adaptive grid density is obtained such that it captures the more complex details of the flow with locally smaller grid size, while less complex flow characteristics are calculated on locally larger grid size. The current study shows that kinematic curvature and torsion calculated from the velocity field in a cerebral aneurysm can be used to find the locations of complex flow where the computational grid needs to be refined in order to obtain an accurate solution. We found that the complexity of the flow can be adequately described by velocity and vorticity and the angle between the two vectors. For example, inside the aneurysm bleb, at the bifurcation, and at the major arterial turns the element size in the lumen needs to be less than 10% of the artery radius, while at the boundary layer, the element size should be smaller than 1% of the artery radius, for accurate results within a 0.5% relative approximation error. This technique of quantifying flow complexity and adaptive remeshing has the potential to improve results accuracy and reduce
Adaptive grid generation in a patient-specific cerebral aneurysm
NASA Astrophysics Data System (ADS)
Hodis, Simona; Kallmes, David F.; Dragomir-Daescu, Dan
2013-11-01
Adapting grid density to flow behavior provides the advantage of increasing solution accuracy while decreasing the number of grid elements in the simulation domain, therefore reducing the computational time. One method for grid adaptation requires successive refinement of grid density based on observed solution behavior until the numerical errors between successive grids are negligible. However, such an approach is time consuming and it is often neglected by the researchers. We present a technique to calculate the grid size distribution of an adaptive grid for computational fluid dynamics (CFD) simulations in a complex cerebral aneurysm geometry based on the kinematic curvature and torsion calculated from the velocity field. The relationship between the kinematic characteristics of the flow and the element size of the adaptive grid leads to a mathematical equation to calculate the grid size in different regions of the flow. The adaptive grid density is obtained such that it captures the more complex details of the flow with locally smaller grid size, while less complex flow characteristics are calculated on locally larger grid size. The current study shows that kinematic curvature and torsion calculated from the velocity field in a cerebral aneurysm can be used to find the locations of complex flow where the computational grid needs to be refined in order to obtain an accurate solution. We found that the complexity of the flow can be adequately described by velocity and vorticity and the angle between the two vectors. For example, inside the aneurysm bleb, at the bifurcation, and at the major arterial turns the element size in the lumen needs to be less than 10% of the artery radius, while at the boundary layer, the element size should be smaller than 1% of the artery radius, for accurate results within a 0.5% relative approximation error. This technique of quantifying flow complexity and adaptive remeshing has the potential to improve results accuracy and reduce
Finite difference time domain grid generation from AMC helicopter models
NASA Technical Reports Server (NTRS)
Cravey, Robin L.
1992-01-01
A simple technique is presented which forms a cubic grid model of a helicopter from an Aircraft Modeling Code (AMC) input file. The AMC input file defines the helicopter fuselage as a series of polygonal cross sections. The cubic grid model is used as an input to a Finite Difference Time Domain (FDTD) code to obtain predictions of antenna performance on a generic helicopter model. The predictions compare reasonably well with measured data.
Three-dimensional elliptic grid generation technique with application to turbomachinery cascades
NASA Technical Reports Server (NTRS)
Chen, S. C.; Schwab, J. R.
1988-01-01
Described is a numerical method for generating 3-D grids for turbomachinery computational fluid dynamic codes. The basic method is general and involves the solution of a quasi-linear elliptic partial differential equation via pointwise relaxation with a local relaxation factor. It allows specification of the grid point distribution on the boundary surfaces, the grid spacing off the boundary surfaces, and the grid orthogonality at the boundary surfaces. A geometry preprocessor constructs the grid point distributions on the boundary surfaces for general turbomachinery cascades. Representative results are shown for a C-grid and an H-grid for a turbine rotor. Two appendices serve as user's manuals for the basic solver and the geometry preprocessor.
Three-dimensional elliptic grid generation technique with application to turbomachinery cascades
NASA Astrophysics Data System (ADS)
Chen, S. C.; Schwab, J. R.
