9 Surface Grid Generation Systems

Structured surface grid generation entails the generation of a curvilinear coordinate grid on a surface. It may be necessary to generate such a grid in order to perform a two-dimensional numerical simulation of a physical process involving the surface. Alternately, surface grid generation may represent a stage in the generation of a volume grid, which itself would be used in a three-dimensional numerical simulation involving the volume or volumes bounded by the surface. We mention here that unstructured surface mesh generation (wherein the surface is usually decomposed into a collection of triangles but no obvious curvilinear coordinate system exists) is covered in Chapter 19. Unstructured surface meshes are arguably easier to construct and have found wide application in numerical simulation as well. Grid quality is a critical area for many numerical simulation problems. The distribution of the grid points and the geometric properties of the grid such as skewness, smoothness, and cell aspect ratios have a major impact on the accuracy of the simulation. The solution of a system of partial differential equations can be greatly simplified by a well-constructed grid. It is also true that a grid which is not well suited to the problem can lead to an unsatisfactory result. In some applications, improper choice of grid point locations can lead to an apparent instability or lack of convergence. This chapter will cover techniques for the generation of structured surface meshes of sufficient quality for use in physical simulations. Before a grid can be generated, the surface geometry itself must be created, usually by one of two methods. In the first method, the object to be simulated has a shape that can be calculated from a mathematical formula, such as a sphere. There are a wide variety of shapes in this class, including airfoils, missile geometries, and sometimes even complete wings. These types of shapes are very easy to define, and lead to an efficient grid generation process, with high-quality resulting grids. The second manner in which surface geometries are specified involves representation of the initial geometry as a computer-aided design (CAD) surface, where CAD systems typically represent the surfaces of a certain geometry with a set of structured points or patches. The CAD surface is then typically converted to a nonuniform rational B-splines (NURBS) surface representation (cf. Part III). Ahmed Khamayseh