TABLE OF CONTENTS Because of exposure to school physics and what in the UK is called applied mathematics, we are conditioned to accept without question that, for instance, an object, missile or projectile, flying through space, can be truthfully represented by a single point located at the object's centre of mass. This practice, while allowing neat examination questions, leads us into a false sense of simplistic security. For instance, as soon as a projectile is made to spin about its axis of travel (a common practice), we may be unprepared for the escalation of complexity of the problem that this simple addition to the problem causes.
Physically large systems can rarely have their characteristics approximated at a point in space without severe and often unacceptable levels of approximation. It seems to be a very interesting law of nature that increased size brings increased non-uniformity.
For instance, a small sample of the Earth's atmosphere, say a few metres square, will be approximately uniform. However, seen on a scale of hundreds of kilometres, there is extreme non-uniformity in the atmosphere, with discrete cloud forms separated by cloudless atmosphere and there are gusting winds interspersed by calm regions.
Given a system whose spatial behaviour needs to be modelled, there are three possible approaches.
To model the global behaviour by a single set of partial differential equations. The solution is then obtained by numerical methods that, depending on discretisation,...