1988-08-01
Described is a numerical method for generating 3-D grids for turbomachinery computational fluid dynamic codes. The basic method is general and involves the solution of a quasi-linear elliptic partial differential equation via pointwise relaxation with a local relaxation factor. It allows specification of the grid point distribution on the boundary surfaces, the grid spacing off the boundary surfaces, and the grid orthogonality at the boundary surfaces. A geometry preprocessor constructs the grid point distributions on the boundary surfaces for general turbomachinery cascades. Representative results are shown for a C-grid and an H-grid for a turbine rotor. Two appendices serve as user's manuals for the basic solver and the geometry preprocessor.
Generation of a composite grid for turbine flows and consideration of a numerical scheme
NASA Technical Reports Server (NTRS)
Choo, Y.; Yoon, S.; Reno, C.
1986-01-01
A composite grid was generated for flows in turbines. It consisted of the C-grid (or O-grid) in the immediate vicinity of the blade and the H-grid in the middle of the blade passage between the C-grids and in the upstream region. This new composite grid provides better smoothness, resolution, and orthogonality than any single grid for a typical turbine blade with a large camber and rounded leading and trailing edges. The C-H (or O-H) composite grid has an unusual grid point that is connected to more than four neighboring nodes in two dimensions (more than six neighboring nodes in three dimensions). A finite-volume lower-upper (LU) implicit scheme to be used on this grid poses no problem and requires no special treatment because each interior cell of this composite grid has only four neighboring cells in two dimensions (six cells in three dimensions). The LU implicit scheme was demonstrated to be efficient and robust for external flows in a broad flow regime and can be easily applied to internal flows and extended from two to three dimensions.
Cell volume control at a surface for three-dimensional grid generation packages
NASA Technical Reports Server (NTRS)
Alter, Stephen J.; Weilmuenster, Kenneth J.
1992-01-01
An alternate method of calculating the cell size for orthogonality control in the solution of Poisson's 3D space equations is presented. The method provides the capability to enforce a better initial guess for the grid distribution required for boundary layer resolution. This grid point distribution is accomplished by enforcing grid spacing from a grid block boundary where orthogonality is required. The actual grid spacing or cell size for that boundary is determined by the two or four adjacent boundaries in the grid block definition, which are two dimensional grids. These two dimensional grids are in turn defined by the user using insight into the flow field and boundary layer characteristics. The adjoining boundaries are extended using a multifunctional blending scheme, with user control of the blending and interpolating functions to be used. This grid generation procedure results in an enhanced computational fluid dynamics calculation by allowing a quicker resolution of the configuration's boundary layer and flow field and by limiting the number of grid re-adaptations. The cell size specification calculation was applied to a variety of configurations ranging from axisymmetric to complex three-dimensional configurations. Representative grids are shown for the Space Shuttle and the Langley Lifting Body (HL-20).
Automatic computation of Euler-marching and subsonic grids for wing-fuselage configurations
NASA Technical Reports Server (NTRS)
Barger, Raymond L.; Adams, Mary S.; Krishnan, Ramki R.
1994-01-01
Algebraic procedures are described for the automatic generation of structured, single-block flow computation grids for relatively simple configurations (wing, fuselage, and fin). For supersonic flows, a quasi two-dimensional grid for Euler-marching codes is developed, and some sample results in graphical form are included. A type of grid for subsonic flow calculation is also described. The techniques are algebraic and are based on a generalization of the method of transfinite interpolation.
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2012-08-07
... From the Federal Register Online via the Government Publishing Office DEPARTMENT OF ENERGY Federal Energy Regulatory Commission The Incorporated Village of Port Jefferson v. National Grid Generation LLC... Jefferson (Complainant) filed a formal complaint against the National Grid Generation LLC...
Generator algebra of the asymptotic Poincare group in the general theory of relativity
Solovev, V.O.
