ABSTRACT
One of the ƒrst steps in computing a numerical solution to the equations that describe a physical process is the construction of a grid. The physical domain must be covered with a mesh so that discrete volumes or elements are identiƒed where the conservation laws can be applied. A wellconstructed grid greatly improves the quality of the solution, and conversely, a poorly constructed grid is a major contributor to a poor result. In many applications, difƒculties with numerical simulations can be traced to poor grid quality. For example, the lack of convergence to a desired level is often a result of poor grid quality. This chapter will predominantly deal with what may be called the conventional approach of constructing grids that conform to the boundaries of the domain including any arbitrary internal body or bodies. This approach typically employs a body conforming curvilinear coordinate system or a system of unstructured grids that likewise conforms approximately to the surfaces. However, there has also been signiƒcant development of methods that deal with complex geometries while maintaining a Cartesian grid in a nonconformal manner. These include methods known as Cartesian grid methods (see Clarke et al. [1986], Zeeuw and Powell [1991]) and immersed boundary methods.
