Geometry-adaptive surface grid generation using a parametric projection

Abstract

A general surface grid generation technique is presented that produces grids on arbitrary three-dimensional surface patches, with geometry-adaptive grid control. The method uses a two-dimensional parametric representation of the surface patch obtained by projecting the surface onto a locally defined screen. Arbitrary surfaces, including those with geometric singularities, are transformed into simple domains in the parametric space. A grid is generated on the parametric domain using a two-dimensional grid generation technique and the grid points are mapped back to the original surface. The method is applied to a variety of configuration s with different geometrical difficulties. ECENT advances in computational technology are mak- ing it possible to obtain numerical solutions to problems with increasing degrees of physical and geometrical complex- ity. As the geometry becomes more complicated and the desired level of confidence in numerical results increases, the demand for suitable grids also increases. The accuracy and efficiency of numerical solutions depend on certain grid prop- erties, such as grid topology, grid density, grid skewness, grid smoothness, cell aspect ratio, and variations of these proper- ties throughout the grid. Also, the total number of grid points should be kept to a minimum for computational economy. The optimum grid qualities suggested by these factors are often conflicting and compromises must be made. Improved grid generation techniques are needed as physical and geomet- rical complexities increase. After choosing a grid topology, surface grid generation is the next step in providing field grids for three-dimensional flow calculations. However, few techniques have been devel- oped specifically for surface grid generation. Algebraic meth- ods are often used, but most of these methods are based on assumed configurations or require excessive amounts of input. Other approaches include a method discussed by Thompson et al.1 using a three-dimensional curvilinear coordinate system with one coordinate constant on the surface. Also, Thomas2 proposed a surface grid generation scheme that uses a quasi- two-dimensional elliptic system for analytically defined, smooth surfaces. The method was later extended by Takagi and Miki3 for arbitrary curved surfaces using a parametric surface representation. Eiseman4 has demonstrated an adap- tive surface grid generation scheme that distributes grid points to optimal positions based on flow solutions. The purpose of this paper is to describe and demonstrate a surface grid generation technique that can be applied to arbitrary surface patches. The method uses a projection con- cept to define a parametric representation of the surface patch and a two-dimensional grid generation technique on the para- metric domain. Geometry-adaptive grid control is achieved through the definition of the parametric coordinates. First, an overall description of the method is presented, followed by discussions of specific items used in the implementation of the method. Then, several example applications are presented to demonstrate the capabilities of the method.