The first of two volumes giving a comprehensive account of the numerical computation of internal and external flows. In this volume, the author explains the use of basic computational methods to solve problems in fluid dynamics, comparing the various methods, so the reader can see which would be the most appropriate way of solving any particular problem. In the first part of the book, mathematical models are introduced; in the second part, the various numerical methods are described briefly; in the third and fourth parts, the workings of these methods are discussed in more detail.