11.1 Introduction

Many of the problems that were solved in the previous chapters required exacting calculations that were originally done either by hand computation or at best with the aid of an adding machine. Numerical methods were invented as far back as Newton, and techniques suited to the computer, such as the use of Green s functions, were known in the nineteenth century, but it wasn t until the mid-twentieth century that mainframe computers were available to researchers. Even then, the need to use storage devices such as punched cards required significant time and effort for all but the smallest calculation.

Today, the personal computer has made the power of the most powerful computer of mid-nineteenth century available to all. Many languages have been invented to make calculating the problems previously covered relatively easy. The first of these was FORTRAN (Formula Translator), developed at IBM in the 1940s. This was followed by similar languages such as BASIC, QUICKBASIC, PASCAL, VISUAL BASIC, C++, and many others. BASIC originally was included as a chip in the original IBM PC, and QUICKBASIC was provided as part of the disk operating system (DOS) until version 4.5 of DOS. These languages required a fair degree of programming skills on the part of the user. Today, MATHCAD, MATLAB, and symbolic manipulators such as MAPLE and MATHEMATICA have greatly increased the availability of mathematical computations. ^[1]

A few of the concepts and techniques used in computational fluid mechanics are presented in this Chapter and Chapter 12, along with sample...