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The application of a new efficient grid generation method in computational fluid dynamics is discussed. After 100 iterations, final grids were produced in about 110 seconds using a VAX 8650 computer in a time-shared mode. Using a SUN 3/50 workstation, a similar version of the program completed 100 iterations in about 15 minutes.
The NASA Steering Committee for Surface Modeling and Grid Generation (SMAGG) sponsored a workshop on surface modeling, grid generation, and related issues in Computational Fluid Dynamics (CFD) solutions at Lewis Research Center, Cleveland, Ohio, May 9-11, 1995. The workshop provided a forum to identify industry needs, strengths, and weaknesses of the five grid technologies (patched structured, overset structured, Cartesian, unstructured, and hybrid), and to exchange thoughts about where each technology will be in 2 to 5 years. The workshop also provided opportunities for engineers and scientists to present new methods, approaches, and applications in SMAGG for CFD. This Conference Publication (CP) consists of papers on industry overview, NASA overview, five grid technologies, new methods/ approaches/applications, and software systems.
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.
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.
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.
The understanding and analysis of three dimensional fluid behavior around reentry vehicles, like the Space Shuttle Orbiter, is of considerable importance for flight applications. Vehicle designers need pressure, heat transfer, and shear distributions to support design activities. Traditionally these have been obtained by experimental data. Significant reduction in design costs can be obtained if the calculated results based on finite difference procedures are used to verify and supplement experimental results. Computing the flow field over Space Shuttle Orbiter, which has complex cross sectional geometries is a major problem. A first step in this direction is development of body definition and grid generation procedure. In this project a digitized body definition and grid generation procedure, developed earlier at JSC, is modified and applied to the Shuttle Orbiter X24C-10D. Two dimensional grid and body definition for various sections of the space vehicle is obtained using the differential equation method. This study demonstrates that this geometry and grid generation procedure can be applied to other aerospace vehicles such as aerospaceplanes.
The past ten years have seen steady progress in surface modeling procedures, and wholesale changes in grid generation technology. Today, it seems fair to state that a satisfactory grid can be developed to model nearly any configuration of interest. The issues at present focus on operational concerns such as cost and quality. Continuing evolution of the engineering process is placing new demands on the technologies of surface modeling and grid generation. In the evolution toward a multidisciplinary analysis-bascd design environment, methods developed for Computational Fluid Dynamics are finding acceptance in many additional applications. These two trends, the normal evolution of the process and a watershed shift toward concurrent and multidisciplinary analysis, will be considered in assessing current capabilities and needed technological improvements.
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.
The objective of this research project is to develop efficient parallel automatic grid generation procedures for use in computational aerosciences. This effort is focused on a parallel version of the Finite Octree grid generator. Progress made during the first six months is reported.
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.
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.
Some computational tools and techniques are described that are integrated into a simplified algebraic grid generation procedure. Major steps of such a procedure are also outlined. Grids generated via this approach for several complex geometries are shown to demonstrate the potential for wide application.
Bezier and B-spline patches are popular tools in surface modeling. With these methods, a surface is represented by the tensor product of univariate approximations. The extension of this concept to three dimensions is obvious and can be applied to the problem of grid generation. This report will demonstrate how three dimensional patches can be used in solid modeling and in the generation of grids. Examples will be given demonstrating the ability to generate three dimensional grids directly from a wire frame without having to first set up the boundary surfaces. Many geometric grid properties can be imposed by the proper choice of the control net.
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.
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.
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.
Bezier and B-spline patches are popular tools in surface modeling. With these methods, a surface is represented by the tensor product of univariate approximations. The extension of this concept to three-dimensions is obvious and can be applied to the problem of grid generation. This report will demonstrate how three-dimensional patches can be used in solid modeling and in the generation of grids. Examples will be given demonstrating the ability to generate three-dimensional grids directly from a wire frame without having to first set up the boundary surfaces. Many geometric grid properties can be imposed by the proper choice of the control net.
We describe a Cartesian grid strategy for the study of three dimensional inviscid flows about arbitrary geometries that uses both conventional and CAD/CAM surface geometry databases. Initial applications of the technique are presented. The elimination of the body-fitted constraint allows the grid generation process to be automated, significantly reducing the time and effort required to develop suitable computational grids for inviscid flowfield simulations.