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All sourcesNASA NTRSDOE OSTI
NASA NTRS1996

Hyperbolic Methods for Surface and Field Grid Generation

This chapter describes the use of hyperbolic partial differential equation methods for structured surface grid generation and field grid generation. While the surface grid generation equations are inherently three dimensional, the field grid generation equations can be formulated in two or three dimensions. The governing equations are derived from orthogonality relations and cell area/volume constraints; and are solved numerically by marching from an initial curve or surface. The marching step size and marching distance can be prescribedly the user. Exact specifications of the side and outer boundaries are not possible with a one sweep marching scheme but limited control is achievable. Excellent orthogonality and grid clustering characteristics are provided by hyperbolic methods with one to two orders of magnitude savings in time over typical elliptic methods. Since hyperbolic grid generation methods do not require the exact specifications of the side and outer boundaries of a grid, these methods are particularly well suited for the overlapping grid approach for solving problems on complex configurations. Grid generation software based on hyperbolic methods and their applications on several complex configurations will be described.

Chan, William M.↗
NASA NTRS1992

IGB grid: User's manual (A turbomachinery grid generation code)

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.

Beach, T. A.↗
NASA NTRS1986

Interactive algebraic grid-generation technique

An algebraic grid generation technique and use of an associated interactive computer program are described. The technique, called the two boundary technique, is based on Hermite cubic interpolation between two fixed, nonintersecting boundaries. The boundaries are referred to as the bottom and top, and they are defined by two ordered sets of points. Left and right side boundaries which intersect the bottom and top boundaries may also be specified by two ordered sets of points. when side boundaries are specified, linear blending functions are used to conform interior interpolation to the side boundaries. Spacing between physical grid coordinates is determined as a function of boundary data and uniformly space computational coordinates. Control functions relating computational coordinates to parametric intermediate variables that affect the distance between grid points are embedded in the interpolation formulas. A versatile control function technique with smooth-cubic-spline functions is presented. The technique works best in an interactive graphics environment where computational displays and user responses are quickly exchanged. An interactive computer program based on the technique and called TBGG (two boundary grid generation) is also described.

Smith, R. E.↗
NASA NTRS2002

A Unified Overset Grid Generation Graphical Interface and New Concepts on Automatic Gridding Around Surface Discontinuities

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.

Chan, William M.↗
NASA NTRS1992

Geometry modeling and multi-block grid generation for turbomachinery configurations

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.

Shih, Ming H.↗
NASA NTRS1993

Bgridi - Interactive three-dimensional turbomachinery grid generation system with applications

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.

Shoemaker, J. M.↗
NASA NTRS1992

Interactive solution-adaptive grid generation

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.

Choo, Yung K.↗
NASA NTRS1992

Recent progress in unstructured grid generation

A number of recent developments and improvements in unstructured grid generation are discussed. Emphasis is given to the enhancement of capabilities of unstructured grid generation code based on the advancing front technique for generating triangular and tetrahedral grids. Two new methods have been devised to facilitate the process of grid generation: (1) structured background grids and their application to 3D unstructured grid generation and (2) grid restart capability. New postprocessing tools to manipulate generated grids include grid optimization, local remeshing, and interpolation for unstructured grids. Examples and references are given to show the applications of these developments.

Pirzadeh, Shahyar↗
NASA NTRS1994

Progress in Grid Generation: From Chimera to DRAGON Grids

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 discretized using the newly proposed flux scheme, AUSM+, which will be briefly described herein. Numerical tests on representative 2D inviscid flows are given for demonstration. Finally, extension to 3D is underway, only paced by the availability of the 3D unstructured grid generator.

Liou, Meng-Sing↗
NASA NTRS2007

Enhanced Elliptic Grid Generation

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 determined automatically as part of the solution of the defining PDEs. Depending on the shape of the boundary segments and the physical nature of the problem to be solved on the grid, the solution of the defining PDEs may provide for rates of decay to vary along and among the boundary segments and may lend itself to interpretation in terms of one or more physical quantities associated with the problem.

Kaul, Upender K.↗
NASA NTRS1989

On the applications of algebraic grid generation methods based on transfinite interpolation

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.

Nguyen, Hung Lee↗
NASA NTRS1992

Grid generation and flow solution method for Euler equations on unstructured grids

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.

Anderson, W. Kyle↗
NASA NTRS1992

Grid generation for 3D turbomachinery configurations

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.

Shih, Ming-Hsin↗
NASA NTRS2007

Modeling and Grid Generation of Iced Airfoils

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.

Vickerman, Mary B.↗
NASA NTRS1999

OVERGRID: A Unified Overset Grid Generation Graphical Interface

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.

Chan, William M.↗
NASA NTRS1990

Applications of algebraic grid generation

Techniques and applications of algebraic grid generation are described. The techniques are univariate interpolations and transfinite assemblies of univariate interpolations. Because algebraic grid generation is computationally efficient, the use of interactive graphics in conjunction with the techniques is advocated. A flexible approach, which works extremely well in an interactive environment, called the control point form of algebraic grid generation is described. The applications discussed are three-dimensional grids constructed about airplane and submarine configurations.

Eiseman, Peter R.↗
NASA NTRS1995

Tuned grid generation with ICEM CFD

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.

Wulf, Armin↗
NASA NTRS1995

Automatic structured grid generation using Gridgen (some restrictions apply)

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.

Chawner, John R.↗