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TBGG- INTERACTIVE ALGEBRAIC GRID GENERATION
Abstract
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.
... Many of the collision detection algorithms [1][2] require a rectangular topology grid to be generated on a 3D terrain, so that algorithms for interaction with surfaces can be run. One of the easiest solutions is to use an algebraic method [3], but as shown in the next sections, it does not always produce pleasing results. ...
... Most of the algorithms for generation of topology grids are applicable both for 3D surfaces and 2D planes. As above mentioned the fastest and easiest method to implement is the algebraic mapping with two-dimensional interpolation [3]. However, in many cases it does not produce good results and more complex methods were developed that generate smoother meshes. ...
This paper presents an approach for 3D grid generation with a rectangular topology. It is an improved direct optimization method. The idea of the paper is to provide a fast algorithm for mesh generation to do a more realistic 3D terrain models. Results and conclusions are presented at the end of the paper.
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. By using a Lagrangian interpolation function, it is possible to enforce the grid continuity across the block interfaces without the derivative information. Monotonic rational quadratic spline interpolation has been employed for the grid distributions on the boundaries. This allows any arbitrary grid spacing without overlapping of the grid lines. An efficient computer program has been developed to generate a multiblock grid around a generic airplane geometry. This procedure has proven to be very simple and effective.
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