1986-06-01
This paper obtains the Poisson brackets of the generators of the Hamiltonian formalism for general relativity with allowance for surface terms of aritrary form. For Minkowski space, there exists the asymptotic Poincare group, which is the semi-direct product of the Poincare group and an infinite subgroup for which the algebra of generators with surface terms closes. A criterion invariant with respect to the choice of the coordinate system on the hypersurfaces is obtained for realization of the Poincare group in asymptotically flat space-time. The ''background'' flat metric on the hypersurfaces and Poincare group that preserve it are determined nonuniquely; however, the numerical values of the generators do not depend on the freedom of this choice on solutions of the constraint equations. For an asymptotically Galilean metric, the widely used boundary cnoditins are determined more accurately. A prescription is given for application of the Arnowitt-Deser-Misner decomposition in the case of a slowly decreasing contribution from coordinate and time transformations.
NASA Technical Reports Server (NTRS)
Arthur, Trey; Bockelie, Michael J.
1993-01-01
Efforts to parallelize the VGRIDSG unstructured surface grid generation program are described. The inherent parallel nature of the grid generation algorithm used in VGRIDSG was exploited on a cluster of Silicon Graphics IRIS 4D workstations using the message passing libraries Application Portable Parallel Library (APPL) and Parallel Virtual Machine (PVM). Comparisons of speed up are presented for generating the surface grid of a unit cube and a Mach 3.0 High Speed Civil Transport. It was concluded that for this application, both APPL and PVM give approximately the same performance, however, APPL is easier to use.
NASA Astrophysics Data System (ADS)
Roache, P. J.
1982-08-01
A computational effort to develop computer codes for rapidly and accurately modeling the electric fields within laser cavities is described. Semidirect/marching methods are used both for the generation of two dimensional boundary fitted grids using the elliptic generating equation approach, and for the solution of electric field problems in those coordinate systems. The efficiency of the semidirect/marching methods makes possible interactive design of the laser electrodes using a modest computer. Also described are techniques for high order accuracy, a method for precise grid control at interior points, and applications to the elliptic grid generation problem of computer symbolic manipulation.
BGRID: A block-structured grid generation code for wing sections
NASA Technical Reports Server (NTRS)
Chen, H. C.; Lee, K. D.
1981-01-01
The operation of the BGRID computer program is described for generating block-structured grids. Examples are provided to illustrate the code input and output. The application of a fully implicit AF (approximation factorization)-based computer code, called TWINGB (Transonic WING), for solving the 3D transonic full potential equation in conservation form on block-structured grids is also discussed.
Applications of Lagrangian blending functions for grid generation around airplane geometries
NASA Technical Reports Server (NTRS)
Abolhassani, Jamshid S.; Sadrehaghighi, Ideen; Tiwari, Surendra N.; Smith, Robert E.
1990-01-01
A simple procedure has been developed and applied for the grid generation around an airplane geometry. This approach is based on a transfinite interpolation with Lagrangian interpolation for the blending functions. A monotonic rational quadratic spline interpolation has been employed for the grid distributions.
Geometry acquisition and grid generation: Recent experiences with complex aircraft configurations
NASA Technical Reports Server (NTRS)
Gatzke, Timothy D.; Labozzetta, Walter F.; Cooley, John W.; Finfrock, Gregory P.
1992-01-01
Important issues involved in working with complex geometries are discussed. Approaches taken to address complex geometry issues in the McDonnell Aircraft Computational Grid System and related geometry processing tools are discussed. The efficiency of acquiring a suitable geometry definition, the need to manipulate the geometry, and the time and skill level required to generate the grid while preserving geometric fidelity are discussed.
Application of Lagrangian blending functions for grid generation around airplane geometries
NASA Technical Reports Server (NTRS)
Abolhassani, Jamshid S.; Sadrehaghighi, Ideen; Tiwari, Surendra N.
