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8 Numerical Grid Generation May 10, 2005 16:28

8.1 Introduction

As mentioned in Chapter 6, curvilinear grid generation for 2D domains involves
specification of functions

x 1 = x 1 (ξ 1 ,ξ 2 ), x 2 = x 2 (ξ 1 ,ξ 2 ), (8.1)

where ξ 1 ,ξ 2 are curvilinear coordinates and x 1 , x 2 are Cartesian coordinates. These
two functions can be generated in two ways: (1) by algebraic specification or
(2) by differential specification.
Algebraic specification is typically employed in 1D problems but can also be
employed in 2D problems when the domain is simple (Section 8.2). For complex do-
mains, however, differential grid generation is preferred. In this type, functions (8.1)
are generated by solving differential equations with dependent variables x 1 and x 2 .
The differential equations can beof parabolic, hyperbolic, orelliptictype[81]. How-
ever, we shall consider the most commonly used elliptic grid generation technique
(Sections 8.3 and 8.4)
The unstructured meshes again can be generated in a variety of ways. Two types
will be considered: (1) generation by exploiting structuredness and (2) automatic
mesh generation (Section 8.5).

8.2 Algebraic Grid Generation

8.2.1 1D Domains

The objective of grid generation is to locate nodes such that they are closely spaced
in regions where the dependent variable in the transport equations is expected to
have steep gradients and sparsely spaced in regions where the gradients are small.
This ensures that accurate solutions are economically obtained.

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