ABSTRACT
The use of computer-based methods for the prediction of fluid flows has seen tremendous growth in the past several decades. Fluid dynamics has been one of the earliest, and most active fields for the application of numerical techniques. This is due to the essential nonlinearity of most fluid flow problems of practical interest — which makes analytical, or closed-form, solutions virtually impossible to obtain — combined with the geometrical complexity of these problems. In fact, the history of computational fluid dynamics can be traced back virtually to the birth of the digital computer itself, with the pioneering work of John von Neumann and others in this area. Von Neumann was interested in using the computer not only to solve engineering problems, but to understand the fundamental nature of fluid flows themselves. This is possible because the complexity of fluid flows arises, in many instances, not from complicated or poorly understood formulations, but from the nonlinearity of partial differential equations that have been known for more than a century. A famous paragraph written by von Neumann in 1946 serves to illustrate this point. He wrote [Goldstine and von Neumann 1963]:
Indeed, to a great extent, experimentation in fluid mechanics is carried out under conditions where the underlying physical principles are not in doubt, where the quantities to be observed are completely determined by known equations. The purpose of the experiment is not to verify a proposed theory but to replace a computation from an unquestioned theory by direct measurements. Thus, wind tunnels are, for example, used at present, at least in part, as computing devices of the so-called analogy type . . . to integrate the nonlinear partial differential equations of fluid dynamics.