1990-01-01
A simple procedure was developed and applied for the grid generation around an airplane geometry. This approach is based on a transfinite interpolation with Lagrangian interpolation for the blending functions. A monotonic rational quadratic spline interpolation was employed for the grid distributions.
An analytical approach to grid sensitivity analysis for NACA four-digit wing sections
NASA Technical Reports Server (NTRS)
Sadrehaghighi, I.; Tiwari, S. N.
1992-01-01
Sensitivity analysis in computational fluid dynamics with emphasis on grids and surface parameterization is described. An interactive algebraic grid-generation technique is employed to generate C-type grids around NACA four-digit wing sections. An analytical procedure is developed for calculating grid sensitivity with respect to design parameters of a wing section. A comparison of the sensitivity with that obtained using a finite difference approach is made. Grid sensitivity with respect to grid parameters, such as grid-stretching coefficients, are also investigated. Using the resultant grid sensitivity, aerodynamic sensitivity is obtained using the compressible two-dimensional thin-layer Navier-Stokes equations.
NASA Astrophysics Data System (ADS)
Konstein, S. E.; Tyutin, I. V.
2016-05-01
The associative algebra of symplectic reflections H: = {H_{1,{v_{1,}}{v_2}}}( {{I_2}( {2m} )} ) based on the group generated by the root system I 2(2m) depends on two parameters, ν 1 and ν 2. For each value of these parameters, the algebra admits an m-dimensional space of traces. A trace tr is said to be degenerate if the corresponding symmetric bilinear form B tr( x, y) = tr( xy) is degenerate. We find all values of the parameters ν 1 and ν 2 for which the space of traces contains degenerate traces and the algebra H consequently has a two-sided ideal. It turns out that a linear combination of degenerate traces is also a degenerate trace. For the ν 1 and ν 2 values corresponding to degenerate traces, we find the dimensions of the space of degenerate traces.
GENIE - Generation of computational geometry-grids for internal-external flow configurations
NASA Technical Reports Server (NTRS)
Soni, B. K.
1988-01-01
Progress realized in the development of a master geometry-grid generation code GENIE is presented. The grid refinement process is enhanced by developing strategies to utilize bezier curves/surfaces and splines along with weighted transfinite interpolation technique and by formulating new forcing function for the elliptic solver based on the minimization of a non-orthogonality functional. A two step grid adaptation procedure is developed by optimally blending adaptive weightings with weighted transfinite interpolation technique. Examples of 2D-3D grids are provided to illustrate the success of these methods.
Computational Needs for the Next Generation Electric Grid Proceedings
Birman, Kenneth; Ganesh, Lakshmi; Renessee, Robbert van; Ferris, Michael; Hofmann, Andreas; Williams, Brian; Sztipanovits, Janos; Hemingway, Graham; University, Vanderbilt; Bose, Anjan; Stivastava, Anurag; Grijalva, Santiago; Grijalva, Santiago; Ryan, Sarah M.; McCalley, James D.; Woodruff, David L.; Xiong, Jinjun; Acar, Emrah; Agrawal, Bhavna; Conn, Andrew R.; Ditlow, Gary; Feldmann, Peter; Finkler, Ulrich; Gaucher, Brian; Gupta, Anshul; Heng, Fook-Luen; Kalagnanam, Jayant R; Koc, Ali; Kung, David; Phan, Dung; Singhee, Amith; Smith, Basil
2011-10-05
The April 2011 DOE workshop, 'Computational Needs for the Next Generation Electric Grid', was the culmination of a year-long process to bring together some of the Nation's leading researchers and experts to identify computational challenges associated with the operation and planning of the electric power system. The attached papers provide a journey into these experts' insights, highlighting a class of mathematical and computational problems relevant for potential power systems research. While each paper defines a specific problem area, there were several recurrent themes. First, the breadth and depth of power system data has expanded tremendously over the past decade. This provides the potential for new control approaches and operator tools that can enhance system efficiencies and improve reliability. However, the large volume of data poses its own challenges, and could benefit from application of advances in computer networking and architecture, as well as data base structures. Second, the computational complexity of the underlying system problems is growing. Transmitting electricity from clean, domestic energy resources in remote regions to urban consumers, for example, requires broader, regional planning