1 Introduction

Computational Fluid Dynamics (CFD) is a science that, with the help of digital computers, produces quantitative predictions of fluid-flow phenomena based on those conservation laws (conservation of mass, momentum, and energy) governing fluid motion. These predictions normally occur under those conditions defined in terms of flow geometry, the physical properties of a fluid, and the boundary and initial conditions of a flow field. The prediction generally concerns sets of values of the flow variables, for example, velocity, pressure, or temperature at selected locations in the domain and for selected times. It may also evaluate the overall behavior of the flow, such as the flow rate or the hydrodynamic force acting on an object in the flow.

During the past four decades different types of numerical methods have been developed to simulate fluid flows involving a wide range of applications. These methods include finite difference, finite element, finite volume, and spectral methods. Some of them will be discussed in this chapter.

The CFD predictions are never completely exact. Because many sources of error are involved in the predictions, one has to be very careful in interpreting the results produced by CFD techniques. The most common sources of error are:

• Discretization error. This is intrinsic to all numerical methods. This error is incurred whenevera continuous system is approximated by a discrete one where a finite number of locations in space (grids) or instants of time may have been used to resolve the flow field. Different numerical schemes may have...