The problem is a non-trivial one, and requires a considerable amount of
time. Development of a grid generation system requires years of work.

### Visualization Issues

Once the grid has been generated, it must be visualized to check for errors (they
come in an infinite variety). For 3-D grids this is a particular difficult stage,
where a computer animated image, or a CAD-based system is absolutely essential, and
this is proven by the fact that the most sophisticated systems currently available
come with visualization facilities. Minor errors can be fixed with ad hoc post-
processing, going under the definition of *grid smoothing*.

### Input Requirements

Given the complexity of the problem just outlined, one can argue also on the amount
of user input required. Some methods excel for the amount of data that must be set
(for example a multi-block structured grid, requiring point bunching on all sides).

Unstructured grids have been sometimes preferred on the structured counterparts
because grids – also in complex domains – can be generated more automatically.

How about the grid quality then ? – If the code runs, do not fix it, otherwise repeat
the fundamental steps.

### Grid Generation Methods

Elliptic methods are based on the solution of elliptic partial differential
equations with some conditions (called *forcing terms*) to force point
bunching. The problem is formulated via a set of Poisson equations (Thompson, 1977)
with forcing terms usually defined by the Thomas-Middlecoff terms (Thomas-Middlecoff,
1982), or by other appropriate control functions (Sorenson, 1995).

The solution of the system is iterative, for example with a Successive Over-
Relaxation (SOR) method. For large grids the computing time is considerable.

Hyperbolic methods are based on the solution of partial differential equations
of hyperbolic type, that are solved marching outward from the domain boundaries.

The idea of using hyperbolic PDEs is very effective for external flows where the wall
boundaries (airfoil, wing, wing-body, etc.) are well defined, whereas the far field
boundary is left arbitrary. This situation also eliminates the need to specify point
distribution on some of the edges of the flow domain, and makes it more handy than
for example the transfinite interpolation methods.

There are several algorithms for generating unstructured grids. The Delauney
triangulation method other Voronoi methods and the advancing front method are the
most popular, also among solution-adaptive systems, and they are the basis of some
commercial fluid dynamic codes (for example Star-CD, Rampant).

The field is in rapid
expansion, and there are *schools of thought* whether the unstructured approach
is better or worse than the structured approach to the solution of PDEs in fluid
dynamics.

Briefly, unstructured grids can be generated faster on most complex
domains, and exists for all domains. Mesh refinement can be done without
difficulties, also on a local basis and adaptively.

For some problems of particular difficult nature scientists have developed *hybrid*
methods that feature both structured and unstructured zones. These methods are the
*chimera technique* and the hybrid structured/ unstructured technique.

The chimera
approach consists in building partially overlapping blocks. Boundary conditions need
to be exchanged at the interface between domains and this is usually done through
some form of interpolation.

The hybrid scheme takes advantage of both unstructured
and structured methods by applying structured body fitted coordinates to the body
and unstructured networks in the outer boundaries.

Presently there is no one *method that fits all*. Most still depends on the
quality of the CFD solution that can be achieved.

The characteristics of the block boundaries depend on the capabilities of the flow
solver. In the structured domain, algebraic methods have been preferred because
faster.

#### Multi-Disciplinary Strategies

The most up-to-date methods have been embedded in sophisticated multi-disciplinary
tools that come with CAD/CAE interface, surface treatment techniques, complex
visualization tools, post-processing, etc. These tools allow multi-block structured.

#### Problem Size

The number of cells that can are necessary depends on the particular problem. Usually
a minimum number is easy to figure out. Most practical aerodynamic problems can be
solved with several million cells. The 10 million mark is current practical bound.

#### More on