Page 273 - Computational Fluid Dynamics for Engineers

Grid Generation

9.1 Introduction

The solution of the conservation equations, described in Chapter 2, requires an
arrangement of a discrete set of grids or cells in the flow field; their determination
for a given body is known as grid generation and is discussed in this chapter.
While the finite-volume methods can be applied to uniform and non-uniform
meshes, the finite-difference methods require a uniform rectangular grid. In prac-
tically all real-life problems, a uniform rectangular grid is not possible in the
physical plane. As a result, it is necessary to use a coordinate transformation
and map the irregular region into a regular one in the computational plane. An-
alytic transformations for this purpose are difficult to construct except for some
relatively simple geometries; for most multidimensional cases it is impossible to
find such a transformation. Three major classes of techniques corresponding to
algebraic methods, differential equation methods and conformal mapping meth-
ods can be used to overcome these difficulties. For example, in the numerical
grid generation technique advanced by Thompson [1], the coordinate transfor-
mation is obtained automatically from the solution of partial-differential equa-
tions. In what is referred to as the structured grid approach, a curvilinear mesh
is generated over the physical domain such that one member of each family
of curvilinear coordinate lines is coincident with the boundary contour of the
physical domain. For this reason, the scheme is also called the boundary-fitted
coordinate method.
While the task of grid generation is an integral part of CFD, it can be sepa-
rate from the task of numerically calculating the resulting flow field. A numerical
method (flow solver) can be developed independently to solve the conservation
equations with the grid generated separately. For methods requiring a solution
in a computational plane, grid generation amounts to computing the metrics