This book provides an introduction to the fundamentals of computational fluid dynamics (CFD) for the engineer and physical scientist. Although it is based primarily on experience in such traditional areas as hydrology, hydraulic and coastal engineering and oceanography it points the way to newer areas of application, including medical fluid dynamics, bioengineering and soil physics and chemistry, with a view to computer-orientated applications. Emphasis is on the numerical treatment of incompressible unsteady fluid flow with primary applications to water problems, using the finite difference method. The first part discusses the principle definitions, basic ideas and most common methods used in CFD; the second part then applies these methods to the description of free surface, unsteady and turbulent flows. The possibilities and limitations of CFD are also presented along with the relation of this subject to other branches of science, such as recursion theory and mathematical logic, and to technology generally. Computational Fluid Dynamics provides those needing an entry level into this complex field with a place to begin. As such, it will be especially appealing to final year undergraduates and postgraduates in engineering as well as to qualified civil engineers.