Computational Fluid Dynamics

iii Preface There is fluid flow everywhere around us: air is flowing past airplanes, cars and buildings; water is flowing past ships, through rivers and harbours; oil is flowing through pipelines and in underground reservoirs; blood is flowing through our arteries. And the most important flow around us has not even been mentioned: the air flow in the atmosphere that determines our weather. It will be clear that for weather prediction and for the design of airplanes, cars, ships, etc. knowledge of flow phenomena is essential. Such knowledge can be obtained along three ways: experiment, theory and computer simulation. Experiment: The oldest way of acquiring flow knowledge is by experiment. The Wright brothers already had built a small windtunnel to design their first airplane. Currently windtunnels are usually impressive buildings; the experiment time required for a new design is typically 10.000 to 20.000 hours. Even with two shifts a day (i.e. 16 working hours per day) such an experiment program takes three to five years. And the time for making the scale model, and for analysing the measurement data has not even been accounted for. Today, such a long time for development is not acceptable anymore, and a faster way has to found. Theory: Flow research can also be carried out along a theoretical way. More than one and a half century ago already (Navier 1823, Stokes 1845) the equations describing the flow of air and water were derived: the Navier–Stokes equations. With pencil and paper these equations cannot be solved. Only if the equations are simplified strongly, this theoretical approach can produce adequate information. Computer simulation: In the modern computer era, another approach has become feasible: computer simulation. Here, the Navier–Stokes equations are solved with methods developed in the realm of numerical mathematics. There is still a role for experiments, but different from before: experiments will mainly serve as validation of the computational results. Contents 1 The convection-diffusion equation 1 1.