over multi-decade time horizons. Yet, it may also mean operational focus on local solutions and shorter timescales, as reactive power and system dynamics (including fast switching and controls) play an increasingly critical role in achieving stability and ultimately reliability. The expected growth in reliance on variable renewable sources of electricity generation places an exclamation point on both of these observations, and highlights the need for new focus in areas such as stochastic optimization to accommodate the increased uncertainty that is occurring in both planning and operations. Application of research advances in algorithms (especially related to optimization techniques and uncertainty quantification) could accelerate power system software tool
Multi-scale grid generated turbulence in an internal flow application
NASA Astrophysics Data System (ADS)
Ranade, Piyush; Morris, Scott
2013-11-01
Turbulence generation using multi-scale, or fractal grids, is a method of creating high turbulence intensity flows passively by utilizing the intrinsic scales associated with the grid. This has become the topic of research in many external flow applications. In turbomachinery, the flow at the exit of the combustor and into the first nozzle stage is highly turbulent. In order to create high turbulence intensities in a lab setting passively, multi-scale turbulence generation grids are proposed. The presence of multiple length scales in the grid geometry innately gives rise to turbulent motions of a wide spectrum being shed immediately downstream of the grid, leading to high turbulence intensity flow. The biggest challenge with using such a grid in an internal flow, however, is to achieve spatial uniformity. In this research, three grid geometries commonly found in literature were tested in an experimental set-up consisting of flow between two flat plates. In addition, several other fractal grid geometries were created and tested in an attempt to maximize turbulence intensity while maintaining spatial homogeneity. This research hopes to begin giving insight into the development of turbulence downstream of a multi-scale grid in an internal flow setting.
Makris, Evangelos; Neofytou, Panagiotis; Tsangaris, Sokrates; Housiadas, Christos
2012-10-01
In this study a description of a new approach, for the generation of multi-block structured computational grids on patient-specific bifurcation geometries is presented. The structured grid generation technique is applied to data obtained by medical imaging examination, resulting in a surface conforming, high quality, multi-block structured grid of the branching geometry. As a case study application a patient specific abdominal aorta bifurcation is selected. For the evaluation of the grid produced by the novel method, a grid convergence study and a comparison between the grid produced by the method and unstructured grids produced by commercial meshing software are carried out. PMID:22209311
NASA Technical Reports Server (NTRS)
Papadopoulos, Periklis; Venkatapathy, Ethiraj; Prabhu, Dinesh; Loomis, Mark P.; Olynick, Dave; Arnold, James O. (Technical Monitor)
1998-01-01
Recent advances in computational power enable computational fluid dynamic modeling of increasingly complex configurations. A review of grid generation methodologies implemented in support of the computational work performed for the X-38 and X-33 are presented. In strategizing topological constructs and blocking structures factors considered are the geometric configuration, optimal grid size, numerical algorithms, accuracy requirements, physics of the problem at hand, computational expense, and the available computer hardware. Also addressed are grid refinement strategies, the effects of wall spacing, and convergence. The significance of grid is demonstrated through a comparison of computational and experimental results of the aeroheating environment experienced by the X-38 vehicle. Special topics on grid generation strategies are also addressed to model control surface deflections, and material mapping.
NASA Surface-Modeling and Grid-Generation (SM/GG) activities
NASA Technical Reports Server (NTRS)
Choo, Yung K.
1992-01-01
A NASA Steering Committee was formed to carry out the recommendations from the NASA Workshop on Future Directions in Surface Modeling and Grid Generation. Its function is to communicate and coordinate within NASA the acquisition and distribution of geometry/grid generation software/data, establish geometry data exchange standards, and interface with other government, university, and industry efforts. Two speakers present the committee's activities in viewgraph format.
