Chapter 11 - Principles of Grid Generation

Abstract

This chapter draws attention to a deeper discussion of surface modeling, structured and unstructured surface, and volume grid generation. The approaches—namely, algebraic grid generation, elliptic grid generation, and hyperbolic grid generationare discussed. The algebraic grid generation approach employs a direct functional description of the coordinate transformation between the computational and the physical space. The most widely used algebraic technique is transfinite interpolation (TFI). The TFI scheme utilizes I-D univariate interpolations in each of the coordinate directions in the computational space. The linear TFI is computationally very efficient. In the case of unstructured grids, nodes and grid cells are quasi randomly ordered, that is, neighboring cells or grid points cannot be directly identified by their indices. This leads to tremendous geometric flexibility of unstructured grids because the grid does not need to conform to any predetermined topology. The adaptation of the grid to the physical solution grid refinement or coarsening is much easier to accomplish on unstructured than on structured grids. Unstructured grid generation methodologies for the CFD applications are mostly based on either a Delaunay method or an advancing-front method. Both approaches can also be combined. The chapter presents the different stages of the advancing-front process, the generation of anisotropic grids, and the differences between mixed grids and hybrid grids.