Online Optimization Method for Operation of Generators in a Micro Grid
NASA Astrophysics Data System (ADS)
Hayashi, Yasuhiro; Miyamoto, Hideki; Matsuki, Junya; Iizuka, Toshio; Azuma, Hitoshi
Recently a lot of studies and developments about distributed generator such as photovoltaic generation system, wind turbine generation system and fuel cell have been performed under the background of the global environment issues and deregulation of the electricity market, and the technique of these distributed generators have progressed. Especially, micro grid which consists of several distributed generators, loads and storage battery is expected as one of the new operation system of distributed generator. However, since precipitous load fluctuation occurs in micro grid for the reason of its smaller capacity compared with conventional power system, high-accuracy load forecasting and control scheme to balance of supply and demand are needed. Namely, it is necessary to improve the precision of operation in micro grid by observing load fluctuation and correcting start-stop schedule and output of generators online. But it is not easy to determine the operation schedule of each generator in short time, because the problem to determine start-up, shut-down and output of each generator in micro grid is a mixed integer programming problem. In this paper, the authors propose an online optimization method for the optimal operation schedule of generators in micro grid. The proposed method is based on enumeration method and particle swarm optimization (PSO). In the proposed method, after picking up all unit commitment patterns of each generators satisfied with minimum up time and minimum down time constraint by using enumeration method, optimal schedule and output of generators are determined under the other operational constraints by using PSO. Numerical simulation is carried out for a micro grid model with five generators and photovoltaic generation system in order to examine the validity of the proposed method.
A Software Demonstration of 'rap': Preparing CAD Geometries for Overlapping Grid Generation
Anders Petersson, N.
2002-02-15
We demonstrate the application code ''rap'' which is part of the ''Overture'' library. A CAD geometry imported from an IGES file is first cleaned up and simplified to suit the needs of mesh generation. Thereafter, the topology of the model is computed and a water-tight surface triangulation is created on the CAD surface. This triangulation is used to speed up the projection of points onto the CAD surface during the generation of overlapping surface grids. From each surface grid, volume grids are grown into the domain using a hyperbolic marching procedure. The final step is to fill any remaining parts of the interior with background meshes.
Elliptic grid generation with orthogonality and spacing control on an arbitrary number of boundaries
NASA Technical Reports Server (NTRS)
White, J. A.
1990-01-01
A procedure for the generation of two and quasi-three-dimensional grids with control of orthogonality and spacing with respect to any and/or all boundaries of the domain is described. The elliptic grid generation equations of Thompson are solved implicitly. Control of the grid behavior is achieved through the introduction of forcing functions terms in the manner of Steger and Sorenson or in a modification of the method of Hilgenstock. The forcing function terms are constructed on the boundaries and propagated into the domain using transfinite Lagrangian bivariate interpolation. An anisotropic transfinite stencil is introduced and is shown to produce excellent grid behavior particularly in the vicinity of corner singularities. Emphasis is placed on the generation of viscous grids and the method is shown to be suited for use in the generation of grids for internal as well as external flow geometries. A FORTRAN program named PISCES has been written to implement the algorithm. Examples of grids for internal and external flows are given that highlight the characteristics and behavior of the algorithm.
NASA Technical Reports Server (NTRS)
Steger, Joseph L.
1989-01-01
Hyperbolic grid generation procedures are described which have been used in external flow simulations about complex configurations. For many practical applications a single well-ordered (i.e., structured) grid can be used to mesh an entire configuration, in other problems, composite or unstructured grid procedures are needed. Although the hyperbolic partial differential equation grid generation procedure has mainly been utilized to generate structured grids, extension of the procedure to semiunstructured grids is briefly described. Extensions of the methodology are also described using two-dimensional equations.